Design of wave spectrum in the Java Sea

Information about wave characteristics plays a crucial role in the design of coastal and offshore infrastructure. This information is necessary to establish safety parameters for structures located offshore. Key parameters of interest include significant wave height and wave period, which are typically described through a wave spectrum. The creation of this wave spectrum involves using the fast Fourier transform, which converts the time domain into the frequency domain. The JONSWAP method describes how wave energy is distributed in the wave spectrum based on specific parameters, such as wind speed, duration of the wind, and the prevailing wave conditions. This method attempts to account for changes in the wave spectrum that occur when the wind blows at different intensities. As a result, the JONSWAP method allows for the generation of more realistic wave spectra under various weather conditions. From this energy spectrum, the JONSWAP shape will be sought to closely match the energy spectrum.


Introduction
Indonesia is an archipelagic nation with approximately 70% of its territory covered by water bodies, supporting the Sustainable Development Goal (SDG) number 9, which focuses on industry, innovation, and infrastructure.Infrastructure in this context encompasses both coastal and offshore structures.There are five stages involved in the planning process of coastal and offshore structures, which include defining operational criteria, establishing environmental criteria, foundation planning, structural planning, and construction and installation.In the stage of determining environmental criteria, environmental data such as wind, currents, and most significantly, waves, are essential.This information is crucial to establish safety standards for offshore structures.Therefore, it's imperative to acquire information about wave characteristics in the intended areas for designing these marine structures.For instance, infrastructure projects like ports, coastal and offshore structures, as well as mooring systems as depicted in Figure 1, are closely tied to hydrogeology factors such as erosion, sediment transport, and ocean wave energy [1;2].
Ocean waves exhibit nonlinear behavior in accordance with wave generation and environmental characteristics [3].Two crucial parameters for monitoring ocean waves are the Significant Wave Height and the time period [4].The Significant Wave Height represents the wave height that characterizes sea conditions, while the time period signifies the duration of the most dominant wave energy.This information about wave height is of paramount importance, particularly for offshore construction, maintenance, and the safety of ships navigating the sea.Therefore, the data accuracy should closely mirror real-world conditions.The characteristics of ocean waves can be depicted or observed through wave spectra.Creating a wave spectrum can be achieved using conventional methods that estimate wave energy distribution based on measurements and analysis of actual waves [5;6].Some commonly used methods for deriving spectrum formulas include the ISSC (Bretschneider or modified Pierson-Moskowitz), International Towing Tank Conference (ITTC), and the Joint North Sea Wave Observation Project (JONSWAP).However, in accordance with statements by Djatmiko (2012) [7] and Mahjoobi (2008) [8] that waves are inherently nonlinear, deterministic equations fall short of accurately describing wave spectra.

Design of wave spectrum in the
Djatmiko & Adrianto (2013) [9] conducted wave height measurements in Indonesian waters, specifically in the western part of the Java Sea.Wave height was measured every second for a year, but data was collected only once a day for each month, resulting in 48 wave data points per month and 576 data points for the entire year.However, based on this data, researchers felt that the periodic monthly observations were insufficient to adequately characterize the wave conditions at that specific location.It is hoped that this study will build upon previous research and yield a new formula that better suits the wave conditions in the Java Sea waters.

FFT generation
The Fast Fourier Transform (FFT) is a mathematical computation technique used to transform analog signals into digital signals based on frequency.The Fast Fourier Transform (FFT) divides a signal into different frequencies using complex exponential functions.It's an algorithm designed for efficiently and rapidly calculating discrete Fourier transforms.Since signals in communication systems are continuous in nature, the results can be applied to Fourier transformation. Where: • X[k] is the frequency representation at index k in the frequency domain.
• x[n] is the signal sample at index n in the time domain.
• k is the frequency index.
• N is the total number of samples in the signal.

JONSWAP Spectrum
The Joint North Sea Wave Project spectrum (JONSWAP) is a spectral model used to describe the distribution of wave energy in a specific area of the sea.This model was initially developed by a team of researchers involved in the JONSWAP project in 1973 to study wave characteristics in the North Sea.
The JONSWAP spectrum illustrates how wave energy is distributed across various wave frequencies.Typically, this model is expressed in the form of mathematical equations that describe the spectrum of wave energy in terms of wave frequency.The equation's form may vary depending on the weather conditions and the ocean wave parameters present at a specific location.The JONSWAP model finds utility in various applications, particularly in marine engineering, offshore structure planning, ship development, and diverse purposes related to ocean dynamics.This model assists experts in comprehending and predicting the characteristics of ocean waves under various weather and geographical conditions.

Results and discussion
In this study, the observed wave heights are located in the Jakarta Bay, indicated by the yellow point in Figure 1.The data collection is based on the European Centre for Medium-range Weather Forecast (ECMWF) data over a span of 9 years, from 2013 to 2021, with hourly intervals, resulting in a total of 78,887 data points for wind speed and wave heights.1.The result of this FFT is then subjected to an inverse FFT validate whether the FFT transformation aligns accurately with the wave height data based on ECMWF (shown in Figure 3).The comparison between ECMWF wave heights and the inverse FFT is illustrated in Figure 5.The blue line represents the wave heights derived from ECMWF data, while the green line represents the wave heights obtained from the inverse FFT.The results indicate that the inverse FFT effectively matches the ECMWF wave height data.This alignment suggests that the generated FFT is correct, validating its accuracy and allowing for progression to the energy spectrum generation phase.In the context of wave height energy spectrum, 'wave height' refers to the amplitude of waves or the difference between wave crests and troughs.This spectrum provides insights into how energy is distributed across different wave frequencies.Within this spectrum, waves with higher frequencies possess greater energy.The wave energy spectrum aids scientists and engineers in comprehending and measuring the characteristics of oceanic or atmospheric waves, which significantly impact navigation, coastal engineering, maritime transportation, and various other aspects.This information is also crucial for understanding climate changes and ocean-atmosphere dynamics.In practical terms, wave energy spectra are often measured using instruments like radar altimeters on satellites, wave buoys, and other equipment.Figure 6 illustrates the energy spectrum formed from the previous FFT process, where the spectrum showcases a single peak at the beginning or 0 Hz.This energy spectrum serves as a reference for JONSWAP analysis and machine learning applications.The Joint North Sea Wave Project (JONSWAP) spectrum is one of the wave energy spectrum models used in oceanography and marine science to describe the distribution of wave energy on the sea surface.Originally developed to depict waves in the North Sea, this model has since been widely adopted for various water bodies.JONSWAP was chosen due to its consideration of higher-frequency components.The JONSWAP spectrum incorporates contributions from higher-frequency components to describe waves with higher and sharper amplitudes that can occur under specific conditions, such as storms.Figure 7 represents the JONSWAP spectrum, where the spectrum pattern aligns with the energy spectrum but still exhibits differences in amplitude.

Figure 1 .
Figure 1.Location map of wave observation Figure 2 represents the wind speed, and Figure 3 represents the wave height, comprising a total of 78,887 data points but in figure 2 and 3 only 8.760 data points wind speed and wave height for one year.The wave height exhibits a similar pattern to the wind speed, which is consistent with the generation of wave height based on the high or low intensity of the blowing wind.In other words, waves are generated by the wind.Within a year, there are peaks and troughs, with peaks occurring during the rainy season, while troughs occur during the dry season.