Tropical Cyclone Modelling for Design of Coastal Infrastructure
Tropical cyclones (also known as hurricanes or typhoons) are among the most catastrophic natural phenomena known to man. These synoptic scale rotating storms are formed over warm waters of the tropical oceans and have the potential to produce intense rain and abnormally high winds. The strong winds and associated low atmospheric pressures drive ocean response in the form of extreme waves, storm surge and currents; which can result in coastal erosion, damage to infrastructure and coastal inundation. This article outlines the difficulties faced by engineers tasked with designing coastal infrastructure to withstand such events and presents some best practise approaches for undertaking this task.
Table of Contents
1 Why is tropical cyclone risk exposure difficult to quantify?
The first task in designing coastal infrastructure to withstand tropical cyclones is to determine the return period event to be designed for. The n year return period event is the event which is expected to occur once every n years on average. ‘Event’ in this case refers to any parameter which needs to be designed for e.g. winds, waves, water levels, currents, erosion, forces on piles etc. While estimating design events is common in many engineering projects, this task is complicated in the case of tropical cyclones largely due to the paucity of historical data. Tropical cyclones occur relatively infrequently, and when they do occur the damaging winds are confined to a relatively small area (generally within 100 km of the eye). The frequency of storms at a given site is therefore typically significantly less than 1 storm per year, which leads to small sample sizes, and consequently large errors in the extrapolation of the historical records to return periods of interest.
To illustrate this point, consider two hypothetical locations on the Mozambique coastline, as shown in Figure 1. Given the proximity of these two locations one would expect the true physical risk exposure to tropical cyclones to be similar. However, if one simulates the wind fields for all of the shown historical events and carries out an extreme value analysis (EVA) on the modelled winds the results are significantly different, as shown in Figure 2. It is clear that the northerly location has by chance been exposed to two particularly strong events in the historical record, while the southerly location happened to be relatively lucky and was ‘missed’ by these events.
When faced with such uncertainty, engineers may take a conservative approach, resulting in the over-design of coastal structures. This can have severe consequences on the cost of the project, which may be deemed unfeasible as a result. Alternatively, not taking the risk seriously can lead to under-design of coastal structures, and their consequent premature failure. Probabilistic tropical cyclone risk modelling is a means to reduce the uncertainty associated with quantifying design parameters for these events.
Figure 1: Historical tropical cyclone best track data (1980 – 2012) in the vicinity of two hypothetical project locations on the Mozambique coastline. The colour of the track denotes the intensity of the cyclone.
Figure 2: Extreme value analysis of modelled wind speeds at two hypothetical locations on the Mozambique coastline. The large discrepancy highlights the error induced by small sample sizes of historical data.
2 Overview of probabilistic modelling approach
The inability of the historical records alone to provide a robust basis for the quantification of extreme tropical cyclone wind speed estimates has led to much research into the development of probabilistic tropical cyclone risk models. The goal of these models is to generate a database of tropical cyclones which is statistically consistent with the historical events but is of sufficiently long duration to avoid errors associated with small sample sizes. Figure 3 shows the typical components of probabilistic tropical cyclone risk models. Each of these components is discussed in the following sections.
Figure 3: Overview of typical components of probabilistic tropical cyclone risk models.
3 Best track data
Best track data provide the most complete historical record of tropical cyclone activity throughout the world, and consequently form the most appropriate basis for the quantification of tropical cyclone risk exposure. Global best track data from various meteorological organisations tracking cyclone activity are freely available online from the International Best Track Archive for Climate Stewardship (IBTrACS- https://www.ncdc.noaa.gov/ibtracs/). Best track data off southern Mozambique for the period 1980 – 2012 is shown in Figure 1. Although different organisations provide varying levels of detail for each tropical cyclone event, the following data are commonly available at 6 hourly intervals:
Location of the eye in geographical coordinates of longitude (ψ) and latitude (φ),
Minimum central pressure (Pc),
Maximum sustained 1 min or 10 min average surface (10 m elevation) wind speed anywhere in the storm (Vmax).
Pc and Vmax are metrics used to classify storm intensity and are inversely related through the so-called wind-pressure relationship (WPR). As Pc decreases, the atmospheric pressure gradient driving the winds becomes steeper, leading to an increase in Vmax. These metrics for storm intensity are used to classify storms into predefined categories, providing a useful tool for the issuing of public warnings. Although several classification systems are in use, the one most widely referenced is the Saffir-Simpson scale, as shown in Table 1.
Table 1: Saffir-Simpson scale for categorising storm intensity
4 Wind model
Best track data provide estimates of the location of the eye and the intensity of a given tropical cyclone, but rarely does it provide any information on the spatial arrangement of wind speeds around the eye. The generation of reasonably realistic tropical cyclone wind fields from best track data forms a vital component of any risk assessment model. Fortunately, the relative uniformity of the intense vortex of a tropical cyclone lends itself to a simplistic parametric representation of the wind field. The basis for all parametric models is the estimation of a wind speed profile (i.e. the profile from the centre of the eye outwards). Although several parametric wind field models have been proposed, one of the most commonly adopted models is the analytical model proposed by Holland (1980). A promising alternative to the Holland (1980) model is an empirical model providing the best fit to nearly 500 measured wind speed profiles from aircraft reconnaissance data (Willoughby et al., 2006). While details of these models are beyond the scope of this article, Figure 4 provides a comparison of the Holland (1980) and Willoughby et al. (2006) wind speed profiles for a range of intensities. Note that the radius to maximum wind speed (Rmax) is not always available in best track data and must therefore be estimated using empirical relationships (e.g. Willoughby & Rahn, 2004). Figure 4 serves to highlight the physical phenomenon that higher intensity tropical cyclones tend to have the highest wind speeds concentrated more locally around the eye. This can be likened to a figure skater drawing in her arms and spinning faster.
Figure 4: Comparison of wind speed profiles from the Holland (1980) and Willoughby et. al (2006) parametric wind field models for a range of intensities.
To generate a realistic two-dimensional wind field from parametric profile models, the wind speed profile is firstly applied radially around the eye of the storm. Adjustments to the wind field are then applied to allow for planetary boundary layer corrections, forward motion asymmetry, wind inflow angle and correcting for the wind speed averaging period. Figure 5 shows a satellite image of a historical tropical cyclone off the east coast of Madagascar and the estimated surface wind vectors resulting from a parametric wind field model. Also shown are the locations of the storm intensity metrics (Pc and Vmax).
Figure 5: Estimated surface vectors from a parametric wind field model for a historical event off the east coast of Madagascar.
The validation of any wind model is important to ensure that the model is in fact producing reasonably realistic wind fields. Figure 6 compares the measured and modelled wind speeds for Tropical Cyclone Geralda (1994) at Tromelin Island (54.52˚E, 15.887˚S), located in a particularly exposed area of the South-West Indian Ocean. Tromelin Island is particularly small, with a land area of approximately 1 km2. The island is flat and sandy, making it free from any notable land-based features. Wind measurements on the island are therefore likely to be fairly representative of open ocean winds.
Figure 6: Modelled vs measured wind speeds at Tromelin Island during Tropical Cyclone Geralda (1994).
5 Probabilistic track model
Probabilistic track models use statistical distributions of best track data parameters to augment the historical archive to many thousands of years of data. This can be done using either site-specific models or basin-wide synthetic track models. An overview of the simulation approach for site-specific models is given in Figure 7.
Figure 7: Overview of simulation approach for site specific probabilistic models (Vickery et al., 2009)
The various components of site-specific probabilistic models (labels 1 to 5 in Figure 7) are described individually below:
The approach begins by identifying historical best track data occurring within a defined threshold distance of a given site of interest. It is assumed that the statistical distributions of the considered parameters can be thought of as homogenous in space within the defined threshold distance of a given site.
Probability distributions of key track parameters of interest are derived from the site specific historical best track data. In the shown example, ΔP (difference between P0 and the background atmospheric pressure) is used as the intensity parameter, however this can be substituted for Vmax. The probability distributions of the track parameters are repeatedly sampled in a Monte Carlo simulation, generating thousands of years of combinations of track parameters.
For each combination of track parameters generated by the Monte Carlo simulation, a straight-line track satisfying the sampled track parameters is generated. The intensity of the track is kept constant until the track makes landfall. The intensity of the track is subsequently reduced as a function of time over land, according to a land filling model.
A wind field model (see section above) is applied along each track generated by step 3, yielding a two-dimensional wind field at each time-step along the track.
The modelled parameters of wind speed and direction, as generated by the wind field model, are recorded at the site of interest.
From the described approach, it is possible to generated thousands of years of tropical cyclone induced wind speeds at any site of interest, from which extreme wind speeds at return periods of interest can be derived.
In a pioneering study, Vickery et al. (2000) extended the techniques used in site-specific probabilistic models through the development of a basin-wide synthetic track model. Rather than generating track parameters at a given site, entire tracks are synthesised over large areas (often over entire basins), from their genesis through to termination. This process effectively produces synthetic best track data in the same format as historical best track data, but over a duration of thousands of years. Figure 8 presents an example of the output of a synthetic track model in comparison to historical best track data for the North Atlantic Ocean (Emanuel et al., 2006). The use of synthetic tracks in this way remains the current state-of-the-art technique for the quantification of extreme tropical cyclone induced wind speeds (Vickery et al., 2009; Zhang & Nishijima, 2012). It is however noted that the accuracy of this approach is limited largely by the ability of the model to reproduce the statistical properties of the underlying historical data. Even then, areas of particularly low occurrence rates may still be problematic as estimated distributions from sparse data may not be accurate representations of the true distributions.
Figure 8: Sixty random tracks from a synthetic track model (a) and a historical dataset (b) over the North Atlantic Ocean (Emanuel et al., 2006).
6 Extreme wind speeds
Having generated a database of synthetic tropical cyclone tracks, via either site-specific or basin-wide approaches as described above, a parametric wind field model can then be applied along each track (as per steps 4 and 5 of Figure 7) to generate thousands of years of modelled wind speeds at any location of interest. Given the length of the synthetic record, there is no need to apply theoretical extreme value distributions to estimate wind speeds at return periods of interest for engineering design (e.g. 200 years). Design wind speeds can be simply determined directly from the synthetic wind record (see Vickery et al., 2000). Applying calculations on a regular grid over the domain in this way allows the estimation of extreme wind speed maps over large areas.
Figure 9 presents an estimate of the 200 year return period tropical cyclone wind speed map for the South-West Indian Ocean. This study employed a novel synthetic track model to produce 5 000 years of tracks and employed the Willoughby et al. (2006) parametric wind field model to estimate extreme wind speeds on a 1˚ geographical grid. Extracting model results along the east coast of southern African coastline provides estimates of extreme wind speeds which could be adopted for design of coastal infrastructure along this stretch of coastline, as shown in Figure 10.
Figure 9: 200 year return period 1-min average wind speeds due to tropical cyclones for the South-West Indian Ocean (Fearon, 2014).
Figure 10: 50, 100, 200 and 500 year return period 1-min average wind speeds due to tropical cyclones as a function of latitude along the south-east African coastline (Fearon, 2014).
7 Ocean response to extreme wind speeds
In addition to extreme wind speeds, the engineering design of coastal structures in regions prone to tropical cyclones requires the estimation of extreme waves, water levels and currents due to these events. This is typically carried out through the application of an ocean response model (coupled hydrodynamic and spectral wave model), using space and time-varying tropical cyclone wind and pressure fields as input to the model. The coupling of hydrodynamics with wave generation can be particularly important as increased storm surge (due to low atmospheric pressure near the eye, and wind setup due to onshore winds) leads to reduced depth-induced wave breaking and therefore higher wave heights at the structure of interest. Higher wave heights in turn lead to increased water levels in the form of wave setup. The approaches used to define extreme ocean response parameters can be broadly classified as deterministic and probabilistic.
In the deterministic approach, the extreme wind speeds (estimated from a probabilistic approach as described above) are used as a basis for the selection of “design storm” parameters, which are the required input to an ocean response model. In this approach, the extreme wind speed estimates (Vmax), are used to estimate the other storm parameters. While deterministic relationships are available for the estimation of the associated minimum central pressure (Pc) and radius to maximum wind speed (Rmax), the parameters of track speed (c) and direction (θ) are however less well correlated with storm intensity. As it is not possible to define a unique design storm from extreme wind speed estimates alone, a small set of candidate design storms are rather defined, so that the sensitivity of the model results to these candidate storms can be ascertained. These storms are often referred to as “screening storms” (Resio et al., 2007).
The probabilistic approach to modelling ocean response is analogous to that used to calculate extreme wind speeds. In this approach, a coupled hydrodynamic and spectral wave model is applied along each synthetic track passing within a defined threshold distance of a given site of interest. Saving the modelled waves, water levels and currents at the site due to each synthetic track, it is possible to generate thousands of years of synthetic ocean response parameters from which extreme values can be derived. An example of the application of this methodology – to the Australian east coast – is provided by Harper et al. (2004). This approach is however limited by the significant computational requirements of modelling ocean response due to thousands of years of synthetic tracks.
The design of coastal infrastructure to withstand tropical cyclone events is complicated by the paucity of historical events, and the catastrophic consequences when they do occur. Much effort has been invested in alleviating the uncertainty in estimating tropical cyclone risk exposure via probabilistic approaches. While these methods have their own limitations, they can go a long way to improving estimates of design parameters and ensure that coastal infrastructure is neither under- nor over-designed.
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