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

VAE based Non-Autoregressive Transformer Model for
Sea Ice Concentration Forecast
Da Wu1,2,3 , Xiao Lang4 , Wengang Mao4 , Di Zhang2,3 , Jinfen Zhang1,2,3 , Rong Liu1,212

Intelligent Transportation Systems Research Center, Wuhan University of Technology, Wuhan, China
National Engineering Research Center for Water Transport Safety, Wuhan University of Technology, Wuhan, China
3
Inland Port and Shipping Industry Research Co., Ltd. of Guangdong Province, Guangdong, China
4
Department of Mechanics and Maritime Sciences, Chalmers University of Technology, Gothenburg, Sweden

ABSTRACTwith the sea ice thickness distribution and suggested that theSIC is primarily thermodynamically controlled. Ye et al. (2016)
introduced a correction scheme to reconstruct the SIC utilizing
ice drift records. Another study by Yu et al. (2017) showed thatanomalous surface air temperatures and low-level wind fields
contribute to changes in the SIC. In Ye et al. (2019), authors
compared and evaluated different sea ice type concentration
methods. Mu et al. (2019) reported an ensemble-based Arctic Ice
Ocean Prediction System for operational Arctic sea ice forecasts.
However, physical models usually demand high computationalcosts and require enormous data. Also, the grid resolution ofdata is sometimes too low to accurately simulate the geography
along the NSR.

Arctic shipping along the Northern Sea Route (NSR) relies on reliable and precise sea ice concentration (SIC) information. However, the SIC forecast used to assist NSR shipping is often inaccurate. This study proposes a VAE based Non-Autoregressive
Transformer model for the long-term SIC forecast task. The
proposed model ensembles the deep generative model of Variational Autoencoder and the deep learning model of Transformer
to overcome the temporal delay and accumulative error problems
shown in traditional time series models. Model validation has
been conducted to compare the forecasts of SIC with other machine learning and deep learning models. The proposed model
outperforms the compared models in terms of different metrics.
The proposed VAE based Non-Autoregressive Transformer canbe used for long-term SIC forecast and achieve stable and good
accuracy predictions.

Additionally, the statistics of SIC data are usually ignored
and little studied. As a statistical method, the auto-regressive
integrated moving average (ARIMA) model needs low computational costs and is highly convenient for time series
analysis (TSA). Such methods have been used in the ocean
environmental analysis; for example, Spanos (1983) compared
an auto-regressive (AR) model, a moving average (MA) model,
and an auto-regressive moving average (ARMA) model tosimulate ocean waves. Soares et al. (1996) modeled significant
wave heights by an AR process that included seasonality.
Interestingly, Agrawal and Deo (2002) compared the ARMA
model and an artificial neural network. These methods havebeen used in applications beyond ocean waves as well. Jiang
et al. (2020) applied the AR model for real-time ship motion
prediction. Mao et al. Mao et al. (2016) employed the AR model
to predict the speeds of container ships. The ARIMA model
has also been employed to analyze SIC. Piwowar and LeDrew(2001) reported the auto-regressive nature of Arctic SIC. Ahnet al. (2014) reanalyzed Arctic sea ice data with the ARIMA
model, considering the temporally varying relationships between
SIC and other climate factors. Nevertheless, the time delay andaccumulative error issues of AR models limit the application ofKEY WORDS: Sea ice concentration; Arctic shipping; Time series analysis; Variational Autoencoder; Transformer; Non autoregressive model.

INTRODUCTION
Sea ice concentration (SIC) is one of the most critical environmental indicators of climatic change in the Arctic region.
In light of changes in SIC, the Northern Sea Route (NSR),e.g., Figure 1, has drawn increased attention during recentyears, as discussed in Milaković et al. (2018).
Therefore,forecasts of SIC are essential for safe and efficient ship operations along the NSR Lang et al. (2019); Zhang et al. (2020, 2019).
The SIC is usually recorded by satellites or onboard mastermariners. Researchers have proposed different coupled oceanatmosphere physical models based on recorded data to determine
the relationship between atmospheric anomalies and the sea iceregime. Stark et al. (2008) included the sea ice rheology together

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