Understanding sea wave height conditions in sumatra waters

. Ocean waves play a crucial role in influencing a wide range of marine and fisheries activities. In this research study, we aim to analyze the climatological conditions of sea wave heights in Sumatran waters over a span of 83 years (1940-2022). We utilize three-dimensional Copernicus numerical model simulations to examine seasonal patterns of sea wave heights and assess the likelihood of extreme wave events. Our findings reveal that high waves, reaching heights of 4-5 meters, are predominantly observed in the western and southern zones off the coast of Sumatra, particularly in the vicinity of smaller islands. Conversely, in enclosed or semi-enclosed waters, such as the lee side of Sumatra and the Malacca Strait, sea wave heights tend to be relatively lower. Seasonally, our study indicates that extreme wave heights are more likely to occur during the west season as opposed to the east season. This research provides valuable insights into the dynamic ocean wave conditions in Sumatran waters, which can have significant implications for various sectors reliant on the ocean environment.


Introduction
Waves have a significant impact on various marine processes, as well as offshore and nearshore activities.Surface waves, through momentum and heat fluxes, play a crucial role in influencing the ocean-atmosphere interface [1][2].Additionally, above the sea surface, waves can influence each other's wind stress [1][2][3].
Climatic variations in wind speed and direction are recognized as significant drivers of annual and seasonal fluctuations in wave heights within the waters of Indonesia [4][5].Notably, the highest wave heights and energy levels are observed during the west monsoon, while they are at their lowest during the east monsoon.It has been estimated that the potential wave energy production could reach 16.83 MW in Indonesian waters [6] and 67.29 kW/m along the western coast of Sumatra [7].These findings underscore the promise of harnessing waves as a viable renewable energy source for both Indonesia and Sumatra.
Surface waves are recognized for their significant impact on the mixing of the upper ocean, often referred to as the Oceanic boundary layer.This influence stems from four primary processes: wave breaking, the Coriolis-Stokes forces [8], Langmuir circulation [9], and mixing attributed to unbreaking waves [1][2].Experiments conducted by Wu et al. [1] have demonstrated that incorporating these four wave-related processes results in a more faithful representation of sea surface temperature dynamics.Wave breaking, in particular, plays a crucial role in the formation and evolution of the Oceanic boundary layer, a pivotal component in the interconnected ocean-atmosphere system.
Increased climate change activities such as the El Niño-Southern Oscillation (ENSO) in the South China Sea and the Indian Ocean Dipole (IOD) in the Indian Ocean induce significant wave height variations or extreme wave phenomena.This storm wave activity can cause disruption to marine activities such as navigation, fishing, engineering and coastal disasters [10].
Waves in Indonesian waters have been studied from several sides [11].Wu et al.
[12] looked at the influence of swell on atmospheric mixing and wind stress.Rachmayani et al [4,13] analyzed wave characteristics with a spectrum model.Nadya et al. [5] identified wave energy in Javanese waters (Pangandaran Beach) using the Shore Protection Manual (SPM) method.Dogan et al. [3] observed global propagation of air pressure waves due to volcanic activity.Rizal and Ningsih [7,11], calculated the potential wave energy in the waters of West Sumatra using numerical simulations of the wave spectrum.Ningsih et al. [10] studied wave climate characteristics and effects of tropical cyclones on high wave occurrences in Indonesian waters with descriptive and inferential statistics.So far, the influence of swell and local winds on the characteristics of significant wave heights in Sumatran waters has not been studied much.
The interaction between swell and wind-generated waves can give rise to unpredictable high waves, posing significant dangers for mariners.This study aims to investigate the characteristics of surface waves in the waters off western Sumatra by analyzing data from a significant wave height (SWH) model.SWH represents the average height of the highest onethird of ocean or sea waves, encompassing those generated by both wind and swell.It quantifies the vertical distance between wave crests and troughs.In this research, we examine patterns and variations in SWH over time, with a particular focus on the peak periods of the western and eastern monsoons.Additionally, our study identifies a high probability of extreme waves with significant SWH occurring in Sumatran waters.We hope that this research will offer valuable insights into the dynamic conditions of ocean waves in Sumatran waters, carrying significant implications for various sectors that rely on the region, including fisheries, navigation, and the overall marine environment.

Research sites
Sumatran waters exhibit a complex array of geographical characteristics.These include active tectonic zones like the Sumatran Fault Zone (SFZ) and the Andaman zone, vast expanses of deep waters such as the Indian Ocean and Andaman Sea, with depths reaching up to 4000 meters.Additionally, there are shallower waters, as seen in the Malacca Strait, with depths of approximately 50 meters.The region also features several small islands, such as Aceh Island, Simeulue, Nias, Siberut, and various other small islands (as shown in Figure 1).The Sumatran Fault Zone (SFZ) extends for about 1900 kilometers and is characterized  [14].Given its unique geographical location and the presence of these islands, Sumatran waters experience spatial variations in wind intensity.Consequently, the northern part of Sumatra, located above the equator, encounters stronger trade winds or northeastern monsoons.In contrast, the southern part, dominated by the southwest monsoon, experiences relatively unobstructed wind circulation from the Indian Ocean.

Research Data
As per ERA5 data, ocean waves are a combination of waves that exhibit diverse characteristics, including height, length, and direction, which are detailed in the twodimensional wave spectrum.The Significant Wave Height (SWH) is defined as the result of the amalgamation of wind-driven waves influenced by local winds and swell generated by distant winds occurring at various times and locations.This SWH metric is calculated as four times the square root of the integral taken across all directions and frequencies within the wave spectrum.
The research is based on hourly instantaneous Significant Wave Height (SWH) data with a spatial resolution of Δx=Δy=0.5 degrees obtained from ERA5 (the 5th major atmospheric reanalysis produced by European Centre for Medium-Range Weather Forecasts (ECMWF)), spanning from 1940 to 2022.ERA5 is a fifth-generation reanalysis dataset developed by the Copernicus Climate Change Service (C3S) at ECMWF.This dataset provides historical global climate and weather information, with data available from 1940 onward.ERA5 employs data assimilation techniques, which involve combining model data with real-world observations to create a comprehensive analysis of the atmospheric state.This approach significantly enhances the quality of historical climate and weather data.Furthermore, ERA5 includes an ensemble dataset with ten members, which serves to estimate uncertainty and identify regions that are particularly sensitive to changes in atmospheric conditions.This ensemble approach adds an extra layer of robustness to the dataset, making it a valuable resource for climate and weather research.

Data analysis
Hourly Significant Wave Height (SWH) data spanning 83 years from 1940 to 2023 were averaged to derive seasonal averages.These seasons are categorized as the northeast season (December-February), the first transition season (March-May), the southwest season (June-August), and the second transition season (September-November). Subsequently, time-series data for SWH in three distinct areas were analyzed.These areas include those located in front of the island (A1-A6), behind the outermost island (B1-B3), and within the Malacca Strait (C1-C3).This analysis was conducted to gain insights into the patterns and impacts of SWH that have formed over the seasons.The seasonal SWH pattern was approximated using a Fourier series equation.
In Eq. ( 1), a0 represents a constant term (intercept) in the data and is associated with the i = 0 cosine term.w stands for the fundamental frequency of the signal, while n represents the number of terms or harmonics in the series, and n = 2.In the realm of probability theory and statistics, the Weibull distribution is a continuous probability distribution.Its primary purpose is to represent a wide spectrum of random variables, particularly those relating to the duration between events or the time until failure.This distribution finds practical application in scenarios such as modeling the highest oneday sea level.In this study, extreme wave heights were analyzed using the Weibull distribution.Weibull distribution memiliki dua parameter pembentuk yaitu scale (a) and shape (b).Probability Density Function (PDF) Weibull distribution (Eq.Ocean, with the westward winds being relatively unobstructed as they cross the Indian Ocean.High SWH values are observed off the coast of the outer islands of Sumatra, including Simelue, Nias, Siberut, Sipura, and Enggano.As the waves approach these islands, they experience reduction and diffraction, resulting in relatively lower wave heights on the lee side of the islands.Notably, in the South China Sea, high SWH is observed, but this phenomenon is limited to the northeast season (December-February).The SWH patterns in Sumatran waters are intricately linked to the coastline profile and water depth.In open and deep waters such as the Indian Ocean, SWH tends to be relatively high.Conversely, in semienclosed waters like the Malacca Strait, SWH is relatively lower.The southwest monsoon, particularly during JJA, induces greater variations in wave height in the waters surrounding Sumatra.This is reflected in a higher standard deviation of SWH (reaching 0.98 meters) during the southwest monsoon compared to other seasons, such as the northeast monsoon (DJF), where the standard deviation only reaches 0.69 meters.
Obtaining information about extreme sea wave heights is critical for effective disaster mitigation.Extreme wave height is determined by considering both the maximum Significant Wave Height (SWH) and the SWH percentile at 0.93 over an 83-year period.The distribution of extreme waves in the waters surrounding Sumatra is illustrated in Fig. 9 and Fig. 10.The analysis results indicate that the maximum wave height in the sea off Sumatra, including the Indian Ocean, can reach heights of up to 4.5 meters.Notably, outer islands like Aceh Island, Simeleu, and Enggano are at a heightened risk of experiencing the impact of these high waves.This information is invaluable for disaster mitigation efforts, particularly in vulnerable coastal areas.Seasonal signals of Significant Wave Height (SWH) at stations located both in front of and behind the Sumatra islands, as well as within the Malacca Strait, are presented in Fig. 6 to Fig. 8.These signals are derived from the analysis of hourly SWH data spanning from 1940 to 2022.In general, high waves are observed during July, with the peak occurring in August, and these conditions are primarily associated with the southwest monsoon.Notably, the outer island regions exhibit a relatively greater seasonal amplitude (as shown in Fig. 6) compared to areas behind the islands (as seen in Fig. 7).Behind the islands, particularly, low waves are prevalent during February and March.In contrast, the Malacca Strait experiences low waves in April and May (Fig. 8).During January and February, waves are slightly higher in the northern part of the Malacca Strait, owing to the influence of the peak of the northeast monsoon [15].East winds favor the formation of high sea waves in the northern of the Malacca Strait and Sumatra Waters.However, it's important to emphasize that, on the whole, the highest waves still occur during the southwest monsoon, notably in August.This is because, in August, the winds are strong enough, and the extreme sea levels increase due to the already heightened wind conditions [16][17].

Conclusions
We conducted an analysis of significant wave heights in the waters surrounding Sumatra using data from the ERA5 reanalysis model.The data we used for analysis has an hourly resolution, which is particularly well-suited for studying wave characteristics resulting from both wind and swell.Our analysis revealed that wave height is significantly influenced by both the season and geographic location.During the southwest monsoon, characterized by prevailing west and southwest winds, high waves are observed in most of Sumatra's waters, including the Malacca Strait.The peak in wave height occurs in August, particularly in the Indian Ocean and the outer islands.In the northern waters of the Malacca Strait and Aceh waters, high waves also form in January, indicating the influence of the northeast monsoon.These areas, especially in front of Sumatra's outer islands, are particularly susceptible to sea wave-related disasters.As waves approach the shore, they induce Stokes drift, a phenomenon involving the net transport of water particles in the direction of wave propagation.This process can contribute to the development of nearshore currents.However, a comprehensive study of the impact of waves on nearshore currents requires a coastal hydrodynamic model with higher resolution.Moreover, it is crucial to conduct further analysis to understand trends in wave height and their correlation with climate changes, such as the Indian Ocean Dipole (IOD) and the El Niño-Southern Oscillation (ENSO).Additionally, research on combined waves and ocean currents, particularly using high-resolution models, is essential.This will provide valuable insights into the broader implications of variations in wave height and their connection to larger climatic phenomena. /doi.org/10.1051/bioconf/2024870201487