The BoB is the northeastern part of the NIO, bounded to the southwest by Sri Lanka, to the west and northwest by India, to the north by Bangladesh, and to the east by Myanmar. Within the bay lie the Andaman and Nicobar Islands (see “ANI” in Fig. 1). The different countries and regions considered in the study are described in Table 1. Per region, one representative location is included for further analysis and shown in Fig. 1 (“Coastal cities”). The entire Bay of Bengal, in particular the northern part, is highly affected by TCs. Extreme sea levels around the bay, including maximum tidal levels and storm surge, increase towards Bangladesh as a result of the bay geometry and the shallow continental shelf (Fig. 1 and Muis et al., 2016).

Different datasets were used in order to set up the numerical modeling system, namely bathymetry, coastal segments and HTC tracks with associated maximum wind speeds.s

Deep-water bathymetry data for the BoB were derived from the GEBCO 2008 global bathymetric dataset (Becker et al., 2009); see Fig. 1. These bathymetric data were used as input for both the hydrodynamic and the wave models.

Output locations were chosen based on DIVA coastal segmentation as in Vafeidis et al. (2008), allowing a global spatial determination of similar stretches (segments) of coastline (linear coastal segments). A total of 197 output locations (1 per segment) along the entire coastline were defined, at which time series of extreme storm surge and significant wave heights were extracted as in Muis et al. (2016). Each segment has a length of approximately 5–25 km. For the wave conditions, the locations in the DIVA segments were translated into locations in deeper water to provide deep-water wave conditions and were therefore not affected by the local bathymetry. For each location, the closest point with a water depth larger than 30 m was chosen (Fig. 1).

HTC data were derived from the IBTrACS (International Best Track Archive for Climate Stewardship) database version v04r00 (Knapp et al., 2018). The IBTrACS database contains the most complete global set of HTCs available. From the IBTrACS dataset, the best-track data of the Joint Typhoon Warning Center (JTWC) for the NIO were chosen as a source, including reliable satellite-derived data (Singh, 2010) available for the period 1972–2020. The data contain TC information including the best-track coordinates and maximum wind speeds. The 1 min averaged wind speeds were converted into 10 min wind speeds using, as a correction factor, the value 0.93, following Harper et al. (2010). In total, 110 historical tracks were available for the NIO, of which 81 originated in the BoB including the recent Cyclone Amphan (2020). In the dataset, two distinct periods with TC activity can be identified, corresponding to the pre-monsoon period (May) and the post-monsoon period (November, e.g., Alam et al., 2003; Islam and Peterson, 2009). Generally, about 2–4 TCs per year are generated in the NIO, though this is not spread evenly through time as the TC generation is influenced by a number of external factors such as the El Niño–Southern Oscillation (ENSO) cycle (e.g., Singh et al., 2000; Hoarau et al., 2012). The HTC tracks were used to derive the STC tracks in TCWiSE. Figure 2a illustrates the selected HTC tracks, with different colors indicating different wind speed categories, while Fig. 2b shows the generated STC tracks based on the HTCs. Note that wind speeds on land may be less reliable as they are affected by several factors (e.g., land friction, local topography). Nevertheless, these uncertainties are not relevant for this study, which instead focuses on storm surge and waves in the ocean and coastal zone.

The methodology which was followed for generating extreme values for surge and waves for both historical and synthetic tracks is described in Fig. 3. From the IBTrACS dataset, a regional subset of HTCs are extracted for the NIO. In particular, TC characteristics (i.e., location, wind speed) describing the HTCs are extracted and used for generating the STCs with TCWiSE. The HTCs and STCs are then converted into wind and pressure fields using WES (Wind Enhancement Scheme; Deltares, 2019), which is a routine incorporated within TCWiSE. The generated wind and pressure fields are then used to force the numerical hydrodynamic and wave models Delft3D FM and SWAN. From these models, time series of storm surge and wave heights are extracted at the DIVA segments, and, per location, an extreme value analysis (EVA) is performed using the peaks-over-threshold (POT) method. The results are extreme values of storm surge and wave heights for different return periods at each location, which are used to perform regional comparisons between the obtained HTC and STC datasets.

Time series of 1000 years of synthetic tracks for the BoB for current climate (STCC) and future climate (STCF) were generated using TCWiSE. Since the synthetic tracks were based on historical data, statistical properties for the STCC should be similar to those of the HTCs. Nederhoff et al. (2021) demonstrated this through an application of TCWiSE for the Gulf of Mexico, by comparing statistical properties for 10 000 years of synthetic tracks and those of 133 years of historical data.

Here, a similar analysis is presented for the BoB. Spatial patterns for genesis, occurrence and termination were compared qualitatively and quantitatively using the correlation parameter R based on the similarity score of Kirchhofer (1974) in Fig. B1 in the Appendix. The closer R is to 1, the more similar the spatial patterns of the HTCs and subsequently generated STCC are. The regions with the highest probability of TC genesis in the historical data were found around the Andaman and Nicobar Islands in the middle of the BoB (Fig. B1a and b). The spatial genesis patterns of the STCC appear very similar to those of the HTCs, which is confirmed by the correlation parameter R being 0.88 (–). For the probability of termination of TCs, the patterns appear similar as well (Fig. B1c and d), but the magnitudes are more spread out for the STCC, leading to a slightly lower R value of 0.82. The main regions of TCs making landfall are around eastern India, Bangladesh and northern Myanmar. The highest TC occurrence is found in the middle of the BoB (Fig. B1e and f). The yearly occurrences are quite well reproduced with an R value of 0.68. The lower correlation is due to the spatial patterns of the synthetic tracks being more smoothed out compared to that of the HTCs due to the much larger number of realizations. The maximum yearly probability of the HTCs is about 0.4 (i.e., return period of 2.5 years), indicating that a particular region in the NIO is likely to be affected by a TC on average once every 2.5 years. The spatial coverage of the probability of genesis, probability of termination and yearly probability estimation over the whole BoB, as well as the similarities in spatial patterns between the HTCs and the STCC, indicate that the STCC can be used as a basis for quantifying wave heights and storm surges along the entire coast.

A comparison between the cumulative distribution functions (CDFs) of maximum wind speeds (vmax⁡) for HTCs and STCC, at nine locations along the BoB, is shown in Fig. 5. The functions are estimated based on TCs within a 200 km radius of each of the nine locations. Per location, the number of samples of time steps of TCs within a 200 km radius is included; this is between a factor 6 and 34 larger for the STCC compared to HTCs and includes 1000 samples or more except in the case of Mawlamyine (Myanmar). The CDFs of the other parameters (i.e., forward speed and heading) are presented in Figs. B2 and B3, respectively, of Appendix B. Additionally, a number of statistical parameters describing the differences between the two distributions are computed (i.e., absolute difference in maxima (Δmax⁡), normalized mean absolute error (nMAE), the relative bias of the median value (bias) and the root-mean-square error (RMSE) of the whole CDF). Locations characterized by a higher HTC occurrence, such as the ones in India and Bangladesh, generally have a lower absolute bias. For locations with a lower HTC occurrence, for example Batticaloa (Sri Lanka) and Mawlamyine (Myanmar), the bias is larger and the CDFs of the HTCs indicate a less smooth distribution as a result of the lower number of tracks included. The nMAE varies between 0.01 and 0.06, according to the location, and the RMSE between 1 and 10 ms-1, with the largest discrepancies seen at Batticaloa. At Batticaloa, there are a limited number of samples for the HTCs with a clear distinction of tracks with a wind speed of either below 15 or above 25 ms-1 (Fig. 5), while for the STCC a more gradual distribution can be seen, including also realizations in between these values. Maximum wind speeds are generally higher for the STCC than for the HTCs, meaning that more extremes are captured in the STCC, with the largest differences observed at Port Blair reaching up to 25 ms-1. Smoother distributions of the parameters describing the TCs are one of the advantages of using synthetic tracks computed over a long period of 1000 years. Similar patterns are also visible for the forward speed, heading and central pressure (Figs. B2–B4). In these cases, the RMSE for the forward speed ranges between 0.4 and 1.4 ms-1 (nMAE 0.1–0.5), the RMSE for the heading ranges between 11.3 and 50.5∘ (nMAE 0–0.04) and the RMSE for the central pressure ranges between 2.3 and 16.4 hPa (nMAE 0–0.08). Here, the central pressure values were not sampled in TCWiSE directly but are derived after applying the Holland (2008) estimates of pressure based on maximum wind speed.

Based on these results it can be concluded that the first-order hazard of wind speed is well resembled by the synthetic tracks created by TCWiSE for the current climate compared to historical observations. Therefore, the computed synthetic tracks and wind speed will be used for further analysis in the paper to estimate the resulting second-order hazards (i.e., storm surge and wave height).

After validation of the synthetic cyclone tracks, spatially varying wind fields were created and used as input to force coupled Delft3D FM and SWAN models to estimate storm surge and wave heights along the BoB. It is first verified how dependent the estimated variables of wind speed, wave heights and storm surge are on the number of years of synthetic data included and if or how fast the results converge. In Fig. 6 an example for Charchenga (Bangladesh) is shown. To verify the convergence, 99 000 EVAs were performed on the time series of wind speeds, wave heights and storm surge to estimate the 100-year return period value while increasing the X number of years extracted from the available 1000-year time series (i.e., X = 10, 20, 30, …, 1000 years). Hereby for every X number of years extracted, these years are selected randomly and combined into one new time series after which an EVA is computed. This is repeated 1000 times per X number of years included to obtain a stable estimate. Estimates of the 2.5th, 50th and 97.5th percentiles for a 100-year return period value were computed at each iteration. Therefore, per X years of data included, the 95 % CI spread of the estimated median value was calculated over the 1000 realizations, which is shown in Fig. 6a, c and e as green fill. The estimated median value of this spread is included as orange line. The same was calculated for the 2.5th- and 97.5th-percentile values, with their respective median values of the spread shown as gray and black lines, respectively, and with their combined total spread as gray fill. Figure 6a, c and e show that the more years of synthetic data that are included, the smaller the CIs become and the more the median values converge to a stable value. The number of years of data to be included to reach this stable value depends on the variable that is analyzed.

To quantify how quickly each of the different variables converges, the relative (%) ratio between the median value of the 50th percentile (i.e., computed based on X years of data) and the same median value based on 1000 years of data (i.e., here assumed to be the “true value”) is presented as orange lines in Fig. 6b, d and f. These results show that, for all variables, the convergence is exponential. While the variables wind speed and wave height already have a relative difference of less than 5 % (dashed orange line) compared to the true value after about 380 and 350 years, respectively, for the storm surge this takes about 450 years. In the same figure, the range describing the difference in spreading of the median value (i.e., the size of the green fill in Fig. 6a, c and e) is also shown as a green line. This range indicates how “wrong” the estimated median values can be after including a certain number of years of data. After including 200 years of data, the 95 % spread of the median values is still 15 ms-1 for the wind speed, 5 m for the wave height and 0.8 m for the storm surge. This decreases more rapidly for the wave heights and more slowly for the wind speed and storm surge. The difference in convergence can be explained by the related probability distribution for each of the variables, also known as “tail dependence” in probability theory. For wind speed and storm surges, the range of possible values is generally larger (type-I tail denotes no upper limit), while this is more limited for wave heights (type-III tail is with an upper limit). This can be explained physically by the influence area of the variables wind speed and resulting storm surge that is limited to close to the landfall location of a TC. Swell waves generated by a TC can travel hundreds of kilometers and have a larger area of influence, so higher wave heights are more often reached, and the range of possible values is more limited. Since all three variables reach a relative difference of a maximum of 5 % within 450 years and a maximum difference of 2 % (dotted orange line) within using 830 years of data, we can assume that results have converged after including the full 1000 years of data, and these are further used in this analysis for comparison with the HTC data.

The effect that a future climate with changes in cyclone wind speed (intensity) and frequency, possibly resulting from climate change, could have on resulting storm surge and wave heights was investigated using synthetic tracks (STCF, Sect. 2.3.1). Using the projected TC frequency and intensity changes in Knutson et al. (2015) for the NIO under RCP 4.5 for 2100, it was quantified how changes in the first-order hazard (wind speed) could result in changes in the second-order hazards (storm surge and waves). In particular, it was estimated that, as a result of a TC frequency increase of 25.6 % and an increase in maximum wind speed of 1.6 %, there could be a relative increase in predicted storm surge of 11 % and 6 % for return periods of 10 and 100 years, respectively, and an increase of 9 % and 6 % for the wave height (see Figs. 10 and 11 and Table 2). Therefore, the increase in storm surge and wave height could be larger than the increase in TC intensity only but lower than the increase in TC frequency as a result of a combined effect resulting from an increase in TC intensity and frequency. If only the TC intensity increase were relevant, one would expect an increase in second-order hazards of 2.56 % since storm surge and wave heights are in the limit proportional to the wind speed squared. Besides, the CIs remain approximately the same as for the STCC case due to the already large number of samples for that scenario (see Fig. B7 in Appendix B).

To summarize the results, the values of Figs. 12 and 13 are combined into Table 2, which also includes the results estimated based on STCF. The values are presented for return periods of 10 and 100 years, as averaged values both over the entire BoB and per region. Included are the CI values (2.5th, 97.5th percentiles), indicating that the CIs are significantly smaller based on synthetic tracks.

As shown by the reduction in the CI in the GPD fit (see, e.g., Fig. 10), the uncertainty in modeling TC-induced second-order hazards (i.e., storm surge and wave heights) is greatly reduced by using synthetic tracks. However, this is a reduction in the uncertainty in the fitting parameters and thus estimates of return values and periods. Uncertainties regarding the wind parametrization and the correct representation of the climate in the underlying dataset of the TCs persist. The former source of modeling uncertainties can be quantified by comparison with locally observed data. The latter, however, is a known unknown. TCWiSE is constrained to reproduce the statistics of the historical record. This means that the tool will not be able to (fully) reproduce physically credible and statistically unlikely tracks that are not recorded in observations. Additionally, in regions of rare TC occurrence, the lack of multiple tracks in historical records as a basis of the climate representation creates an unknown in terms of how accurately the generated STC tracks represent the “real climate” here. They will resemble the observed historical data with more realizations, where the historical data could in themselves be biased within the limited time span of the observations compared to the real climate. This cannot be verified but means that, in these regions, the results should be handled with care. However, for determining design criteria it is very common to use datasets of this (limited) time span.

Also, the STCs have been generated using TCWiSE only once and used for both current and future climate conditions. When rerunning TCWiSE multiple times the generated tracks will be different (though with the same statistics). The effect of this difference in sampling has not been investigated. Additionally, using the HTC data, only one method to generate STC tracks was used although many more methods exist besides TCWiSE, e.g., Vickery et al. (2000), Hardy et al. (2003), James and Mason (2005), Emanuel et al. (2006), Haigh et al. (2014), Nakajo et al. (2014), Lee et al. (2018), and Bloemendaal et al. (2020). Furthermore, looking at physics-based methods rather than historical track-based methods (e.g., Emanuel et al., 2008; Mori et al., 2019) could also lead to different results, though it is expected that the main patterns and general conclusions will remain the same.

The currently used numerical models still have a relatively coarse resolution near the shore (> 2 km) and therefore are not capable of representing nearshore bathymetric features and their effects on nearshore wave conditions (e.g., wave shoaling, refraction, breaking) or very local wind-induced setup changes to storm surge. The use of a higher-resolution model would not be computationally feasible when run in combination with thousands of tracks and for a large domain such as the BoB. For this reason, the estimated wave conditions were extracted at a water depth larger than 30 m, under the assumption that waves would not be affected by bathymetric features at this depth. The extraction depth was not changed for storm surge since this larger-scale process generally is less sensitive to the exact extraction depth, which is however an assumption in the model setup.

As the scope of the paper lies in the comparison between hazards estimated by using historical and synthetic tracks and how the use of synthetic tracks can reduce the confidence intervals around the estimation of these hazards, the difference between simulated storm surge and wave heights on the one hand and observed values on the other was not quantified. Combined with the limitations of the model resolution nearshore, presented results should be considered indicative results and not as values to be used directly in detailed design.

Only storm surge induced by wind and by the inverse barometric effect is considered for modeling extreme water levels since tides are not included. This is justified by the purpose of the paper (i.e., comparison between hazards induced by historical and synthetic tracks) and makes the comparison easier. Nevertheless, tidal effects would be important for the simulation of the total extreme water levels (see, e.g., Chiu and Small, 2016). Additionally, river runoff due to extreme precipitation events could also increase local extreme water levels.

The current approach of incorporating climate-change-induced effects via only including the change in TC intensity and frequency is still heuristic and limited in terms of physical representation. Potential effects like changes in sea surface temperature that result in changes in the statistics used of locations of TC generation and termination, forward speed, and heading have not yet been incorporated. Also, changes to the central pressure of TCs are not forced directly but only through the relation to the intensity increase in wind speed. Moreover, a multi-model ensemble of different climate models feeding into the model train could result in more robust findings. The cyclone frequency increase used in this study based on Knutson et al. (2015) is of a similar order of magnitude to that of, e.g., Sugi et al. (2017), which for the NOI describes a 21 % frequency increase for category 3–5 TCs, and also to similar trends described in other literature (e.g., Walsh et al., 2016). However, uncertainty remains as at the same time, for low-wind-speed categories, Sugi et al. (2017) found a reduction in cyclone frequency. In general, for specific regions/countries within the BoB the exact effects of climate change on TCs are still the subject of debate in the literature, as for instance seen in the spread of the model results in Knutson et al. (2020). Furthermore, in Knutson et al. (2015), different cyclone frequency increases are mentioned for different wind speed categories, not all of which are statistically significant. The 200 % frequency increase for categories 4–5 mentioned in Knutson et al. (2015) would lead to even stronger increases in derived values of storm surge and wave height, but the likelihood of such an increase is uncertain and marked as statistically insignificant (Knutson et al., 2015). Also, so far, historical data do not seem to suggest any clear local trends. These predictions will also keep on being extended and improved, for example to investigate more extreme relative changes (e.g., Knutson et al., 2020; Walsh et al., 2019). For instance, Knutson et al. (2020) indicate, after comparing results from different studies, a small decrease in the median frequency change for the NIO for categories 0–5 combined and a small frequency increase for the more intense categories 4–5. For the intensity increase, the median increase is about 5 % (Knutson et al., 2020). A large spread in projections remains, indicating that the results in this study following Knutson et al. (2015) alone should be interpreted as a proof of concept on the possible effects of climate change, based on one of many possible and different future scenarios.