Proceedings of the Thirty-second (2022) International Ocean and Polar Engineering Conference
Shanghai, China, June 5–10, 2022
Copyright © 2022 by the International Society of Offshore and Polar Engineers (ISOPE)
ISBN 978-1-880653-81-4; ISSN 1098-6189

www.isope.org

An Empirical Spectral Wave Model Based on Deep Learning
Yuhao Song, Haoyu Jiang
Hubei Key Laboratory of Marine Geological Resources, China University of Geosciences
Wuhan, Hubei, China

complicated calculation of the five-fold Boltzmann integral), also
impacts the accuracy of the model outputs.

ABSTRACT
Directional wave spectra are of importance for many practicalapplications. Previous studies show that the wave spectral densities at agiven point are correlated with the local or remote wind field. Thisfeature can be used to predict the wave spectrum empirically. In thisstudy, a deep neural network (DNN) to estimate point-wise wave
spectra were constructed using historical wind field data. The DNN
model gives a reasonable estimation of the wave spectral shape.
Compared to the numerical wave models, this model can effectively
predict the directional wave spectrum with a lower cost of computing
resources.

Previous studies show that the wave spectral densities at a given pointin the ocean are correlated with the local or remote wind field. Pérez etal. (2014) presented a method that can conveniently describe the area ofinfluence of a site on the ocean and enable the wave energy and travel
time of that area to be described. Jiang and Mu (2019) proposed thateach frequency and direction of the ocean wave spectrum at a given
location can be approximately correlated with the wind field in ageographical area, which implies the feasibility of reconstructing thewave spectrum using observed wind field data. Such a statisticalcorrelation between wave spectra and wind field offers the possibilityof establishing an empirical model to predict the wave spectrum at agiven point.

KEY WORDS: wave spectra; wind field; DNN; wave model.
INTRODUCTION

Wave forecasting requires the extraction of useful information fromlarge amounts of data, and deep neural networks (DNNs) are well
suited to deal with this type of problem. James et al. (2018) used neuralnetworks to predict SWH and MWP. O'Donncha et al. (2018)combined machine learning and numerical modelling to predict wave
parameters. Naithani and Deo (2005) used neural networks to estimate
one-dimensional wave spectra. These studies illustrate that it is feasible
to use DNNs to forecast wave, but they mainly forecast wave
parameters or one-dimensional wave spectra. Therefore, this study aims
to establish an empirical spectral wave model based on deep learning toestimate directional wave spectra using wind field data.

Wind-generated surface gravity waves are a very common phenomenonon the surface of the sea, playing an important role in many humanactivities, such as maritime transport and fishery. The study of wave
conditions is therefore of great social and scientific significance.
Traditionally, integral ocean wave parameters such as the significant
wave height (SWH), mean wave direction (MWD), and mean wave
period (MWP) are often used to describe the wave state. However, they
only provide a limited description of the wave field and might bemisleading in a sea state with multiple wave components (Jiang and Mu,
2019). A better way of characterizing the wave field is the wave
spectrum which can describe the information of waves from different
origins.

The rest of the paper is as follows. Section 2 describes the data sources
and pre-processing methods of the wind field and wave spectra data
used in this study, as well as the theoretical introduction to deeplearning and the process of modelling. In section 3, the results areshown and discussed. Section 4 is the conclusions of the overallfindings of the study.

At present, wave spectra are mainly predicted by numerical wave
models (NWMs), such as WaveWatch III and SWAN (Booij et al.,
1997; Tolman, 2014). After the development of several decades,
contemporary NWMs have achieved good results. However, they often
need relatively high cost in computing resources. There are also several
other problems of the NWMs. For instance, some physical process
cannot be well taken into account. Some numerical effects, such as thedispersion of the swell propagation process (also termed “gardensprinkler effect”) and the numerical approximation of the solution ofthe quadruplet wave-wave interactions (the exact solution needs theDATA AND METHODOLOGYWind Field and Directional Wave Spectra Data
25-year (1994-2018) record of 10-m wind field and directional wave2020