Storm-wave trends in Mexican waters of the Gulf of Mexico and Caribbean Sea

Thirty-year time series of hindcast wave data were analysed for 10 coastal locations along the eastern Mexican coast to obtain information about storm events occurring in the region, with the goal of examining the possible presence of interannual trends in the number of storm-wave events and their main features (wave height, duration and energy content). The storms were defined according to their significant wave height and duration, and the events were classified as related to either tropical cyclones or Norte events. The occurrence and characteristics of both types of events were analysed independently. There is no statistically significant change in the number of storm-wave events related to Nortes or their characteristics during the study period. However, there is a subtle increase in the number of events related to tropical cyclones in the western Caribbean region and a more evident increase in wave height and energy content of these events.

study, TC waves were separated from the rest of the register using the National Hurricane Center best-track record and an increase in the number of TC-related events over the last decades was found. However, this increase was neither associated with increases in significant wave height related to the TC events, nor with the duration of the TC events. Their study also found a shift in the intra-annual distribution of TC-related events between the first and second parts of the register, with the majority of events taking place during August and September in the first half of the register and during September and October 5 in the second half of the register.
Along the coast of the Mexican GoM, extreme wave storm events are mainly caused by tropical cyclones and Nortes. Nortes are anticyclonic cold surges that enter the Gulf of Mexico from North America, generating strong northern winds and, therefore, present ideal conditions for fetch causing mature wind waves. The study of the occurrence and interannual trends of extreme wave storm events related to both TC and Nortes must be regarded separately, given that possible long-term changes 10 in the behaviour of TC and Nortes and their responses to climate change are not expected to be analogous (Komar and Allan, 2008).
As for the western Caribbean Sea (WCS), storminess trend studies based on wave datasets are absent to the authors' knowledge.
Projected changes in wind shear suggest a decrease in the number and intensity of TCs in the region (Biasutti et al., 2012), although studies suggest an intensification of wind speed of higher-category events on a global scale (Holland and Bruyère, 15 2014). Wave condition models do not project increases in wave height in this area (Appendini et al., 2014), although no analyses specifically for extreme events exist.
Along the eastern coast of Mexico (Gulf of Mexico and Western Caribbean Sea), in situ and satellite data are scarce and temporally discontinuous. This contribution analyses a 30-year time series of hindcast wave data, covering the period of 1979 to 2008 (Appendini et al., 2013). The selection of this time interval allows for comparison to previous work in the region and 20 is considered the standard period by the World Meteorological Organization to characterize climate, although the use of shorter time periods has been suggested to characterize non-stationary climates, i.e. under climate change conditions (Arguez and Vose, 2011). Appendini et al. (2013) did not find any significant trend in time series of extreme wave heights (using the 99 th percentile) along the eastern Mexican coast, but their research examined the entire time series without regard of the type of extreme event.

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The aim of this work is to determine possible interannual trends in the number of wave storm events and their main features (wave height, duration and energy content). This was achieved by first identifying extreme wave storm events for a number of near-coastal locations along the eastern Mexican coast, and then classifying them according to the meteorological conditions that caused these events (TC or Nortes).

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The eastern coast of Mexico extends along the GoM and the WCS. The study area is within the region with the highest correlation coefficient (best performance) of the hindcast data, and comprises eight nodes located in the Mexican GoM at 50m depth, and two nodes in the WCS within 100-m depth. Additionally, the nodes were selected based on the proximity of coastal settlements: Matamoros, Tampico, Veracruz, Coatzacoalcos, Paraiso, Campeche, Progreso, Holbox, Cancun and Tulum (Fig. 1).

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Campeche, Puerto Progreso and Holbox are characterized by an ubiquitous wide continental shelf of approximately 245 km with a slope of 1/1000 and a low-lying topography of the adjacent emerged areas (Enriquez et al., 2010).
Wave conditions are generally mild with mean significant wave heights (SWH) around 1 m, although wind waves with maximum individual wave heights of approximately 27 m have been measured by wave gauges in the northern GoM (Wang et al., 2005) during Hurricane Ivan. The main meteorological systems contributing to storm wave conditions are mid-latitude 40 anticyclonic meteorological systems that generate northerly cold fronts known as Nortes with an average of 11 to 21 Nortes Nat. Hazards Earth Syst. Sci. Discuss., doi:10.5194/nhess-2016-392, 2017 Manuscript under review for journal Nat. Hazards Earth Syst. Sci. Discussion started: 8 February 2017 c Author(s) 2017. CC-BY 3.0 License. per season (Reding, 1992), and cyclonic systems that include tropical depressions, tropical storms and hurricanes. There is some overlap of the occurrence of either type of event during the year and the two systems can interact, mainly in October.
The North Atlantic tropical cyclone season runs from 1 June to 30 November, with September being the month with the highest number of tropical cyclones directly affecting the Mexican coasts (Rosengaus and Vázquez, 2002). Norte events usually occur from October to April, with the most intense events taking place from December to March (Appendini et al., 2014).

3 Datasets
Three datasets are used in this study: 1) 30 years of hindcast wave data, 2) the International Best Track Archive for Climate Stewardship (IBtracs) dataset for discerning TCs affecting the study area, and 3) a Norte dataset designed for the GoM and WCS regions.

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The hindcast wave data cover the period from 1979 to 2009 in three-hour intervals for the entire eastern Mexican coast (Appendini et al., 2013). We used the 30-year wave data in order to comply with the World Meteorological Organization's recommendation for characterizing non-stationary climates, i.e. under climate change conditions (Arguez and Vose, 2011).
As mentioned before, eight nodes located in the Mexican GoM at 50-m depth and two nodes in the WCS at 100-m depth were evaluated. These isobaths were selected to assure that the nodes are in deep water to avoid any shoaling, refraction and bottom 15 friction.

IBtracs
The IBtracs (Knapp et al., 2010) record was used given that this platform includes the most complete set of historical TCs available. The data were downloaded from the NCDC website (https://www.ncdc.noaa.gov/ibtracs) in May 2016.

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The Norte dataset includes the dates when Nortes entered and left the Gulf of Mexico. This dataset was derived from the Climate Forecast System Reanalysis (CFSR) data (Saha et al., 2010), and the Nortes are identified based on the pressure difference between Yucatan and Texas, as well as wind speed at different positions over the Gulf of Mexico.

Methodology
In this study, the occurrence and interannual trends of extreme wave storm events caused by TCs and Nortes were regarded 25 separately, given that their behaviour and response to climate change are not expected to be analogous (Komar and Allan, 2008). The present study of the GoM and WCS wave data examines the use of a common tool for coastal management where the dataset is inspected looking for individual storm events based on the register of significant wave heights, establishing a minimal duration for storm events (Mendoza et al., 2011) and associated meteorological conditions based on the identification and separation of TC and Nortes events. This approach not only provides improved insight into wave formation compared to 30 using a summer and winter events distribution (Komar and Allan, 2008), but also allows further analyses of the number, energy content and duration of storm events, as well as possible trends associated with a given type of meteorological storm.

Storm definition
From an oceanographic point of view, a storm can be defined as an increase in wave height and sea level (storm surge) exceeding a certain threshold during a certain amount of time (e.g. Mendoza et al., 2011). A common way to characterize 35 Nat. Hazards Earth Syst. Sci. Discuss., doi:10.5194/nhess-2016-392, 2017 Manuscript under review for journal Nat. Hazards Earth Syst. Sci. Discussion started: 8 February 2017 c Author(s) 2017. CC-BY 3.0 License. extreme events is using a Peak-Over-Threshold methodology, which implies that an extreme wave event (storm event) occurs when the significant wave height exceeds a given threshold during, at least, a certain period of time.
Conventionally, the selection of the wave height threshold takes local characteristics of the wave regime into account. In this study, a storm is defined as an event reaching a SWH greater than Hthreshold for at least 12 hours. Hthreshold is calculated for each node as where the chevrons refer to average values and σ is the standard deviation of the SWH time series. The SWH criterion is based on the methodology used by Walker and Basco (2011), while the minimum duration criterion is applied taking the reported decrease in the duration of Nortes events as a result of climate change (Pérez et al., 2014) into account. Finally, in order to separate consecutive storm events and make certain that the events are statistically independent, a minimum time between 10 consecutive events was established (48 hours). If the SWH is below the threshold for less than 48 hours, two consecutive events will be considered as one event.
For each of the identified storms, the following main characteristics were obtained: mean and maximum SWH, storm duration (ts), mean storm energy content and maximum energy content. The ES is related to the storm beach erosion potential (Mendoza and Jiménez, 2006), and is given by where t1 and t2 define the storm duration and SWH > Hthreshold. This equation leads to a more accurate value for ES than the traditional wave power equation that uses a single wave height value (usually the maximum SWH) to characterize the entire event.

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In order to separate TCs from Nortes events, the IBtracs database was used to identify TCs, while Nortes were identified using the Norte identification index. Regarding TCs, two regions of influence were defined: the WCS region (62° to 89.5°W, 7° to 23°N), covering events affecting the Tulum and Cancun nodes, and the GoM region (81° to 100°W, 17° to 32°N) covering the rest of the nodes. Wave conditions are considered to be caused by a TC when an event occurred during the pass of a TC through its regions of influence or during the following 36 hours. Regarding the Nortes, wave conditions are considered to be related 25 to a Norte event when the initial storm event (wave conditions) started during the occurrence of the Norte.
For a considerable number of events (between 7 and 25, depending on the node), a wave storm event occurred during both types of events. To discriminate the responsible event in these cases, the first approach was to compare the number of hours during which the meteorological and wave events coincided. If one of the meteorological events had a larger number of coincident hours, it was chosen to be the responsible event. If the hours were equal, the second approach was to look at the 30 date of occurrence; events occurring from November to April were considered as Nortes, while those occurring from July to September were considered as TCs. When the events occurred in the months of May, June and October, the wind direction related to the maximum SWH of the event was considered. Winds coming from N230°E to N45°E were considered caused by Nortes, while the rest of the events were considered TCs. Events that did not correspond to either type were not considered in this study.

Decadal trends of event characteristics
Time series of the event characteristics per season evaluated for the TC and Nortes series are: the number of storm events, the mean and maximum SWH (SWHmean and SWHmax), the mean and maximum Es, (Es,mean and Es-max), the mean duration of the storm events and the sum of storm event durations.  (Kendall, 1975;Mann, 1945) was performed for the time series of the different evaluated characteristics of the storm events caused by TCs and Nortes. This non-parametric test is used to identify if there is a monotonic upward or downward trend through time, but it does not specify whether the detected trend is a linear or nonlinear trend. The null hypothesis assumes that the data are independent and identically distributed over time. Mann-Kendall tests were performed in order to confirm the occurrence of trends that were significantly different from zero at the 90 % confidence level or higher.

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Following Casas-Prat and Sierra (2010) the Es and SWH data were log-transformed, which implies that the relationships obtained by linear regression between Es and SWH and time become exponential. In the case of the TC time series, a considerable number of years with no TC occurrence is present in the different datasets. For this reason, the probability of storm occurrence is introduced in the analysis to avoid biasing the data with the zero values. The SWHmean, SWHmax, Es,mean and Es,max time series are analysed removing the zero data to obtain the temporal trends conditioned to storm occurrence: 10 where aE and bE are the regression coefficients and ^ stands for predicted. The probability of storm occurrence (̂( )) is estimated for the binary TC time series (1 = event occurred, 0 = no event occurred) by binomial logistic regression. The product of Es (t|storm) and ̂( ) results in the estimated temporal evolution of the Es: 15 In this contribution, the term "trend" is defined, for the number of storm events and their duration, as the slope of the linear relationship (LR) between each variable and time. For SWHmean, SWHmax, Es,mean and Es,max, calculated trends are complex and are simplified as the mean rate of annual increase, calculated as the slope between the initial (t = 1979) and final (t = 2008) estimations.
5 Results and discussion 20

Data overview
The largest SWH values in the region occur in Matamoros, with <SWH> of 1.34 m, clearly exceeding the 1.06 m occurring at the closest southern node, Tampico (Table 1). Mean monthly SWH during the study period show an analogous distribution for the GoM nodes, with lower values during the summer months reaching a minimum in August and higher values during the winter months, from November to March (Fig. 2). The wave registers in the WCS nodes (Cancun and Tulum) present similar 25 overall statistics (Table 1), but differ in the mean monthly SWH distribution (Fig. 2), as the yearly variability in SWH is not as apparent as in the GoM nodes and there is not a clear summer/winter pattern.

Storm classification
Storms are defined for each node based on its SWH time series. The critical SWH value (Hthreshold) that defines storm events varies from 1.87 m in Tulum to 2.56 m in Matamoros; for all cases, Hthreshold is exceeded for less than 5 % of the data. The total 30 number of storms identified at the different nodes varies from 245 in Cancun to 407 in Matamoros (Fig. 3).
The classification into Nortes and TC-related events shows that between 5 % and 13 % of the events were caused by TCs.
Nortes were responsible for between 51 % (Matamoros) and 88 % (Coatzacoalcos) of the events in the GoM. These numbers are significantly lower in the WCS, where Nortes were responsible for up to 28 % of the events (Fig. 3).
A number of events were not classified as related to Nortes or TC events and, therefore, were not considered in this study. This

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number varies greatly between nodes, from 5 % in the southern GoM to >58 % in the WCS (Fig. 3). An unexpected result is that a considerable number of events occurring in Matamoros are not related to any of the considered meteorological systems.
This location is subject to the most restricted fetch among all analysed locations, so that storms are most likely related to other systems such as "suradas" or northerly winds that occur after the pass of a Norte. In Matamoros, suradas could occur while the Norte is still in the Gulf of Mexico, generating southerly winds in most of the other locations. This requires more detailed analysis, particularly to establish the duration of Norte events at particular locations instead of in the GoM as a whole. The large percentage of unclassified events in the WCS is an expected result given that wave conditions in the WCS are largely influenced by the trade winds, which is supported by the findings of Appendini et al. (2014).
A more detailed view of the annual distribution of both types of events (Fig. 4) shows that GoM events resulting from the The results of the annual distribution of TC-and Norte-related events (Fig. 4) demonstrate that the definition of the winter and summer season given by Komar and Allan (2008) is not applicable to the present study because a large percentage of events would be excluded from the analysis. For example, during October both Norte-and TC-related storm events are common in results presented by Bromirski and Kossin (2008). However, the nodes in the Bay of Campeche (Veracruz, Coatzacoalcos, Paraiso and Campeche) show that events related to TCs occur between August and December, with no registered events during June or July and the majority of events taking place in September and October.

Decadal trends in the number of events and their characteristics
Nortes and TCs are evaluated by season: from May to December for TCs and from September to the following August for Nortes. For this reason, there are 30 seasons for TCs, but only 29 seasons for Nortes because the last season is only partially represented in the dataset.
As expected, the patterns of the number of events caused by Nortes and TCs differ ( Fig. 5 and Fig. 6), as well as the trends and the Mann-Kendall test results obtained for each parameter, which are summarized in Table 2 and Table 3 for the Nortes and TC events, respectively.

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The time series of the number of storm events related to Nortes per season are given in Fig. 5. The trends obtained from a simple linear regression show a positive slope of less than 0.03 events yr -1 in all cases and do not indicate a particular organization among the nodes in the study area (Table 2). Furthermore, according to the Mann-Kendall test results, none of the nodes shows significant trends (at the 90 % confidence level) in the number of events caused by Nortes.
There is more consistency in the time series of the number of events caused by TCs (Table 3) Tulum nodes, the entire study area shows a certain organization, with Paraiso and Coatzacoalco showing trends close to zero and increasing slopes of the regression lines with increasing distance from these nodes.

Events caused by Nortes
According to the Mann-Kendall test results at the 90 % confidence level, none of the nodes, with the exception of Matamoros, Tampico and Progreso, show significant trends for the intensity or the duration of the Nortes. The significant trends that were A decrease in duration is observed in our results for the northernmost nodes of the GoM and in the WCS, but is not statistically 25 significant based on the Mann-Kendall test performed on the results. However, this might be related to the definition of a storm event used in this work, which requires more than 12 hours with SWH > Hthreshold to define an event, therefore biasing the effect of possible shorter events.

Events caused by TCs
The TC time series show a considerable number of years without the presence of storm events occurring at the different nodes.

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This number ranges between 43 % and 57 % of the analysed years, depending on the node (Fig. 6). This result is corroborated by Ramírez (1998), who investigated TCs arriving at the Yucatan Peninsula during the 1970-1995 period. In general, the percentage of years with no events related to TCs is larger during the first half of the study period, a circumstance more obvious for the WCS nodes, and in agreement with Bromirski and Kossin (2008), who found a general tendency for more significant wave events related to TCs since 1995, consistent with an increasing overall count of named storms during recent years. The trends in the number of storm events shown in Fig. 6 reveals that, in addition to an increase in the probability of occurrence of a storm event (̂( )) during the study period (Fig. 7), there is also an increase in the number of TC events per season. This, however, is not the case for the Coatzacoalcos and Paraiso nodes, which are the only two nodes where ̂( ) shows a negative 40 slope (Fig. 7).
Nat. Hazards Earth Syst. Sci. Discuss., doi:10.5194/nhess-2016-392, 2017 Manuscript under review for journal Nat. Hazards Earth Syst. Sci.  (Fig. 7). The ̂( | ) trends (calculated as the slope between the first and last value of each time series) are given in Table 4. The combination of both factors contributes to the trends in the time series of events caused by TCs (Table 3), 5 which show, in general, larger values than the trends in events caused by Nortes ( Table 2).
The effect of TCs in both regions is strongly influenced by the surrounding landmasses. In the GoM, the MK test only hurricane that moved erratically in the GoM waters from 26 October to 1 November ,, causing SWHmax at the GoM nodes of less than 5 m, but storm conditions with a duration of around five days (Fig. 8).
In contrast, the WCS nodes show significant trends according to the Mann-Kendal test results for all analysed parameters and the effect of the increase in the number of TC events since 1995 is more obvious than for the GoM nodes (Fig. 9).

Summary
Based on the intra-annual distribution of storm events and the trends found for TC-and Norte-related events, the studied nodes can be separated into four regions: i) the northernmost nodes (Matamoros and Tampico) are characterized by a TC season starting earlier than at the other nodes, with a majority of TC events taking place in August and September and no registered TC events in November and December.

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The nodes show a similar monthly distribution of the occurrence of Norte-and TC-related events, similar values regarding the probability of TC occurrence with time and a certain consistency in the trends of TC-related events. However, there are also significant differences between these two nodes, the most noticeable being the large number of unclassified events occurring in Matamoros.
ii) the Bay of Campeche nodes (Veracruz, Coatzacoalcos, Paraiso and Campeche) show no events (of any type) occurring 30 during June and July during the study period. The majority of events occur during the months of January, February and December, mostly associated with Nortes. Most of the TC-related events take place during September and October, but events have been recorded from August to December (with only one recorded event in December which corresponds to Tropical Storm Olga). These nodes do not show significant trends for any of the evaluated parameters, neither for Nortes nor for TCs.
iii) the Progreso and Holbox nodes show a behaviour partly comparable to the WCS nodes, mainly Holbox, which is closer to 35 the WCS. In general, they record a lower number of storm events than the rest of the GoM nodes, with a slightly lower number of Norte-related events and a slightly larger number of TC-related events than the rest of the GoM region. The trends found for events caused by TCs present steeper slopes than (ii) but the Mann-Kendall test does not support the presence of a statistically significant trend. iv) the WCS nodes (Cancun and Tulum), where the majority of events cannot be attributed to TCs or Nortes. In this region, the number of events related to Nortes is considerably lower and the majority of events related to TCs that have been recorded Nat. Hazards Earth Syst. Sci. Discuss., doi:10.5194/nhess-2016-392, 2017 Manuscript under review for journal Nat.

Conclusions
In the GoM region, Nortes are responsible for the majority of extreme wave events occurring from 1 November to 30 April, while TCs are responsible for the majority of extreme wave events occurring during August. During the months of September

Acknowledgments
The Mexican National Council for Science and Technology (CONACYT) and the Universidad Nacional Autónoma de México provided financial support through projects INFR-2014-01-225561 and Proyecto Interno 6602 Dinámica temporal de la vegetación de playas y dunas costeras y su participación como elemento de estabilización en la morfología del frente de playa.