INTRODUCTION

Hydrometeorological and climatic events are complex phenomena that result from the interaction of several spheres on planet Earth combined with processes within and outside it that also influence them. To characterize the climate of a region based on meteorological time series or estimate subsequent values, it is essential to consider and identify the climatic interactions between the ocean-continent and the atmosphere. The most significant of all these interactions is likely the one between the ocean and the atmosphere. Oceans cover 71% of the Earth and play a key role in most atmospheric phenomena, including the provision of moisture, transporting moment and energy, and storing heat in oceans and the atmosphere (^{IPCC, 2019}).

Multiple studies have sought to identify the main impacts of global warming on ocean waters. The major effects include the rise in surface water temperature, acidification, loss of Arctic and Antarctic ice cover, imbalance in oxygen content in deep water, and rise in mean sea level in coastal areas worldwide (^{Cazenave and Cozannet, 2014}). Of all of the above, the rise-decline in mean sea level is the effect representing the most worrying threat and potential hazard to coastal inhabitants (^{McGranahan et al., 2007}).

Sea level refers to the average height of the sea surface between high and low tides. Temporal changes in tides and waves are averaged to determine a stationary water level, thus identifying whether the sea level has changed or the height of the land above sea level has varied (^{British Geological Survey, s.f.}). This and other oceanographic variables allowed for identifying trends - generally positive - in ocean height behavior at different temporal and spatial scales (^{IPCC, 2021}).

This increase observed at the local level can be attributed to countless phenomena, from continental movements, coastal management, thermodynamic processes, orographic modifications due to infrastructure construction, extreme hydrometeorological events, to the presence/absence of El Niño. At the global level, there are different time scales through which various phenomena influence the mean sea level. Thus, pointing out a single cause is intricate. However, the most recent assessment by the ^{IPCC (2021)} considers human activity the key driver of this rise in mean sea level since 1971 (^{IPCC, 2021}).

Due to long-term movements of the Earth's surface over long periods, local-scale changes may be observed even though the absolute height of the oceans remains unchanged, or changes cannot be identified despite the varying height (^{British Geological Survey, s.f.}).

Analyses of the evolution in sea-level height have been carried out in different coastal regions worldwide, most detecting an increase. In Australia, ^{White et al. (2014)} obtained an increasing trend of +1.6 ± 0.2 mm year^-1 for the period 1966-2010; for southern Europe, ^{Marcos and Tsimplis (2008)} estimated a positive trend of +1.5 ± 0.1 mm year^-1 during the 20th century. Studies such as these are considered to calculate global average trends, hence the importance of conducting regional or local analyses in various parts of the world.

The special Intergovernmental Panel on Climate Change report on oceans and the cryosphere (^{IPCC, 2019}) established an average sea level rise of +0.16 meters from 1902 to 2015 and an average global trend of +3.6 mm year^-1 from 2006 to 2015. According to the sixth assessment report of the ^{IPCC (2021)}, a global mean sea level rise of approximately +0.20 meters has been recorded from 1901 to 2018, with an updated trend in the mean sea level of +3.7 mm year^.1.

In line with the evolution observed so far, the global annual rate is expected to increase and remain over the next centuries; some future scenarios estimate a rise of between +0.30 and +2 meters by 2200, depending on the management of greenhouse gas emissions (^{IPCC, 2021}).

In Mexico, studies of changes in the mean sea level have started to emerge, each with its own methods, objectives, and databases. To note, like most studies at the global level and despite the pragmatic differences between them, the studies conducted in the coastal areas of Mexico report a positive trend in sea level in the region, consistent with the reports issued by the ^{IPCC (2019}, ²⁰²¹⁾ and previous studies.

^{Zavala-Hidalgo et al. (2011)} analyzed the sea-level behavior on the Mexican coast from data recorded in 16 stations of the National Mareographic Service at Univerisdad Nacional Autónoma de México. They used monthly averages of the longest available series and considered only years with data for all months to avoid biases from seasonal variation. A positive trend was identified in the Pacific and Gulf of Mexico basins. Generally, a positive but irregular trend was established on the Mexican Pacific and Atlantic coasts.

Regional events also influence the data used to construct trends, and this complicates the characterization of a unique trend, although patterns can be derived for each coastal region of the country. ^{Ruiz-Ramirez et al. (2014)} found an overall rise in sea level in Mexico; it rises at a greater rate on the Gulf and Pacific coasts (+3.8 and +3.5 mm year^-1, respectively), while the Mexican Caribbean shows a lower rate of increase (+1.6 mm year^-1) relative to the overall average considered in the study.

OBJECTIVES

This article has a local scope, limited to the central coast of the Gulf of Mexico. Our results are expected to be consistent with the literature on sea-level trends at different scales. Therefore, the primary objective is to compare recent sea-level trends in this region with the values reported by ^{Zavala-Hidalgo et al. (2011)} and ^{Ruiz-Ramirez et al. (2014)} for the Mexican coasts and, in turn, with the global average reported by the ^{IPCC (2019}, ²⁰²¹⁾.

For a coastal region, anomalies in its adjacent waters will involve various risks and impacts. Factors such as topography, the extent of the coastal plain, and infrastructure will largely determine what effect of global warming on the ocean represents the greatest risk and involves the greatest vulnerability. ^{Conde Alvarez and Palma Grayeb (2006)} state that the rise in mean sea level poses a significant risk for human settlements on the Gulf of Mexico's coast, given their vulnerability to floods and tidal waves, among other responses. The analysis and characterization of the effective plain and an assessment of the most vulnerable areas and mareographic data are essential for coastal states. It is necessary to understand the root cause of the issue using a reliable methodology for decision-making since natural disasters can determine the distribution of the population (^{Rodríguez Villafuerte. 2006}; ^{Gómez Villerías et al., 2022}). Coastal planning would save losses and damage in key sectors such as energy and is necessary for risk management and an optimum location of houses.

In this context, the Gulf of Mexico littoral was selected as a study area to assess whether the effects of global warming reported by the ^{IPCC (2021)} and observed on the Mexican coasts in previous studies occur in this coastal region (^{Zavala-Hidalgo et al., 2011}; ^{Ruíz-Ramírez et al., 2014}).

The small-scale temporal behavior of sea level was characterized by calculating daily and annual cycles and constructing time series of annual averages. The large-scale temporal behavior of sea level in the region was characterized based on predictions of the future. Numerical results are also displayed graphically to visualize and identify the patterns or anomalies found.

MATERIALS AND METHODS

In the present study, we quantitatively described the behavior of the mean sea level in the Gulf of Mexico littoral by analyzing hourly mareographic data for three stations of the Secretariat of the Navy’s National Mareographic Network, using the procedure described by ^{Zavala-Hidalgo et al. (2011)}. This study was carried out using the historical hourly records for three stations located on the Gulf of Mexico coast: Coatzacoalcos, Veracruz (18°09’ N, -94°26’ W); Frontera, Tabasco (18°32’ N, -92°38’ W); and Veracruz, Veracruz (19°12’ N, -96°08’ W) (Figure 1) to quantitatively describe the behavior of the mean sea level on the Gulf of Mexico coast. It should be noted that the tidal data used do not consider the geophysical changes that may influence relative sea-level height measurements.

Figure 1 Location of the stations that define the region “central coast of the Gulf of Mexico”. 

To estimate values of sea-level trends in the Gulf of Mexico littoral, the tide was first characterized through daily and annual cycles. In addition, we used the calculated trend values to construct graphs of future sea-level behavior for the next century through extrapolations. These graphs were then compared with other sources and are discussed at the end.

For the three sites, evolution time series were constructed for the years available at each database (1999 to 2018 at Frontera and 2000 to 2018 at Coatzacoalcos and Veracruz), averaging the values for a given year at each station - annual average databases. In general, the stations have relatively high percentages of missing data, especially the Coatzacoalcos station, with only 55% of the data available. Frontera was the station with the most information and the only one to have data for a full year. Years with no data were excluded from trend calculation.

A variation on the methodology of ^{Zavala-Hidalgo et al. (2011)} is the auto-correlation analysis for the annual average databases. Figure 2 shows the autocorrelation function for annual averages. A semi-cyclic behavior is observed that is not complete because the length of the series only covers 18 years. Data were processed under this premise.

Figure 2 Auto-correlation function (Y-axis) for annual average (X-axis) databases. 

Subsequently, a trend line was fit to each evolution time series using the least-squares linear regression method.

An uncertainty interval was calculated for each trend value, as defined by ^{Zavala-Hidalgo et al. (2011)} as the product of the critical value by the typical error (TE):

Where 𝜎 is the standard deviation and n is the size of the hourly data series. The critical value was calculated with a significance level of 0.01 (1%) and n-2 degrees of freedom. The calculations described and all the products reported in this article were made using the Rstudio software (^{Rstudio, 2018}).

Given that we found full years with missing data, this study calculated three different types of trends: the overall trend, considering time series as a single segment; the segmented trend, calculated for each uninterrupted period of data; and the corrected trend, considering the entire series after the missing data are imputed. Data were imputed based on the average value of the respective station. This substitution followed the procedure by the Secretariat of the Navy in the calculations for the tide prediction calendars (CECOPROD, personal communication, 6 January 2022).

According to the IPCC glossary (2013), a prediction is the result of an attempt to estimate the actual evolution of the variable in the future from a particular state of the system. In this study, using extrapolations based on the segmented trends calculated for each site, we estimated the future sea-level height using prediction graphs for the central coast of the Gulf of Mexico up to the year 2200. The same glossary establishes the term ‘forecast’ as a synonym in this context.

These graphs were compared with sea level predictions constructed by the ^{Central Climate (2020)}, corresponding to the Representative Concentration Pathway (RCP) scenarios 2.6, 4.5, and 8.5. For the graphs included in the Results section, RCP predictive lines are based on the 50th percentile for each emission scenario.

Sea level estimates related to RCPs 2.6, 4.5, and 8.5 calculated by the ^{Central Climate (2020)} are based mainly on the work of ^{Kopp et al. (2014)} and ^{Kopp et al. (2017)}. These results also consider IPCC’s global predictions and, in some cases, recent investigations of potential ice cap instability in Antarctica (^{DeConto and Pollard, 2016}). The pollution scenarios from greenhouse gas emissions include “rampant pollution” (technically, RCP 8.5), “moderate reduction in concentrations” (RCP 4.5), and “extreme reduction in concentrations” (RCP 2.6). This latter assumption represents a peak in emissions near 2020, followed by a sharp decline close to zero in 2070 (^{Climate Central, 2020}). The estimates of this server were used because of data availability, the coincidence in the locations used in this study, and the robustness of its references.

RESULTS AND DISCUSSION

The first graphical results obtained were daily and annual tidal cycles at each station, which served to get a first approximation of the sea-level behavior on the central coast of the Gulf of Mexico.

All available values in the series with the same hour indicator were averaged to obtain the mean daily behavior for each site (Figure 3 a, b, and c). Similarly, all available values in the series with the same monthly indicator were averaged to obtain the mean annual behavior at each site (Figure 4 a, b, and c).

Figure 3 Characterization of daily cycles in a) Coatzacoalcos, b) Frontera, and c) Veracruz. 

Figure 4 Characterization of annual cycles in a) Coatzacoalcos, b) Frontera, and c) Veracruz. 

As described above, the results of this study include three different trends. To simplify this section, the graphical trend results are included only after missing data are imputed.

Figure 5 (a, b, and c) represents the corrected time series and their overall associated trends. Figure 6 (a, b, and c) shows corrected segmented trends for the central coast of the Gulf of Mexico. The latter cover the periods from 2000 to 2010 for Coatzacoalcos and Veracruz, 1999 to 2010 for Frontera, and 2011 to 2018 for the three stations.

Figure 5 Evolution of sea level with the corrected overall trend in (a) Coatzacoalcos, (b) Frontera, and (c) Veracruz. 

Figure 6 Evolution of sea level with corrected segmented trend in a) Coatzacoalcos, b) Frontera, and c) Veracruz. 

Frontera stands out for being the only time series without discontinuities; however, segmented and corrected segmented trends were nonetheless calculated for the period 2011-2018, which includes the only uninterrupted period common to the three sites: 2012-2018. Table 1 contains the numerical values of the trends with their associated uncertainty.

Finally, using the trends whose behavior coincides with the results of ^{Zavala-Hidalgo et al. (2011)}, sea-level height values were extrapolated for the following century. These data were graphically compared with the predictions on the ^{Climate Central (2020)} webpage to find similarities or disparities and draw discussion. Figures 7, 8, and 9 illustrate the behavior of each prediction for different emission scenarios against the predictions calculated in the present study. The data available in ^{Climate Central (2020)} included predictions for Coatzacoalcos but not for Frontera or Veracruz, so the last two stations were compared with neighboring sites: Ciudad del Carmen (18°38’ N, -91°50’ W) and Alvarado (18°46’ N, -95° 46’ W), respectively.

Note: Lines 00-10 and 11-18 show the results of corrected segmented trends calculated for Veracruz.

Figure 7 Comparison of predictions in Alvarado, Veracruz. The XTRM, MDRT, and UCKD lines correspond to RCPs 2.6, 4.5, and 8.5, respectively. 

Figure 8 Comparison of the predictions for Ciudad del Carmen, Campeche. The XTRM, MDRT, and UCKD lines correspond to RCPs 2.6, 4.5, and 8.5, respectively. 

Note: Lines 00-10 and 11-18 show the results of corrected segmented trends calculated for Coatzacoalcos.

Figure 9 Comparison of the predictions for Coatzacoalcos, Veracruz. The XTRM, MDRT, and UCKD lines correspond to RCPs 2.6, 4.5, and 8.5, respectively. 

The key findings of the study are briefly discussed for each time scale.

CONCLUDING REMARKS

The responses of ocean dynamics, like almost any response on our planet, depend on several factors and may occur in multiple forms. In this sense, identifying ocean responses caused directly or indirectly by the anthropogenic effects of natural causes is a complex task.

This work aimed to evaluate the contribution of global warming - through the increase in heat content in the ocean and the melting of ice sheets - to the rise in mean sea level. However, multiple factors affect the average sea level on different temporal and spatial scales, two of the most important ones being the total volume of seawater and the movements of the subsoil and the seabed, which affect the size and shape of ocean basins. In addition, dynamic factors such as wind, atmospheric pressure, ocean currents, and waves also play a central role (^{Mimura, 2013}).

In the present study, the sea level on the central coast of the Gulf of Mexico showed a negative trend, even after the imputation of missing data of about -1.86 mm in the year^-1 over the period 1999-2018. The period 2000 to 2010 showed a steady rise in sea-level height of about 3.6 mm year^-1, consistent with the global average established by the ^{IPCC (2019}, ²⁰²¹⁾. The period 2011 to 2018 shows a decrease in sea level of approximately -1.26 mm year^-1 with a slight recovery in post-2015 records. The magnitude of trends across the sites analyzed does not show a clear increase or decrease pattern on a spatial scale.

The negative trends for the periods 1999-2018 and 2011-2018 do not coincide with any values reported in the literature consulted for the present work.

The prospects for the future behavior on the central coast of the Gulf of Mexico underestimate the rise in sea level relative to the values predicted by RCPs 2.6, 4.5, and 8.5 of ^{Central Climate (2020)}. According to the trends for the period 1999 to 2010, a rise of approximately 0.47 to 1.07 meters is expected in the region by the end of the 22nd century; in contrast, estimates based on trends from 2011 to 2018 predict a decrease of about -0.41 to -0.02 meters in sea level is expected by the end of the present century.

The negative results in the analysis of the current behavior may derive from several causes: continental movements, the presence or absence of El Niño and La Niña events, or mesoscale hydrometeorological events.

The three series used had a relatively high percentage of missing data - approximately 50%. In this regard, it is essential to continue recording measurements at the stations studied and improve the quality of records. More extended time series and a larger dataset will improve the estimation of sea-level trends and reduce the associated uncertainty.