Ocean Dynamics DOI 10.1007/s10236-015-0861-7
Hurricane-induced waves and storm surge modeling for the Mexican coast Rafael Meza-Padilla 1 & Christian M. Appendini 2 & Adrián Pedrozo-Acuña 3
Received: 27 February 2015 / Accepted: 29 June 2015 # Springer-Verlag Berlin Heidelberg 2015
Abstract This paper describes the application of a thirdgeneration wave model and a hydrodynamic model to determine extreme waves and water levels associated to the incidence of tropical cyclones along the Mexican coast. In addition to historical records and to overcome the limitation associated to data scarcity in Mexico, we employ information from 3100 synthetic events generated from a statistical/deterministic hurricane model. This enables the generation of a more robust database for the characterization of extreme water levels along the Mexican coast. The procedure incorporates a storm track modeling approach where, for each hurricane (historic and synthetic), the entire track is numerically reproduced as it crosses the ocean and makes landfall. Extreme values for both, waves and storm surge, are determined through an extreme value analysis at each mesh element, allowing for the identification of their spatial variability. Results for the Gulf of Mexico show that highest waves are expected along both the Caribbean Sea and the northern coast of the Gulf of Mexico, while extreme water levels due to storm surge are identified in the northern part of the Yucatan
Responsible Editor: Carlos Augusto França Schettini This article is part of the Topical Collection on Physics of Estuaries and Coastal Seas 2014 in Porto de Galinhas, PE, Brazil, 19–23 October 2014 * Christian M. Appendini
[email protected] 1
Instituto de Ingeniería, Universidad Nacional Autónoma de México, Sisal, Mexico
2
Laboratorio de Ingeniería y Procesos Costeros, Instituto de Ingeniería, Universidad Nacional Autónoma de México, 97356 Sisal, Yucatan, Mexico
3
Instituto de Ingeniería, Universidad Nacional Autónoma de México, Ciudad Universitaria, Mexico
Peninsula. On the other hand, along the Pacific coast, extreme values for waves are identified at the central mainland Mexico while storm surge is minimal. The methodology is proved to be a good alternative in the reproduction of continuously varying tropical cyclone climatology along the Mexican coastline, and it provides a rational approach for assessing the hurricane-induced risk in coastal areas. Keywords Tropical cyclones . Storm surge . Waves . Mexico . Extreme value analysis
1 Introduction Mexico is one of the few countries that are subject to the landfall of tropical cyclones from two different cyclogenesis areas: the Eastern Pacific and the North Atlantic basins. As a result, Mexico is vulnerable to disasters generated by tropical cyclones, including rain, winds, waves, and storm surge. During the last decades, Mexico has suffered extreme damage from these events, related to inland flooding, landslides, coastal flooding, and beach erosion. The country has even experienced simultaneous landfall of events generated in abovementioned basins, as in 2013 when tropical cyclones Ingrid and Manuel made landfall within 18 h of difference (Pedrozo-Acuña et al. 2014). It is evident that an assessment of the probability of occurrence of tropical cyclones is a priority in Mexico for planning and disaster management. Storm surge and waves from tropical cyclones are responsible for most of the damages when the event does landfall (Dube et al. 2010), being the main cause of disasters in the coastal zone around the world. While, in Mexico, rainfall from tropical cyclones is the main source of damage, due to river flooding and landslides (Breña-Naranjo et al. 2015; PedrozoAcuña et al. 2014), storm surge and wave damage cannot be
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overseen. For instance, hurricane Wilma (2005) removed approximately 7 million m3 of sand from Cancun, resulting in an estimated 1 billion USD loss in tourism revenues and a 50 million USD beach nourishment program (Silva-Casarin et al. 2012). It is also important to acknowledge that river overflown can be directly affected by storm surge, which can act as a hydraulic head and even reverse the river flow direction. This was observed in the Mississippi River during hurricane Isaac in 2012 (Stewart 2013). Moreover, this effect may exacerbate inland flooding (e.g., floodplain) due to a reduced fluvial drainage capacity (Pedrozo-Acuña et al. 2012). Considering that storm surge and waves from tropical cyclones are a key player for disasters in the coastal zones, their characterization is a top priority for planning, management, and disaster preparation and response. Historical events are commonly used to characterize such events, for instance Panchang et al. (2013) uses of historical hurricanes to characterize extreme wave climate in the Gulf of Mexico while different authors have used historical records to characterize extreme events at specific locations (MezaPadilla et al. under review; Wang and Oey 2008; Appendini et al. 2014a, b). Nevertheless, historical data from tropical cyclones is sparse and may not constitute a representative dataset for doing extreme value analysis, leading to the generation of other databases, such as those by Vickery et al. (2000) and Emanuel et al. (2006). In particular, Emanuel et al. (2006) proposed a methodology to generate synthetic events based on the physical properties of generation, propagation, and dissipation of tropical cyclones in order to overcome the sparse historical information. This methodology produces reliable results that are not biased with lower values in the dataset used to fit the extreme value distribution. As a result, these synthetic databases have been used to characterize extreme values for wind speed (Emanuel and Jagger 2010) and storm surge (Lin et al. 2010) as well as to provide estimations of the effect of climate change over tropical cyclone intensity (Emanuel et al. 2008) and storm surge (Lin et al. 2012). In the case of storm surge, Lin et al. (2014) demonstrate how the historical hurricane database may overestimate storm surge values when compared to the use of a synthetic event database, which, in turn, provides estimates in accordance to paleorecords of hurricanes, as derived from overwashed deposits. Thus, these databases have shown to be useful to characterize extreme events in a long-term period. In Mexico, the determination of extreme water levels due to storm surge has been mainly done through the numerical reproduction of historic events (Ruiz-Martínez et al. 2009; Posada-Vanegas et al. 2011). While this provides important information, we have developed new estimates based on 3100 synthetic events generated in the North Atlantic and Eastern Pacific [1550 in the Gulf of Mexico and Caribbean Sea, hereafter referred as North Atlantic Cyclones (NAC), and
1550 in the Pacific Ocean, hereafter referred as Eastern Pacific Cyclones (EPC)]. The genesis of the events is done by random seeding, while the track and intensity is driven by environmental factors such as potential intensity, depth of ocean mixing, and environmental winds (Emanuel et al. 2006). All the generated events make landfall in Mexico. We used the lifetime characteristics from each event to generate the wind fields to drive wave and hydrodynamic models that will provide significant wave height (SWH) and storm surge water levels (WLs). From the model results, we constructed time series for each mesh element by concatenating the maximum values obtained in the individual events. Each element maximum value series was fitted to a generalized extreme value (GEV) distribution to produce maps of SWH and WLs for different return periods. The results of this study aim to provide better estimation of extreme levels (waves and storm surge) due to the incidence of tropical cyclones in Mexico. The paper is organized as follows. Section 2 provides information regarding the synthetic events and the generation of wind fields. Section 3 presents the wave and the hydrodynamic models and the results from the numerical simulations. Section 4 shows the extreme value analysis, and finally, discussion and conclusions of this study are given in Section 5.
2 Synthetic events 2.1 General description and climatology To overcome the limitations of historical datasets, we used 1550 synthetic tropical cyclones (from tropical storms to category 5 hurricanes) for each basin studied (i.e., EPC and NAC). The synthetic events are generated based on the random seeding of warm core vortices that are stirred by a betaadvection model driven by the large-scale wind fields as obtained from the NCEP/NCAR reanalysis data (Kalnay et al. 1996). The intensity of the developed vortices is based on the thermodynamic state derived from the reanalysis data and the ocean temperature climatology. Further details on the generation of synthetic events are reported in Emanuel et al. (2006, 2008). The synthetic events used in this study were generated and provided by Prof. Kerry Emanuel. Figure 1 shows the example of 100 synthetic events doing landfall on the Mexican coast (NAC and EPC). While this figure is limited to a few events, the most vulnerable areas in the Mexican coasts become apparent. For instance, the Caribbean facing side of the Yucatan Peninsula and the central area of Mexico in the Pacific appear more susceptible for tropical cyclone incidence, which is in correspondence to previous studies based on historical events, as the tropical cyclone climatological atlas developed by Rosengaus-Moshinsky et al. (2002).
Ocean Dynamics Fig. 1 Example for 100 synthetic tropical cyclones doing landfall in Mexico from a the Eastern Pacific and b the Northern Atlantic
The synthetic events were validated by comparison to the HURDAT database from the satellite era (1980– 2010 period), which is considered more reliable (Mann and Emanuel 2006; Landsea 2007) and corresponds to the time frame used to generate the synthetic events. The comparison is shown in Fig. 2 for wind speed, annual cycle, and landfall position. The differences in the histograms are expected since the historical dataset is non-extensive, consisting of 65 EPC and 38 NAC (~30 years), while the synthetic dataset would correspond to approximately 5500 years for the EPC and 1500 for the NAC, if we extrapolate the frequency of historical events in each basin. The use of the same frequency for historical and synthetic event is based on the present climate scenario and thus would neglect any effects of climate change beyond those included in the 30 years of the reanalysis data. Still, both databases show a similar pattern, indicating that the synthetic events, while providing a more robust database, follow the physics dictated by the historical events.
Another important aspect in the comparison of synthetic and historical events is that in the 30-year period of historical events, many areas did not experienced tropical cyclones (e.g., in the Gulf of Mexico at latitudes 23 and 26 and longitudes −90, −94, and −95). Still, there are synthetic events, indicating that these areas are susceptible to experience tropical cyclones, despite the lack of historical records. Thus, the synthetic events represent a more reliable database for calculating long-term design parameters from tropical cyclone data as has been done by authors such as Emanuel and Jagger (2010), Klima et al. (2012), and Lin et al. (2012). 2.2 Tropical cyclone wind fields The generation of wind fields was based on the synthetic event properties related to date (year, month, day, hour), position (latitude, longitude), maximum wind speed, radius of maximum wind speed, atmospheric pressure in the hurricane eye,
Ocean Dynamics
Fig. 2 Comparison of synthetic events and best track frequency histograms for wind speed in a the Gulf of Mexico/Caribbean Sea (GoM/CS) and b the Pacific Ocean, annual cycle in c the GoM/CS and
d the Pacific Ocean, and landfall position related to longitude in e the GoM/CS and f the Pacific Ocean and to latitude in g the GoM/CS and h the Pacific Ocean
and neutral atmospheric pressure. This information was used to generate wind fields for the entire tropical cyclone lifetime, using the parametric formulation proposed by Emanuel and Rotunno (2011) and atmospheric pressure based on Holland (1980). The equation that describes the pressure at any given radius is given in Eq. 1.
The equation describing the wind speed at any given radius is provided in Eq. 2. 1 2r Rmw V m þ f Rmw fr 2 ð2Þ V ðr Þ ¼ − 2 2 2 Rmw þ r
Rmw Pr ¼ Pc þ ðPn −Pc Þexp − r
B
ð1Þ
where Pc is the central pressure, Pn the ambient pressure, r is any given distance between the eye of the hurricane and its domain, Rmw is the radius of maximum winds, and B is the Holland shape parameter.
where Rmw is the radius of maximum winds, Vm is the maximum wind speed, r is the radial distance from the eye of the hurricane to any given point surrounding it, f is the Coriolis parameter, and Vr is the wind speed of the hurricane at radius (r). The selection of the parametric model was based on the assessment done by Lin and Chavas (2012) for different
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parametric formulations, where they determine that the model most likely to provide accurate estimations for extreme storms is the one proposed by Emanuel and Rotunno (2011). Such conclusion was confirmed by Ruiz-Salcines (2013) who tested different parametric wind models for the use in wave modeling. Following Lin and Chavas (2012), the wind fields were adjusted from gradient height to 10 m above surface using an empirical wind reduction factor of 0.85 and a storm inflow angle as described by Bretschneider (1972). While the use of Emanuel and Rotunno (2011) formulation generates an axisymmetric wind field, it is known that the wind fields from tropical cyclones are rarely axis symmetric due to different factors, summarized by Xie et al. (2011). In this study, we included the asymmetry generated by the effect of the surface background winds, related to the tropical cyclone translation velocity, which was added to the storm winds to provide more realistic wind fields. The estimation of the background wind component for the wind fields was based on Lin and Chavas (2012), who suggest the use of a reduction factor of 0.55 for the storm translation velocity and a counterclockwise rotation of 20°. As an example of the resulting wind fields, Fig. 3 shows the wind velocity vectors and atmospheric pressure contours for a synthetic event in the Pacific and the wind velocity vectors and wind speed contours for an event in the Gulf of Mexico, showing an asymmetric wind field.
3 Numerical modeling The numerical models used in this study are part of MIKE by DHI suite of models. In the following subsections, we provide a brief description of the MIKE 21 HD (hydrodynamic) model and MIKE 21 SW (spectral wave) model. Although the models can be run in a coupled mode, the high number of simulations requires to optimize CPU time by running the models independently. While it is known that there is an important feedback between models in the nearshore areas and that the wind stress is affected by the sea state (e.g., Mastenbroek et al. 1993; Moon 2005; Brown and Wolf 2009; Bertin et al. 2012; Olabarrieta et al. 2012), it was considered that the induced errors would be smaller than those induced by the nearshore bathymetry inaccuracies. Still, the models were based on the same meshes and bathymetries, as described in the following subsection.
2009), together with information from nautical charts in coastal areas and local surveys when available (e.g., Tuxpan, Veracruz, Sisal, and Progreso in the Gulf of Mexico1) (Fig. 4). A flexible mesh with a grid resolution of 10 km offshore to finer elements near the coastline (~250 m) was constructed for each basin (Fig. 4). The flexible mesh allows us to pinpoint the highest resolution to the area of interest, leaving the rest of the model with a coarse grid in order to improve the computational performance. The grid resolution in this study varies from a coarse grid (i.e., ±10 km between nodes) to a finer grid (i.e., ±1 km between nodes) on the main ports of Mexico. 3.2 Hydrodynamic model The hydrodynamic model MIKE 21 HD FM was used to simulate the water surface elevation generated by tropical cyclone winds from 3100 synthetic events (1550 on each model domain). The model solves the momentum, continuity, temperature, salinity, and density equations with turbulent closure scheme equations. It is based on the incompressible Reynoldsaveraged Navier–Stokes equations (RANS) subject to the Boussinesq and hydrostatic pressure assumptions. The spatial discretization of the equations is based on a centered finite volume method over unstructured meshes. For further information of the model, the reader is referred to DHI (2014a). The simulation period in the HD model varies according to the event, while the time step is based on a multisequence integration step, specified with a minimum value of 0.01 s and a maximum value of 1800 s and each time step defined according to the Courant–Friedrichs–Levy (CFL) condition. The time integration and space discretization are of low-order fast algorithm, considering a critical CFL number of 0.80. Tides were not included in the simulations in order to account only for storm surge generated by the tropical cyclone wind field. For calibration and validation, there were no tropical cyclone-induced water level measurements found along the Mexican coastline. Alternatively, we simulated hurricane Ike (2008) and compared with measured data in the seaside of Galveston Bay, obtaining good match between measured and simulated data (not shown). The final setup of the model considered a barotropic density model with a varying Coriolis force according to the domain, a constant eddy viscosity of 0.28 under the Smagorinsky formulation, and a constant bed resistance of 32 m1/3/s using the Manning number. The drag coefficient parametrization in the hydrodynamic model corresponds to the one proposed by Wu (1980, 1994). Since the drag coefficient has been found to increase with wind speed until reaching a maximum value at approximately 30 m/s
3.1 Bathymetry and meshes Two different modeling domains were established, one for the EPC and the other for the NAC. The bathymetry used for both domains was the ETOPO 1 bathymetry (Amante and Eakins
1 Tuxpan and Veracruz survey was provided by Roberto Uribe from Comisión Federal de Electricidad, Port of Veracruz area survey by Sokaris de la Luz Aranda from Administración Portuaria Integral, Sisal survey by Laboratorio de Ingenieria y Procesos Costeros, and Progreso survey by Ismael Mariño from Cinvestav.
Ocean Dynamics Fig. 3 Wind field for a synthetic event in a the Pacific Ocean showing wind velocity vectors and atmospheric pressure contours and in b the Gulf of Mexico/Caribbean Sea showing wind velocity vectors and wind speed contours
(Moon et al. 2008; Takagaki et al. 2012), the parametrization was based on a constant value of wind friction of 0.0012 for wind speeds below 7.5 m/s and a constant value of 0.0024 for wind speeds above 27.5 m/s, with a linear variation of the wind friction between them. Such values were defined during the calibration process. 3.3 Wave model The third-generation spectral wave model MIKE 21 SW (Sørensen et al. 2004) was used in this study to simulate growth, decay, and transformation of wind-generated waves as a result from each of the synthetic events. For detailed information on the model, the reader is referred to DHI
(2014b). The model setup was based on Ruiz-Salcines (2013), who calibrated a model for mean and extreme conditions (including tropical cyclones) in the Gulf of Mexico and Caribbean Sea. The fully spectral and nonstationary time formulation was used in the model, with a logarithmic spectral discretization with a minimum frequency of 0.05 Hz, 17 frequencies, and a frequency factor of 1.1; and a directional discretization for 360° divided in 18 directions. The time step is also based on a multisequence integration step, with a minimum value of 0.01 s and a maximum value of 3600 s. The energy transfer includes quadruplet-wave interactions, and the wave-breaking factor is a constant gamma value of 0.80 and an alpha value of 1.0. The bottom friction was based on the Nikuradse roughness with a constant value of 0.04 m.
Ocean Dynamics Fig. 4 Mesh and bathymetry for a the Pacific Ocean and b the Gulf of Mexico/Caribbean Sea
Whitecapping is controlled via constant values of the dissipation coefficient, with a Cdis value of 3.5 and a Deltadis set to 0.6. The initial condition uses the JONSWAP fetch growth expression with shape parameters a and b of 0.07 and 0.09, respectively. The peakness parameter is 3.3, and the offshore boundaries are considered closed, that is, no waves enter the model domain through this boundary and the outgoing waves are fully absorbed. 3.4 Maximum value envelops The numerical models provided the time series of SWH and WLs at all mesh elements for the whole domain
during the period covered by each event. To provide an overview of the SWH and WL climatology from the synthetic events, the extreme conditions, represented by the 99th percentile, are shown in Fig. 5. The results are in accordance to the tropical cyclone climatology as presented in Section 2 and described herein. The central area of Mexico in the Pacific side is the area more exposed to extreme waves from tropical cyclones, with diminishing wave heights towards the north and south. In the Atlantic side, the Caribbean Sea is the most exposed area to tropical cyclone waves as well as the northern part of Mexico near the US border, while the Sound of Campeche experiences the lowest wave
Ocean Dynamics
Fig. 5 Significant wave height (a, b) and storm surge (c, d) extreme climate (99th percentile) for the Pacific Ocean (a, c) and the Gulf of Mexico/ Caribbean Sea (b, d)
heights. For storm surge, the North Pacific mainland Mexico and Gulf of California coasts are more exposed to storm surge as well as the Yucatan Peninsula and the Mexican coast of the Northern Gulf of Mexico near the US border. While the climatology and individual time series are valuable information for other applications (Appendini 2014), in this study, it is required to use the maximum obtained values at each mesh element and for all storms. As such, the time series for individual events at each mesh element was analyzed to create an envelope of maximum values for each of the events. As a result, we obtained maps of maximum SWH and WLs for each event, for a total of 6200 maximum value maps (1550 for each basin and 1550 for each process, i.e., waves and storm surge). As an example, Fig. 6 shows the maximum SWH and WLs for synthetic event 0011 in the Pacific Ocean and 0016 in the Gulf of Mexico/Caribbean Sea.
4 Extreme value analysis Currently, the GEV and the generalized Pareto distribution are the most commonly used distributions for extreme value analyses. However, we initially centered our attention only to the GEV because it combines the Gumbel, Fréchet, and Weibull families into one single distribution function,
allowing it to be adaptive to the data. The GEV method is described in Coles (2001) and follows Eq. 3. h z−μ i− 1ε GEV ¼ exp − 1 þ ε ð3Þ σ where ε, μ, σ, and z are the shape parameter, location parameter, scale parameter, and block maxima values, respectively. The GEV distribution was not applied to the maximum value vector for each element mesh, but each element was analyzed for a peak over threshold value. The selection of the threshold was based on Arns et al. (2013), who consider the percentile approach as a suitable way to avoid subjective choices in the threshold selection techniques. Based on a sensitivity analysis, the 98th percentile was selected as threshold to the storm surge data and the 99th percentile to the wave data. These percentiles were selected differently for each parameter in order to lower the weight on the lower tail and to get a better fit of the extreme data. The extreme value analysis was performed at each mesh element based on the results from the historical simulations complemented with the synthetic events, as proposed by Meza-Padilla et al. (under review). Applying the GEV function, it was found that, in some cases, the fitted curve will extrapolate to unlikely extreme values. As a result, we decided to test the Weibull distribution, which has been applied in similar studies in the area (Posada-
Ocean Dynamics
Fig. 6 Maximum envelope of significant wave height in a the Pacific Ocean for event 0011 and b the Gulf of Mexico/Caribbean Sea for event 0016 and of water levels in c the Pacific Ocean for event 0011 and d the Gulf of Mexico/Caribbean Sea for event 0016
Vanegas et al. 2011). The Weibull distribution is described in Coles (2001) and follows Eq. 4. b x b−1 −ð ax Þb WBL ¼ exp ð4Þ a a where b and a are the shape and scale parameters, respectively, and x is the sample. Figures 7 and 8 show the GEV and Weibull distributions at selected sites for the EPC and the NAC, respectively. These sites were selected as examples and correspond to areas of high-resolution mesh, distributed in the north and south of Mexico, where important ports are located. Clearly, in both Figs. 7 and 8, there are several discrepancies in the return periods of storm surges derived from both theoretical distributions. This is particularly true in the case of values with low probability (e.g., RP=1000 years). Indeed, in both cases, the behavior of the tail of the distribution is completely different, indicating a more extreme scenario for those values derived from GEV. In general, a better agreement is observed for those values derived from the Weibull distribution, which may point towards an advantage when predicting storm surge design values in Mexico. On the other hand, it is very clear that the extreme value analysis carried out with both distributions, is very sensitive to the maximum observed value in the data to which they are fit. It should be noted that, in order to have more reliable information of storm surge levels, it is necessary
to consider bathymetric data of higher resolution, since this information is a key for an accurate propagation of the storm surge as it travels towards the coast. Despite this fact, the technique presented here represents a significant advance to determine design levels of storm surge to the traditional approach that employs parametric equations for their definition. In the case of SWH, the GEV and Weibull distributions show similar results, although more reliable results are provided by GEV, since the Weibull distribution rarely goes above the maximum value from the sample data. It is worth mentioning that the extrapolation to different return periods is based on the present climate, and such results are expected to vary in a climate change scenario. The issue of unreliable results obtained in some cases with the GEV distribution has been noted by several authors, such as Irish et al. (2011), who apply the GEV distribution but made a recalculation using the Gumbel distribution for those cases in which the 1000-year return period value of the distribution exceeds by 75 % the largest surges appearing in their samples. While a similar approach was tried using different thresholds to discriminate the distribution function used, the results did not have an overall improvement. As a consequence, we decided to do the maps using separately GEV and the Weibull functions. For the case of 100-year return period, these maps are shown in Figs. 9 and 10 for the Pacific and Gulf of Mexico/Caribbean Sea, respectively.
Ocean Dynamics Fig. 7 GEV and Weibull distributions for water levels (a, b) and significant wave height (c, d) for selected sites in the Pacific Ocean: Guaymas (a, c) and Puerto Chiapas (b, d)
The 100-year return period maps using the GEV distribution for WLs show areas with patterns unlikely to occur in Fig. 8 GEV and Weibull distributions for water levels (a, b) and significant wave height (c, d) for selected sites in the Gulf of Mexico: Tampico (a, c) and Campeche (b, d)
nature both in the Pacific and the Gulf of Mexico. On the contrary, the Weibull distribution shows more uniform
Ocean Dynamics
Fig. 9 Extreme significant wave height (a, b) and water levels (c, d) for a 100-year return period using GEV (a, c) and Weibull (b, d) distributions in the Pacific Ocean
patterns. A similar situation is found for SWH in both basins. As a result, the maps using the Weibull distribution are
considered more adequate even if the values may be underestimated.
Fig. 10 Extreme significant wave height (a, b) and water levels (c, d) for a 100-year return period using GEV (a, c) and Weibull (b, d) distributions in the Gulf of Mexico/Caribbean Sea
Ocean Dynamics
From the above results, it is clear that extreme value analysis should be localized and studied in an individual basis (i.e., a particular location) and not performed for large-scale areas, since the extreme values are very sensitive to the distribution selected. When doing an extreme value analysis in a local area, it is possible to try different distributions in order to select the most adequate, but for large-scale assessment such as the one presented, it is not possible to do such analysis for each element of the mesh. In that case, a distribution such as Weibull would be more adequate, although one should consider that the values might possibly be underestimated.
5 Discussion and conclusions Synthetic tropical cyclones were used to drive numerical models in order to characterize extreme climate of waves and storm surge in the Mexican Pacific Ocean and Gulf of Mexico/Caribbean Sea. Based on the present climate, a total of 3100 synthetic events doing landfall in Mexico (divided between both basins) were used to create a robust database that allows for a better estimation of extreme events, while covering areas that otherwise would not be correctly evaluated due to the lack of historical records. The tropical cyclone climatology of the synthetic events is found to be in accordance to the historical events in both basins. A third-generation wave model and a hydrodynamic model were driven with the synthetic tropical cyclone database to derive the spatiotemporal distribution of waves and water levels generated by each of the events. The results were analyzed to generate maximum envelope maps, and the extreme climate was derived from the 99th percentile. The results showed that the extreme wave climate follows the tropical cyclone climatology in both basins. Using the 98th (water levels) and 99th (waves) percentiles derived from the maximum envelope maps, an extreme value analysis was performed for each mesh element by applying both the generalized extreme value and the Weibull distributions. In the case of storm surge values, clear discrepancies between the fit of these distributions were found, especially for the larger values close to the upper tail. While in the case of the waves, the fitting of both extreme value distributions were found to be similar. In this sense, it is reflected that an extreme value analysis is very dependent on the distribution selected and should be site and parameter specific. In general and for both waves and water levels, it is shown that the Weibull distribution provides more plausible estimates for extreme values, but likely underestimated at higher return periods. Based on the Weibull distribution for waves and storm surge, it was found that the highest waves are expected at the Mexican Caribbean and the northern coast of the Gulf of Mexico while highest storm surge in the northern part of the Yucatan Peninsula. As for the Pacific, the highest waves and
storm surge values are expected at the central mainland Mexico coast and diminishing towards the north and south while storm surge is minimal. These results provide estimates for future extreme conditions under the present climate, and the results should be taken, acknowledging that climate change is not considered. The methodology is proved to be a good alternative in the reproduction of continuously varying tropical cyclone climatology along the Mexican coastline, and it provides a rational approach for assessing the hurricane-induced risk in coastal areas. Acknowledgments The authors would like to thank Dr. Kerry Emanuel for supplying the synthetic events used in the study; CONACYT for providing support to Rafael Meza-Padilla with scholarship 555771 and funding for this research through project 167003; the Inter-American Institute for Global Change Research (IAI, Grant CRN II 2048), supported by the U.S. NSF (Grant GEO-0452325); and Roberto Uribe, Sokaris de la Luz Aranda, Ismael Mariño from Cinvestav, and José López from UNAM for the survey data used in this work as well as the two anonymous reviewers for their valuable comments in improving this manuscript.
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