We use high-resolution (4.4

Bangladesh is one of the most disaster-prone countries in the world, ranking
seventh in the 1999–2018 Long-Term Climate Risk Index (Eckstein et al.,
2019). Large portions of the population are exposed to the multiple natural
hazards, including those derived from tropical cyclones (TCs), such as
high winds, storm surge and flooding (e.g. Dilley et al., 2005). In the last 30 years, TCs impacting Bangladesh, from the Bay of Bengal (BoB), have been responsible for damages of ca. USD 8.9 billion and affected 45 million people (EM-DAT, 2021), with average annual extreme-weather-event-related losses amounting to 1.8

Recently, the International Monetary Fund (2019b) highlighted the early response Bangladesh is taking to the challenges posed by climate change; however, they also emphasise the importance of insurance mechanisms to enhance financial cover against impacts of natural disasters (International Monetary Fund, 2019a). Insurance facilitates disaster risk resilience and adaptation by transferring residual risk away from individuals and communities. Cost-effective and risk-informed sustainable development is based on the comprehensive understanding of hazards; the vulnerability of economies, societies and governments; and the exposure of society, people and belongings (UNDRR, 2019), but the lack of understanding of one or more of these components frequently limits the use of insurance mechanisms in many regions of the world most at risk from weather and climate hazards. This leaves significant populations around the world more vulnerable to the economic consequences of events that are otherwise manageable in countries with well-developed insurance markets (von Peter et al., 2012).

Detailed understanding of hazards is an essential part of understanding risk,
but a relatively sparse meteorological observational network and interrupted
non-continuous data records impose fundamental constraints on the description
of TC hazards. Simulations of tropical cyclones in the BoB remain challenging
for the current generation of seasonal forecasting systems (Camp et al.,
2015), global climate models (Shaevitz et al., 2014) and reanalyses (Hodges
et al., 2017), partly due the relatively coarse spatial and temporal
resolution of the numerical simulations. It is well understood that
large-scale thermodynamics and vertical wind shear have a significant impact on
TC intensity, but there are also numerous vortex, convective, turbulent and
frictional dissipative processes (e.g. Bryan and Rotunno, 2009; Nolan et al.,
2007; Tang et al., 2015 amongst others) that occur on much smaller scales and
also influence TC intensity, the impacts of which are not captured in low-resolution modelling. For example, extreme gusts associated with vigorous
(deep) convection will generally be underestimated without kilometre-scale
grid spacing that can explicitly resolve deep convection (e.g. Leutwyler
et al., 2017; Weisman et al., 1997). More generally, as summarised by
Leutwyler et al. (2017, and references therein), grid spacings of

Previous insights into TC hazards affecting Bangladesh focus on compiling catalogues of events (see Alam and Dominey-Howes, 2015, and references therein), or apply statistical analysis to event catalogues (e.g. Bandyopadhyay et al., 2018; Bhardwaj et al., 2020), and can only provide limited insight into the spatial extent, variability and magnitude of events based on first-hand eyewitness reports and limited observational records. Other authors take a parametric wind-field approach, combing the geostrophic (gradient) wind with a planetary boundary layer model to produce hazard maps at kilometre-scale resolution (e.g. Done et al., 2020; Krien et al., 2018; Tan and Fang, 2018); although this is a relatively computationally inexpensive approach, the quality of the result appears highly variable between global TC basins. Additionally, there are several holistic risk assessment views that combine multiple sources of hazard data, recognising that there are multiple hazards associated with TCs and that a combined risk assessment is non-trivial. However, these techniques are often limited to particular events (e.g. Hoque et al., 2016, 2019) or particular areas (e.g. Alam et al., 2020). In both cases, the quality of hazard and/or risk assessment is limited by available observational and track data.

In this study we seek to improve our understanding of the historical extreme
gust speed hazard associated with recent TCs. To address the lack of
observation data in this region, we use the latest-generation Met Office
regional model over the BoB to simulate nine versions of 12 historical tropical
cyclone cases representing 1979–2019. This generates spatially and temporally
consistent counterfactual simulations (relative to observed TC cases), albeit
limited by the constraints of the model configuration and computational
resources. This ensemble configuration enhances our understanding of how each
cyclone may evolve if a similar event were to happen again. We combine the
ensemble information in a spatially coherent manner to produce hazard maps at
4.4

Tropical cyclone simulations are derived from a nine-member ensemble for 12
historical events, using the latest-generation Met Office Unified Model (Brown
et al., 2012) convection-permitting regional atmosphere configuration RAL2-T,
based on Bush et al. (2020) – hereafter referred to as RAL2. The RAL2
4.4

The parameterised RAL2 gust diagnostic represents a prediction of the
3

We use the ensemble output to first derive event “footprints” – a common
method within the catastrophe modelling community to define peak hazard
relating to a given event. In this case, footprints are based on the maximum
wind gust speed achieved within each model run of 48

In general, median peak gust speeds from the RAL2 model ensemble are found to
be 22 to 43

To summarise information from all nine regional model ensemble member footprints
into a coherent spatial summary of the tropical cyclone hazard, we use a
generalised additive model (GAM), after Hastie and Tibshirani (1986), based on
the R package

For our purposes, we use a Gaussian location-scale (GLS) model family (Wood
et al., 2016) to describe the natural logarithm (log) of the gust speed, where
both the mean and the log of the standard deviation are smooth functions of
predictors – in this case, longitude and latitude. Although other model
families were trialled (such as generalised extreme value and gamma
distributions), the GLS family was found to have the best trade-off between
computational efficiency and model fit. The general form of our GAM is

The smooth model parameters are estimated using restricted maximum likelihood
(REML). However, once the model is fitted, it can be shown that it has a
Bayesian interpretation. In particular, the coefficients of the smooth
functions are assumed to have a multivariate normal prior distribution, whose
covariance matrix determines the wiggliness penalisation (see Wood, 2017, for
further details). A Gaussian approximation of the posterior distribution for
the coefficients then provides a multivariate normal distribution as the
posterior (Gelman et al., 2013). In practice, once a GAM model is fitted to
each named storm, under the Bayesian interpretation, we obtain 1000
simulations from the posterior distribution of the smooth function
coefficients via random draws from a multivariate normal distribution
(MVN). The MVN mean vectors are the REML coefficient estimates, and the MVN
covariance is derived as a function of the covariance matrix of the sampling
distribution of the model coefficients. In Bayesian inference, sampling from
the posterior distribution implies we can then derive samples from the
posterior predictive distribution of gust speed for each grid cell,

Summary of generalised additive modelling and the derivation of the posterior predictive gust speed distribution. The posterior predictive distribution is derived for each grid cell of the regional model domain. Gust speed prediction intervals are found from the percentiles of the posterior predictive distribution.

Detrended quantile–quantile (worm) plots for each GAM model per storm. We discretise the quantiles into 50 bins (open circles). The red dashed line represents zero deviance between data and theoretical quantiles defined in the GAM. Where model quantiles deviate below (above) the zero deviance line, this implies that the model predictions are overestimated (underestimated) relative to the data: for any given theoretical model quantile, the data quantile is lower (higher). Deviance residuals respect the model family used when fitting the GAM and are calculated via the simulation method of Augustin et al. (2012).

Assessing the GAM specification for

Aggregating the 12 historical tropical cyclones ensembles, Fig. 3 shows the
50th, 95th and 99th percentiles of the posterior predictive maximum gust speed
distribution across Bangladesh. Based on historical cases, the provinces of
Chittagong, Barisal and Khulna are most exposed to high wind speed associated
with tropical cyclone gusts, whilst Sylhet and Rajshahi are least exposed. The
cities of Chittagong and Cox's Bazar are particularly at risk of maximum
tropical cyclone gust speeds exceeding 45

Gust speed exceedance thresholds for the 50th

Event exceedance probabilities for a severe cyclonic storm

The gust speed hazard can also be considered in terms of the probability of
exceeding a threshold. Using WMO thresholds for tropical cyclone wind speeds
(WMO, 2018), Fig. 4 shows that significant areas of southern provinces
(Khulna, Barisal and Chittagong) will experience maximum wind speed in excess of “severe” cyclonic storm condition

Exceedance probability curves for 18 of the most populated towns and cities in Bangladesh (grey lines), with four key cities highlighted: Dhaka (orange), Comilla (blue), Chittagong (green) and Cox's Bazar (red). For reference, the minimum and maximum range of exceedance probabilities (across all of Bangladesh) are represented by the dashed lines. Note that storm exceedance probability is shown on a log scale.

In addition to specific thresholds, exceedance probability curves (Fig. 5)
summarise information for gust speeds up to 80

By defining a loss function, it is possible to exploit the information in the
Bayesian posterior predictive distributions to create a warning model based on
decision theory (Lindley, 1991). Following Economou et al. (2016), defining a
loss function

Example warning status given an impending landfalling tropical cyclone over Bangladesh. These warnings represent the most effective action minimising the loss as defined in Table 1.

Dummy loss function for actions associated with four Bangladesh TC warning levels and their associated wind speed intensity. In this case loss is defined on a 100-point scale, where 0 means no loss and 100 means maximum loss, associated with a given landfall TC event.

Figure 6 illustrates the optimal warning that should be issued based on
Table 1 and the range of gust speed information summarised by our GAM. This
can be interpreted as the default optimal action to take for planning and
preparation purposes, and in this case, the northern extent of TC risk, as
highlighted in Figs. 2 and 3, is again reflected in the warning level, but in
practice separate loss functions could be defined for each province or for
different economic sectors of society. By understanding the exposure,
vulnerability and decision-making process of each user, bespoke warnings could
be issued. For operational forecasting purposes, the optimal action (

Despite the ensemble simulation framework, our analysis is still restricted to
only 12 historical cases, which represent the recent 40-year period. The
number of events was determined by the availability of source data (ERA5) for
driving the regional model (RAL2), for TC events that made landfall over
Bangladesh – in this case limited to the period of ERA5 data availability,
which at the time of analysis extended back to 1979. Given the relatively low
ERA5 resolution (31

The initial conditions posed in the regional model play a significant role in
determining the outcome of each event. In forecasting situations this is
desirable behaviour: well-chosen initial conditions ensure the model retains a
realistic representation of reality. Even though the modelling domain that
produced these 4.4

A different limitation is posed by the initial aggregation of the
4.4

Generalised additive models (GAMs) provide a useful framework for condensing spatial hazard information in an interpretable way, from multiple numerical model simulations, into a single spatially coherent hazard map. Using a restricted maximum likelihood approach to fit the GAM allows us to interpret model predictions in a Bayesian fashion that logically provides credible exceedance estimates. High-resolution convection-permitting numerical predictions of 12 historical cyclone events, in an ensemble model set-up, give an improved sense of the plausibility and likelihood of possible extreme events without being constrained by the lack of observational history in this region. Combining ensemble simulations with a GAM then allows us to robustly quantify the likelihood of maximum gust speed exceedances in a spatially coherent manner.

Our new maps of exceedance intervals show that north-western provinces of Bangladesh are relatively exposed to high-wind-speed hazards – in some areas the exceedance probabilities are equal to those experienced along the coast. Our hazard-to-decision-making framework suggests that these areas may need to be considered in an equivalent manner to coastal regions from a disaster risk reduction perspective. In coastal areas of Cox's Bazar and Chittagong we show super cyclonic conditions may occur as frequently as 1-in-20 to 1-in-100 years. We hope that these kilometre-scale hazard maps facilitate one part of the risk assessment chain to improve local ability to make effective risk management and risk transfer decisions. Future work to co-produce a proper loss function, given wind speed thresholds, would facilitate a method of transparent operational decision-making that could be used as the basis of an operational warning system.

Python, R and data analysis code, including the fitted GAM model, is available at

The data used in this study are available at

HS prepared the manuscript, with input from TE, and undertook the data analysis. TE and HS jointly developed and coded the GAM model. TE developed and coded the decision-making framework used in Sect. 3.1.

The authors declare that they have no conflict of interest.

This study is part of the Oasis Platform for Climate and Catastrophe Risk
Assessment – Asia (

The authors thank Saiful Islam, Erasmo Buonomo, Richard Jones, Jane Strachan, Tamara Janes and two anonymous reviewers for comments that improved early versions of this paper.

This research has been supported by the International Climate Initiative (IKI) supported by the Federal Ministry for the Environment, Nature Conservation and Nuclear Safety, based on a decision of the German Bundestag.

This paper was edited by Animesh Gain and reviewed by two anonymous referees.