Abstract

To predict the evolution of wave spectrum in the real ocean, a machine learning framework is developed by training a long short-term memory (LSTM) neural network on a physics-based third-generation wave model (Simulating WAve Nearshore (SWAN)). Considering the realistic ocean waves are usually mixtures of windsea and swells, the wave spectrum is partitioned using a watershed algorithm, such that the windsea and swells are analyzed and predicted separately. Four parameters are selected to capture the wave spectrum of each system, including the significant wave height Hs, peaked wave period Tp, mean propagation direction θm, and directional spreading width σθ. The results demonstrate that the LSTM neural network can achieve accurate prediction of wave condition, the mean absolute error percentage (MAEPs) of 1-h prediction is less than 5.9%, 3.3%, 3.5%, and 3.3% for Hs, Tp, θm, and σθ, respectively, and accurate prediction of wave spectra is achieved. Even for the 10-h prediction, satisfactory results are obtained, e.g., the MAEP of Hs is less than 15.5%. The effects of output size (i.e., prediction duration), input data size (i.e., number of delays), as well as different combinations of input features on predictions of wave conditions are examined.

References

1.
Yasukawa
,
H.
, and
Sakuno
,
R.
,
2020
, “
Application of the MMG Method for the Prediction of Steady Sailing Condition and Course Stability of a Ship Under External Disturbances
,”
J. Marine Sci. Technol.
,
25
, pp.
196
220
.
2.
Hasselmann
,
K.
,
1962
, “
On the Non-Linear Energy Transfer in a Gravity-Wave Spectrum
,”
J. Fluid. Mech.
,
12
(
15
), pp.
481
500
.
3.
WAMIDI
,
1988
, “
the WAM Model—A Third Generation Ocean Wave Prediction Model
,”
J. Phys. Oceanogr.
,
18
(
12
), pp.
1775
1810
.
4.
Tolman
,
H. L.
,
1991
, “
A Third-Generation Model for Wind Waves on Slowly Varying, Unsteady, and Inhomogeneous Depths and Currents
,”
J. Phys. Oceanogr.
,
21
(
6
), pp.
782
797
.
5.
Booij
,
N.
,
Ris
,
R. C.
, and
Holthuijsen
,
L. H.
,
1999
, “
A Third-Generation Wave Model for Coastal Regions: I. Model Description and Validation
,”
J. Geophys. Res. Atmos.
,
104
(
4
), pp.
7649
7666
.
6.
Ou
,
S. H.
,
Liau
,
J. M.
,
Hsu
,
T. W.
, and
Tzang
,
S. Y.
,
2002
, “
Simulating Typhoon Waves by SWAN Wave Model in Coastal Waters of Taiwan
,”
Ocean. Eng.
,
29
(
8
), pp.
947
971
.
7.
Mori
,
N.
,
2012
, “
Freak Waves Under Typhoon Conditions
,”
J. Geophys. Res. Oceans
,
117
(
C11
), p.
C00J07
.
8.
Akpinar
,
A.
,
Bingolbali
,
B.
, and
Van Vledder
,
G. P.
,
2016
, “
Wind and Wave Characteristics in the Black Sea Based on the SWAN Wave Model Forced With the CFSR Winds
,”
Ocean. Eng.
,
126
(
1
), pp.
276
298
.
9.
Vieira
,
F.
,
Cavalcante
,
G.
, and
Campos
,
E.
,
2020
, “
Analysis of Wave Climate and Trends in a Semi-Enclosed Basin (Persian Gulf) Using a Validated SWAN Model
,”
Ocean. Eng.
,
196
(
1
), p.
106821
.
10.
Soares
,
C.
,
Rusu
,
L.
,
Bernardino
,
M.
, and
Pilar
,
P.
,
2011
, “
An Operational Wave Forecasting System for the Portuguese Continental Coastal Area
,”
J. Oper. Oceanogr.
,
4
(
2
), pp.
16
26
.
11.
Toropov
,
P. A.
,
Myslenkov
,
S. A.
, and
Shestakova
,
A. A.
,
2012
, “
Numerical Simulation of Novorossiysk Bora and Related Wind Waves Using the WRF-ARW and SWAN Models
,”
Russian J. Earth Sci.
,
12
(
6
), pp.
1
7
.
12.
Ponce de Leon
,
S.
, and
Orfila
,
A.
,
2013
, “
Numerical Study of the Marine Breeze Around Mallorca Island
,”
Appl. Ocean. Res.
,
40
, pp.
26
34
.
13.
Londhe
,
S. N.
,
Shah
,
S.
,
Dixit
,
P. R.
,
Nair
,
T. M. B.
,
Sirisha
,
P.
, and
Jain
,
R.
,
2016
, “
A Coupled Numerical and Artificial Neural Network Model for Improving Location Specific Wave Forecast
,”
Appl. Ocean. Res.
,
59
, pp.
483
491
.
14.
Kumar
,
N. K.
,
Savitha
,
R.
, and
Al Mamun
,
A.
,
2017
, “
Regional Ocean Wave Height Prediction Using Sequential Learning Neural Networks
,”
Ocean. Eng.
,
129
(
1
), pp.
605
612
.
15.
Wang
,
W.
,
Tang
,
R.
,
Li
,
C.
,
Liu
,
P.
, and
Luo
,
L.
,
2018
, “
A BP Neural Network Model Optimized by Mind Evolutionary Algorithm for Predicting the Ocean Wave Heights
,”
Ocean. Eng.
,
162
(
15
), pp.
98
107
.
16.
Fan
,
S.
,
Xiao
,
N.
, and
Dong
,
S.
,
2020
, “
A Novel Model to Predict Significant Wave Height Based on Long Short-Term Memory Network
,”
Ocean. Eng.
,
205
(
1
), pp.
107298
.
17.
James
,
S. C.
,
Zhang
,
Y.
, and
O’Donncha
,
F.
,
2018
, “
A Machine Learning Framework to Forecast Wave Conditions
,”
Coastal Eng.
,
137
, pp.
1
10
.
18.
Saha
,
S.
,
Moorthi
,
S.
,
Wu
,
X.
,
Wang
,
J.
,
Nadiga
,
S.
,
Tripp
,
P.
,
Behringer
,
D.
,
Hou
,
Y.
,
Chuang
,
H.
,
Iredell
,
M.
,
Ek
,
M.
, et al
,
2012
, “
The NCEP Climate Forecast System Version 2
,”
J. Clim.
,
27
(
6
), pp.
2185
2208
.
19.
Hanson
,
J. L.
, and
Phillips
,
O. M.
,
2001
, “
Automated Analysis of Ocean Surface Directional Wave Spectra
,”
J. Atmos. Ocean. Technol.
,
18
(
2
), pp.
277
293
.
20.
Fedele
,
F.
,
2015
, “
On the Kurtosis of Deep-Water Gravity Waves
,”
J. Fluid. Mech.
,
782
(
7
), pp.
25
36
.
21.
Xu
,
Y.
,
Zhang
,
J.
,
Xu
,
Y.
,
Ying
,
W.
, and
Zhu
,
Y.
,
2019
, “
Analysis of the Spatial and Temporal Sensitivities of Key Parameters in the SWAN Model: An Example Using Chan-Hom Typhoon Waves
,”
Estuarine Coast. Shelf Sci.
,
232
(
5
), p.
106489
.
22.
Lamont-Smith
,
T.
, and
Waseda
,
T.
,
2008
, “
Wind Wave Growth At Short Fetch
,”
J. Phys. Oceanogr.
,
38
(
7
), p.
1597
.
23.
Toba
,
Y.
,
1972
, “
Local Balance in the Air-Sea Boundary Processes: I. On the Growth Processes of Wind Waves
,”
J. Phys. Oceanogr.
,
28
, pp.
109
121
.
24.
Ebuchi
,
N.
,
Toba
,
Y.
, and
Kawamura
,
H.
,
1992
, “
Statistical Study on the Local Equilibrium Between Wind and Wind Waves by Using Data From Ocean Data Buoy Stations
,”
J. Oceanogr.
,
48
(
1
), pp.
77
92
.
25.
Hochreiter
,
S.
, and
Schmidhuber
,
J.
,
1997
, “
Long Short-Term Memory
,”
Neural Comput.
,
9
(
8
), pp.
1735
1780
.
26.
Duan
,
Y. J.
,
Lv
,
Y. S.
, and
Wang
,
F. Y.
,
2016
, “
Travel Time Prediction with LSTM Neural Network
,”
IEEE International Conference on Intelligent Transportation Systems
,
Rio de Janeiro, Brazil
,
Nov. 1–4
.
27.
Polson
,
N. G.
, and
Sokolov
,
V. O.
,
2017
, “
Deep Learning for Short-Term Traffic Flow Prediction
,”
Trans. Res. Part C Emerg. Technol.
,
79
, pp.
1
17
.
28.
Makarynskyy
,
O.
,
Pires-Silva
,
A. A.
,
Makarynska
,
D.
, and
Ventura-Soares
,
C.
,
2005
, “
Artificial Neural Networks in Wave Predictions at the West Coast of Portugal
,”
Comput. Geosci.
,
31
(
4
), pp.
415
424
.
You do not currently have access to this content.