Long-Term and Seasonal Analysis of Storm-Wave Events in the Gulf of California

Abstract

Coastal zones are threatened by extreme meteorological phenomena such as storm–wave events. Understanding storm-wave events is essential for sustainable coastal management. This study analyzed the temporal variability (both long-term and seasonal) of the frequency and energy content of storm-wave events in the Gulf of California for the period 1980–2020 using storm-wave data from the fifth-generation climate reanalysis dataset (ERA5). The results indicate that storm events in the Gulf of California are becoming more frequent and energetic. Storm-wave events coming from the north are more frequent but less energetic than those coming from the south. Throughout the year, storm-wave events from both the north and south show seasonal behavior. This paper aims to enhance the understanding of storm-wave events in the Gulf of California and serve as a foundation for future studies, such as coastal impact assessments.

1. Introduction

Due to the threats posed by climate change to coastal regions, the intensification of storm events has become a key research focus in recent years [1,2,3,4,5], along with their associated environmental consequences [6,7,8]. A comprehensive understanding of the impact of storm events on the ocean surface is pivotal to fostering sustainable coastal management. This knowledge serves as a cornerstone for conducting thorough coastal impact assessments, formulating policies related to shoreline management, and guiding the construction of coastal facilities [9,10,11]. It plays a crucial role in the development of climate change adaptation plans [12,13].

A storm event can be defined as a violent atmospheric disturbance accompanied by strong winds, among other elements [14]. The most immediate effects of a storm event are an increase in wave height (storm wave) and sea level (storm surge) [15] which can lead to beach and dune erosion, flooding, and damage to coastal facilities [16,17,18,19,20]. In meteorological terms, the genesis of a storm event can be attributed to various phenomena such as cold fronts, tropical cyclones, and other atmospheric systems, depending on the geographical location [21,22,23].

Changes in the intensity, frequency, duration, and direction of storm events reflect climate change’s impact on synoptic weather patterns [24,25,26,27,28], and can significantly alter coastal morphology, ecosystem health, and sedimentary processes [29]. Additionally, the region’s human development and economic activities, such as fishing, tourism, and urban growth, have increased the vulnerability of coastal communities and adjacent ecosystems to the impacts of storms and associated waves.

Therefore, the analysis of their effects (storm waves and storm surge) can be used to understand the impact of climate change on the coastal evolution of a specific region. For example, in the western Mediterranean Sea, storm surge events were analyzed over the past four decades by examining the variability in storm surge frequencies, duration, and direction, with an increase in storm wave intensity related to storm duration found [30]. A detailed study of storm-wave events was also performed along the Algiers coast [31]. Similarly, an analysis in the Sea of Marmara over a 40-year period examined the variability of storm-wave events and their effects on coastal areas [32], finding that extreme wave events have become more frequent and severe in the last decade. Ref. [33] Reveal that extreme storm waves in the Black Sea are seasonal, with higher frequency in winter and lower occurrence in summer. Ref. [34] evaluated the storm wave characteristics in the Gulf of Mexico and the Caribbean Sea.

With projected global warming, more intense storm events are expected to occur in certain coastlines worldwide in the future such as the southern Brazilian coast [35], the western Mediterranean coast [36], the southwest coast of India [37], and the east China sea coast [38]. Indeed, the ramifications of heightened storm-induced erosion may surpass the gradual effects attributed to rising sea levels [39]. This challenge is further exacerbated by the increasing concentration of population and infrastructure in coastal areas, which significantly amplifies the potential damage caused by storm events upon landfall [40,41,42,43].

This is a particularly important issue for the extensive coastline of the Gulf of California, as it is potentially exposed to cold fronts and tropical cyclones [44,45,46,47]. The Gulf hosts remarkable marine biodiversity and distinctive coastal ecosystems that are continually subjected to pressures from both climatic factors and anthropogenic activities [12].

However, the study of storm events has received little attention, especially in the context of climate change. While studies such as [48] have focused on quantifying the long-term seasonal variability of wave climate across Mexico, and ref. [12] has analyzed long-term trends in wave height, period, and energy in the Gulf of California, they do not provide insights into the patterns and effects of storm events. This lack of knowledge hinders the integration of storm event effects into coastal climate change impact assessments, which are necessary for adaptation plans.

To address this issue, the present study investigated the temporal variability (both long-term and seasonal) of the frequency and energy content of storm event waves using the ERA5 dataset [49] and examined the patterns of storm-wave events and their relationship with climate change in the Gulf of California, where observational data is limited.

The subsequent sections of this paper are organized as follows: Section 2 delineates the study site, Section 3 explains the methodology employed in this research, Section 4 presents and discusses the results, and Section 5 summarizes the study and the overall conclusions.

2. Site Study

Located in northwestern Mexico, the study site is the Gulf of California (Figure 1). The Gulf of California is a semi-enclosed basin that separates the Baja California Peninsula from the Mexican mainland. Connected to the Pacific Ocean, the Gulf spans approximately 150 km in width and a length of 1100 km. In the northern reaches of the region, the average offshore depth is about 200 m, gradually deepening toward the mouth, where depths exceed 3000 m [50].

The western coastline of the Gulf of California is characterized by its narrow and steep profile, predominantly rocky environment, interspersed with isolated sandy stretches (0.50–1.00 mm), and featuring a relatively shallow and narrow continental shelf. Notably, the region lacks river drainage due to its sub-desert climatic conditions. In contrast, the eastern coast of the Gulf of California showcases a wide and level topography, with vast sandy beaches (0.25–0.50 mm), expansive coastal lagoons, and open muddy bays. This area has a shallow and wide continental shelf, with fluvial drainage influenced by sporadic storm events and human interventions, particularly through dam construction [51,52].

The astronomical tide in the Gulf of California co-oscillates with the Pacific Ocean. The tidal regime is predominantly mixed, trending toward semi-diurnal type in the north-ern upper Gulf and toward diurnal type in the middle Gulf, especially along the east coast [53]. The average tidal amplitude varies from less than 1.0 m in the lower Gulf to approximately 3.5 m in the upper Gulf [54].

In the Gulf of California, the prevailing wind direction is largely seasonal [55]. From summer through late fall (June–November), strong winds—those capable of producing storm events—come primarily from the south [56,57]. Conversely, from late autumn to spring (December–May), strong winds from the north are predominant [58].

3. Methodology

In this investigation, storm-wave events coming from the north and those from the south were analyzed independently. This approach is based on the premise, as previously stated, that their behaviors and responses to synoptic weather patterns and large-scale climate phenomena are expected to exhibit distinct patterns. The schematic diagram of the overall methodology is shown in Figure 2.

3.1. Offshore Wave Data

The ERA5 dataset, generated by the European Centre for Medium-Range Weather Forecasts (ECMWF) and accessible at https://www.ecmwf.int/en/forecasts/dataset/ecmwf-reanalysis-v5 (accessed on 18 February 2025), provided the wave data used in this study. The dataset covers a span of 41 years, from January 1980 to December 2020. Two deep-water points were considered at the northern and southern ends of the Gulf of California: NG (30° N, 113.5° W) and SG (25° N, 109° W) (see Figure 1). The spatial resolution of the data is 0.5°, with an hourly temporal resolution. Given these constraints, the study aimed to analyze the long-term trends and seasonal variability of storm-wave events coming from the north and south, identified at points NG and SG, rather than providing a detailed assessment of storm waves along the entire Gulf of California. Consequently, the effects of wave breaking, refraction, reflection, and diffraction caused by the islands were not considered.

3.2. Analysis of Storm-Wave Events

In this study, a storm-wave event was defined as an event in which the significant wave height $\left({\mathrm{H}}_{\mathrm{s}}\right)$ exceeds the threshold wave height $\left({\mathrm{H}}_{\mathrm{u}}\right)$ for at least 12 h [59,60]. The height was obtained with Equation $\left(1\right)$ [61]:

$${\mathrm{H}}_{\mathrm{u}}=\overline{{\mathrm{H}}_{\mathrm{s}}}+2\mathsf{\sigma }\left[\mathrm{m}\right]$$

(1)

where $\overline{{\mathrm{H}}_{\mathrm{s}}}$ is the mean and $\mathsf{\sigma }$ is the standard deviation of the time series of ${\mathrm{H}}_{\mathrm{s}}$. Furthermore, if ${\mathrm{H}}_{\mathrm{s}}$ between two consecutive storm-wave events is below the ${\mathrm{H}}_{\mathrm{u}}$ at least 48 h these events are considered independent.

For each identified storm-wave event, the energy content $\left(\mathrm{E}\right)$ was obtained with Equation $\left(2\right)$ [62]:

$$\mathrm{E}={\int }_{{\mathrm{t}}_1}^{{\mathrm{t}}_2}{\mathrm{H}}_{\mathrm{s}}^2\mathrm{d}\mathrm{t}\left[{\mathrm{m}}^2\mathrm{h}\right]$$

(2)

where ${\mathrm{t}}_1$ and ${\mathrm{t}}_2$ define the storm-wave event duration, and ${\mathrm{H}}_{\mathrm{s}}>{\mathrm{H}}_{\mathrm{u}}$.

3.3. Spatial Assessment of Storm-Wave Events

The spatial assessment aimed to provide insight into the spatial variability of storm-wave events along the Gulf of California. This involved quantifying both the total number of identified events and their cumulative energy content. Furthermore, the Mean Annual Frequency (MAF) of identified events was computed by dividing the total number of identified events by the study period (41 years). Additionally, the Mean Energy Content (MEC) of the identified events was determined as the cumulative energy content divided by the total number of identified events.

3.4. Temporal Assessment of Storm-Wave Events

The temporal analysis of storm-wave events was undertaken on a seasonal scale and a long-term scale.

The seasonal analysis comprised sorting the identified storm-wave events and their energy content by the month in which they occurred. Then, the total number of identified events, and the accumulated energy content per month were quantified. Afterwards, their distribution over the year was examined to determine whether there is seasonal behavior.

The long-term analysis was undertaken using a combination of simple linear regression and binomial logistic regression methods. This technique was previously used by [34] to assess the inter-decadal variability of storm-wave event characteristics in the Gulf of Mexico and the Caribbean Sea in Mexico. The time series of the number of identified events per year $\left(n\right)$ and their cumulative energy $\left(\overline{E}\right)$ were the data assessed. In a physical meaning, these series provide a measure of the frequency and energy impact of storm-wave events over time. First, the data $n$ and $\overline{E}$ were log-transformed, which implies that the relationships obtained by linear regression between $n$ and $\overline{E}$ data over time become exponential. Afterwards, the time series of $n$ and $\overline{E}$ were assessed to obtain the temporal trends with linear regression by the least-squares method using Equation (3):

$$\widehat{M}\left(t\right)=exp\left(a_{M}t+b_M\right)$$

(3)

where $M$ is a generic variable that can refers to $n$ or $\overline{E}$, ^ represents the prediction, $t$ is time, and $a_M$ and $b_M$ are the linear regression coefficients.

The probability of occurrence of storm-wave events in any given year $\left(\widehat{{\mathrm{P}}_{\mathrm{s}}}\left(\mathrm{t}\right)\right)$ were estimated for the binary series of $n$ (1: event occurred; 0: no event occurred) by logistic regression using the maximum likelihood method using Equation (4):

$$\widehat{P_s}\left(t\right)={\displaystyle \frac{1}{1-{exp}^{-\left({\beta }_{1}t+{\beta }_0\right)}}}$$

(4)

where ${\beta }_1$ and ${\beta }_0$ are the logistic regression coefficients. When all the data in the binary series is equal to one, Equation (4) equals the value of one.

The product of $M\left(t\right)$ and $\widehat{{\mathrm{P}}_{\mathrm{s}}}\left(\mathrm{t}\right)$ leads to the estimated time evolution of $M$ as Equation (4):

$$\widehat{M_s}\left(t\right)=\widehat{P_s}\left(t\right)exp\left(a_{M}t+b_M\right)$$

(5)

The units of $M$ depend on whether it refers to $n$ or $\overline{E}$. If $M$ refers to $n$ it is the number of events, and if $M$ refers to $\overline{E}$ it is m²h. To compare trends, the Mean Annual Rate (MAR) of the assessed variable was calculated as the slope between the initial (1980) and final (2020) estimates.

Afterward, the Mann–Kendall (MK) test [63,64] was applied using XLSTAT version 2021 to assess whether a consistent upward or downward trend exists in the $n$ and $\overline{E}$ data over time. This nonparametric test, widely used in wave climate studies [65,66], evaluates randomness against a potential trend by sequentially comparing values within the time series [67]. In this study, this test conducted at a significance level of 10% meaning there is an accepted probability of up to a 10% that the detected trend is due to randomness rather than a real effect.

4. Results

4.1. General Description of Wave Heights

$\overline{{\mathrm{H}}_{\mathrm{s}}}$ and ${\mathrm{H}}_{\mathrm{u}}$ calculations (

Table 1. Characteristic wave heights and percent exceedance of ${\mathrm{H}}_{\mathrm{u}}$.

Node	$\overline{{\mathbf{H}}_{\mathbf{s}}}$	${\mathbf{H}}_{\mathbf{u}}$	% Exceedance
	$\left(\mathbf{m}\right)$	$\left(\mathbf{m}\right)$	${\mathbf{H}}_{\mathbf{u}}$
NG	1.01	1.40	3.82
SG	1.19	1.48	5.31

) showed that, in general, wave heights associated with storm-wave events are higher in the southern Gulf than in the northern Gulf of California. The highest values of $\overline{{\mathrm{H}}_{\mathrm{s}}}$ and ${\mathrm{H}}_{\mathrm{u}}$ were obtained at node SG and the lowest at node NG. The percentage of ${\mathrm{H}}_{\mathrm{s}}$ exceeding the ${\mathrm{H}}_{\mathrm{u}}$ defining storm events is slightly greater than 5% at the SG node, while at the NG node it is less than 5% (see Table 1).

4.2. Spatial Variability of Storm-Wave Events

Results of the spatial analysis of storm-wave events (Figure 3) showed that the frequency and energy content of such events vary along the Gulf of California. The number of identified events coming from the north was 407 and 136 for events coming from the south at the NG node, while at the SG node it was 233 for events coming from the north and 146 for events coming from the south (see Figure 3). The cumulative energy content at the NG node was estimated at 46,507 m²h for events coming from the north and 9332 m²h for events coming from the south, while at the SG node, it was estimated at 19,198 m²h for events coming from the north and 23,689 m²h for events coming from the south (see Figure 3).

Likewise, $\mathrm{M}\mathrm{A}\mathrm{F}$ and $\mathrm{M}\mathrm{E}\mathrm{C}$ calculations (

Table 2. Mean storm-waves events characteristics.

Node	Storm-Waves Coming from the North		Storm-Wave Coming from the South
	$\mathbf{M}\mathbf{A}\mathbf{F}$	$\mathbf{M}\mathbf{E}\mathbf{C}$	$\mathbf{M}\mathbf{A}\mathbf{F}$	$\mathbf{M}\mathbf{E}\mathbf{C}$
NG	9.90	114 m2h	3.30	69 m2h
SG	5.70	82 m2h	3.60	162 m2h

) showed that storm-wave events coming from the north are more frequent along the Gulf of California, while storm-wave events coming from the south are more energetic in the southern Gulf. The highest values of $\mathrm{M}\mathrm{A}\mathrm{F}$ correspond to the storms-waves events coming from the north at both the SG and NG nodes, whereas the highest value of $\mathrm{M}\mathrm{E}\mathrm{C}$ value corresponds to events from the south at the SG node (see Table 2). It should be noted that some storm events were identified at both the NG and SG nodes, but with different characteristics.

4.3. Temporal Variability of Storm-Wave Events

The seasonal analysis of storm-wave events (Figure 4 and Figure 5) showed that the frequency and energy content of such events in both the northern and southern Gulf of California varies throughout the year. However, it was observed that the frequency and energy content present a seasonal behavior, except for the events coming from the south identified in the northern Gulf of California. As a general trend, over 90% of the events identified coming from the north and their estimated energy content occurred from September to May, mainly from November to January, at nodes NG (see Figure 4a and Figure 5a) and SG (see Figure 4b and Figure 5b). As for the identified events coming from the south and their estimated energy content, over 90% occurred from August to April in the NG node (Figure 4a and Figure 5a), while from June to October, mainly August/September, they occurred in the SG node (see Figure 4b and Figure 5b).

The long-term analysis of storm-wave events (Figure 6 and Figure 7) showed statistically significant upward trends with a 90% level of precision in the frequency and energy content of such events in both the northern and southern Gulf of California, except for events coming from the south that occurred in the north. For the study period, the mean annual rate of the number of events identified was +0.080 events per year for events coming from the north and +0.001 events per year for events coming from the south at node NG (see Figure 6a), while at node SG it was +0.075 events per year for events coming from the north and +0.012 events per year for events coming from the south (see Figure 6b). As for the mean annual rate of energy content, it was +12.994 m²h for events coming from the north and −1.353 m²h for events coming from the south at the NG node (see Figure 7a), and at the SG node it was +7.606 m²h for events coming from the north and +7.973 m²h for events coming from the south (see Figure 7b).

5. Discussion

The frequency and energy content of storm-wave events coming from the north and south differ spatially (see Figure 3) and throughout the year (see Figure 4 and Figure 5), as well as in the long-term trend (see Figure 6 and Figure 7).

In terms of frequency, storm-wave events coming from the north dominate the Gulf of California coast (see Figure 3) and, regarding energy content, contribute the most total energy (see Figure 3); however, storm-wave events coming from the south are the most energetic (see Table 1 and Table 2) [12,68].

The frequency and energy content of storm-wave events in the Gulf of California are seasonal (see Figure 4 and Figure 5) and show long-term upward trends, except for events coming from the south that impact the northern Gulf coast (see Figure 6 and Figure 7). The dynamics of storm-wave events are linked to synoptic weather patterns and large-scale climatic phenomena [66,69,70,71]. In the Gulf of California, the dynamics of these events are dominated by summer tropical systems and winter systems, as well as by interannual patterns such as El Niño-Southern Oscillation (ENSO), the Pacific Decadal Oscillation (PDO), the Atlantic Multi-decadal Oscillation (AMO), and climate change [72,73,74,75]. Tropical cyclones in summer and cold fronts in winter are likely the predominant meteorological phenomena responsible for generating storm-wave events from the south and north, respectively. However, other meteorological systems, such as monsoonal winds, troughs, and tropical waves, can also generate strong winds and/or sudden pressure changes that contribute to storm-wave formation [72,76]. ENSO is the primary driver of interannual climate variability in the region [77]. During its warm phase (El Niño), it can increase the frequency and intensity of tropical cyclones, amplifying storm-wave events coming from the south, whereas in its cool phase (La Niña), it suppresses cyclonic activity, leading to fewer storm-wave events coming from the south [78,79]. However, La Niña may intensify winter systems from the north [80], increasing the frequency of storm-wave events coming from that direction. The PDO, through its warm and cool phases, modulates ENSO variability [81]. When PDO and ENSO are in phase, their effects intensify; otherwise, they can counteract each other [82]. The AMO can also interact with ENSO and PDO, indirectly influencing storm-wave activity, although its direct impact on the Gulf of California is less evident [83]. Additionally, climate change is expected to alter global climate variability [84]. Recent research on wave dynamics in the Gulf of California suggests that climate change is modifying the long-term wave climate under both mean and extreme conditions [12]. These findings align with our long-term analysis, but continued monitoring and further investigation are necessary to fully understand the specific impacts. Moreover, it is plausible that the anomalous behavior of the southern events affecting the northern coast of the Gulf of California is due to natural processes not identified with the information available in this study.

The results in this paper are comparable with those reported by [34] for the Mexican waters of the Gulf of Mexico and the Caribbean Sea. The Gulf of Mexico and the Mexican Caribbean have $\overline{{\mathrm{H}}_{\mathrm{s}}}$ (about 1.07 m and 1.06 m, respectively) like those of the Gulf of California, but the ${\mathrm{H}}_{\mathrm{u}}$ (about 2.25 m and 1.89 m, respectively) are higher (see Table 1). The number of storm-wave events identified per year in the Gulf of Mexico (about 13 events per year) is comparable to that of the Gulf of California, while in the Mexican Caribbean (about 8 events per year) is lower (see Table 2). The general trend in the monthly distribution of storm events coming from the northern Gulf of Mexico, the Mexican Caribbean, and the Gulf of California is similar (approximately 90% of these storm-wave events occur from October to April, see Figure 5a and Figure 5b). The same applies to the monthly distribution of storm-wave events coming from the south (around 90% of the identified events coming from the south occur from July to October, see Figure 5b), except for the events coming from the south that impact the northern coast of the Gulf, which are distributed throughout the year (see Figure 5a).

It is essential to continue studying storm events in the Gulf of California to obtain detailed information on aspects not addressed in this article, such as storm surge. In addition, an in-depth analysis of the possible links between the variability of these events and global climate indices will allow for a better explanation of the overall pattern. Undoubtedly, if knowledge gaps in coastal zone climatology persist, studies such as the one presented here will continue to be necessary.

6. Conclusions

In this study, the temporal variability (both long-term and seasonal) of the frequency and energy content of storm-wave events in the Gulf of California has been analyzed. This was accomplished by using ERA5 wave reanalysis data from 1979 to 2020 from two buoys located in the northern and southern Gulf of California. Storm-wave events coming from the north and those coming from the south were analyzed separately. In this sense, the regional, seasonal and long-term studies obtained contribute to the knowledge-building process regarding the dynamics of storm-wave events, even though the Gulf of California represents a relatively small part of the world.

The results indicate that storm-wave events coming from the north are the most frequent and largest contributors to the total energy content along the Gulf of California, though storm-wave events coming from the south are the most powerful when considered individually. The behavior of the frequency and energy content of storm-wave events throughout the year is markedly seasonal, except for events coming from the south identified in the northern Gulf of California. Storm-wave events have become more frequent and energetic over the years, particularly those coming from the north. Although this study did not perform a detailed analysis of the specific drivers of seasonal variability and long-term trends in storm-wave events, the existing literature suggests that these patterns arise from the combined effects of ENSO, PDO, AMO, and climate change. These interactions among these factors create a complex climate system that warrants further investigation.

The findings of this study are highly significant for coastal management of the Gulf of California and should be incorporated into coastal impact assessments for long-term planning and for the design of engineering interventions. Nevertheless, the results are subject to the limitations of the ERA5 hindcast data. Further research, including in situ measurements, is necessary to address these limitations.