Significant Wave Height Forecasting in the Singapore Strait: Deep Learning Ensemble Stacking with ERA5-IDW Data

Saruan, Sandy Salomo; Yanti, Gusti Ayu Dwi

doi:10.20956/48n17666

Open access Journal

Significant Wave Height Forecasting in the Singapore Strait: Deep Learning Ensemble Stacking with ERA5-IDW Data

Jurnal Matematika, Statistika dan Komputasi · Vol. 23 No. 1 (2026) · pp. 20–37

DOI: 10.20956/48n17666
ISSN: 2614-8811, 1858-1382
Published: 2026-09-15
Publisher: Department of Mathematics, Hasanuddin University
Language: en
License: creativecommons.org/licenses/by/4.0

Abstract

Accurate significant wave height (SWH) forecasting in the Singapore Strait is critical for maritime safety and marine risk assessment along one of the world’s busiest shipping corridors. This study develops a deep learning ensemble stacking framework for one-step-ahead SWH forecasting using hourly ERA5 reanalysis data spanning January 2021 to December 2025, spatially interpolated to a single target point via Inverse Distance Weighting (IDW) from five ERA5 grid points. Four architectures: Long Short-Term Memory (LSTM), Gated Recurrent Unit (GRU), Patch Time Series Transformer (PatchTST), and inverted Transformer (iTransformer) are systematically evaluated against a persistence baseline (RMSE = 0.0188 m), with GRU achieving the best individual performance (RMSE = 0.0153 m, MAPE = 4.58%, = 0.9814), while ridge regression stacking of GRU with Transformer-based models achieves the overall best performance (RMSE = 0.0151 m, MAPE = 4.54%, = 0.9820) classified as highly accurate. Transformer-based architectures individually fail to capture SWH variability in this fetch-limited regime yet contribute complementary residual information as stacking base learners. The proposed pipeline establishes a replicable methodology for wave climate forecasting in narrow straits under resolved by global reanalysis products, with potential utility as an environment risk covariate for actuarial modeling in marine cargo insurance underwriting

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Co-author	Organisation	Joint articles
Dian Ariesta Yuwaningsih	Affiliation unknown	1
Yassin Dwi Cahyo	Affiliation unknown	1
Rima Aksen Cahdriyana	Affiliation unknown	1
Dea Apriani	Affiliation unknown	1

Affiliations come from OpenAlex; journal OAI-PMH metadata carries none. Authors without an OpenAlex ID are matched by name, which can merge or split people.

Metadata source: OAI-PMH (metadata jurnal) https://journal.unhas.ac.id/index.php/jmsk/oai, first harvested 5 Nov 2026, last seen 5 Nov 2026.

Original metadata (oai_dc)

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	<dc:title xml:lang="en">Significant Wave Height Forecasting in the Singapore Strait: Deep Learning Ensemble Stacking with ERA5-IDW Data</dc:title>
	<dc:creator xml:lang="en">Saruan, Sandy Salomo</dc:creator>
	<dc:creator xml:lang="en">Yanti, Gusti Ayu Dwi</dc:creator>
	<dc:subject xml:lang="en">significant wave height forecasting</dc:subject>
	<dc:subject xml:lang="en">ensemble stacking</dc:subject>
	<dc:subject xml:lang="en">deep learning</dc:subject>
	<dc:subject xml:lang="en">singapore strait</dc:subject>
	<dc:subject xml:lang="en">inverse distance weighting</dc:subject>
	<dc:subject xml:lang="en">Deep Learning</dc:subject>
	<dc:subject xml:lang="en">Marine Risk</dc:subject>
	<dc:description xml:lang="en">Accurate significant wave height (SWH) forecasting in the Singapore Strait is critical for maritime safety and marine risk assessment along one of the world’s busiest shipping corridors. This study develops a deep learning ensemble stacking framework for one-step-ahead SWH forecasting using hourly ERA5 reanalysis data spanning January 2021 to December 2025, spatially interpolated to a single target point via Inverse Distance Weighting (IDW) from five ERA5 grid points. Four architectures: Long Short-Term Memory (LSTM), Gated Recurrent Unit (GRU), Patch Time Series Transformer (PatchTST), and inverted Transformer (iTransformer) are systematically evaluated against a persistence baseline (RMSE = 0.0188 m), with GRU achieving the best individual performance (RMSE = 0.0153 m, MAPE = 4.58%,   = 0.9814), while ridge regression stacking of GRU with Transformer-based models achieves the overall best performance (RMSE = 0.0151 m, MAPE = 4.54%,   = 0.9820) classified as highly accurate. Transformer-based architectures individually fail to capture SWH variability in this fetch-limited regime yet contribute complementary residual information as stacking base learners. The proposed pipeline establishes a replicable methodology for wave climate forecasting in narrow straits under resolved by global reanalysis products, with potential utility as an environment risk covariate for actuarial modeling in marine cargo insurance underwriting</dc:description>
	<dc:publisher xml:lang="en">Department of Mathematics, Hasanuddin University</dc:publisher>
	<dc:date>2026-09-15</dc:date>
	<dc:type>info:eu-repo/semantics/article</dc:type>
	<dc:type>info:eu-repo/semantics/publishedVersion</dc:type>
	<dc:type xml:lang="en">Text</dc:type>
	<dc:format>application/pdf</dc:format>
	<dc:identifier>https://journal.unhas.ac.id/index.php/jmsk/article/view/51084</dc:identifier>
	<dc:identifier>10.20956/48n17666</dc:identifier>
	<dc:source xml:lang="en">Jurnal Matematika, Statistika dan Komputasi; Vol. 23 No. 1 (2026): September 2026; 20-37</dc:source>
	<dc:source>2614-8811</dc:source>
	<dc:source>1858-1382</dc:source>
	<dc:language>en</dc:language>
	<dc:relation>https://journal.unhas.ac.id/index.php/jmsk/article/view/51084/15000</dc:relation>
	<dc:coverage xml:lang="en">Singapore Strait, 2021-2025</dc:coverage>
	<dc:rights xml:lang="en">Copyright (c) 2026 Jurnal Matematika, Statistika dan Komputasi</dc:rights>
	<dc:rights xml:lang="en">https://creativecommons.org/licenses/by/4.0</dc:rights>
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