Arctic and Antarctic Sea Ice Extent Forecasting using hybrid LSTM Techniques

Arctic and Antarctic Sea Ice Extent Forecasting using hybrid LSTM Techniques | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Arctic and Antarctic Sea Ice Extent Forecasting using hybrid LSTM Techniques Spandan Sureja This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4316516/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Recent changes in global climate patterns have triggered the melting of polar sea ice, especially in Arctic regions. A decrease in the extent of sea ice is observed at a much faster rate than previously expected. The Antarctic region, on the other hand, has shown a stable sea ice pattern throughout the last few decades. However, the southern polar region is not completely unaffected. Recent studies of the Bellingshausen and Amundsen Seas have shown a downward trend in sea ice. The extent of sea ice is crucial for regulating global climate patterns, ocean circulation and human activities, including shipping and fishing. Hence, forecasting sea ice extent is vital for global economy planning and climatology studies. In this paper, time-series forecasting of 5 Antarctic and Arctic regions is evaluated using a hybrid convolutional long short-term memory (ConvLSTM) and a bidirectional long short-term memory (LSTM) and compared with a standalone long short-term memory (LSTM). This study uses regional sea ice extent data rather than considering the extent across entire hemispheres. Evaluation metrics such as the root mean squared error (RMSE) and mean absolute error (MAE) are used to compare the performances of the models. With lower RMSE scores across all lead times, the proposed hybrid models show better performance in regional sea ice forecasting than does the standalone LSTM. The study also indicated that the climatic conditions of a particular region play a crucial role in forecasting efficiency, especially at longer lead times. Sea ice extent time series forecasting long short-term memory (LSTM) bidirectional long short-term memory (LSTM) Arctic SIE Antarctic SIE Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 1. Introduction The increase in greenhouse gases, which has resulted in an increase in global temperature, has eventually caused notable changes in polar regions. The Arctic ice cover is declining at an accelerated rate, along with a significant reduction in its thickness (Walsh 2013 ). Over the past few decades, an increase in the near-surface air temperature called the 'Arctic Amplification' has been observed (Screen and Simmonds 2010 ). This temperature increase and continuous melting have led to a feedback mechanism in the Arctic. This will result in additional ice melting. The Arctic is expected to be 'seasonally ice-free' once all layers of its multilayered ice are lost (Serreze and Meier 2018 ). On the other hand, in contrast to its gradual increase in ice cover since the 1970s, Antarctica experienced a remarkable decline between 2014 and 2017. Over these four years, the reduction in the extent of Antarctic sea ice exceeded the total Arctic sea ice loss observed in the four decades from 1979 to 2018 (Parkinson 2019 ). However, after 2017, several recoveries were noted, but they have yet to reach the peak achieved in 2014, indicating a decreasing trend. The reason behind the irregular pattern of Antarctic ice remains a subject of debate. The sea ice extent (SIE) is defined as the area of the ocean with a minimum of 15% ice concentration (Vinnikov et al. 1999 ). The reduction in the SIE commonly occurs during the summer because of melting, followed by a rise in the SIE during the winter due to ice formation. The Antarctic SIE follows a seasonal pattern, with February as the month of minimum coverage and September as the month of maximum coverage (Parkinson and Cavalieri 2012 ). Similarly, for the Arctic extent, March and September are the months with the maximum and minimum coverage, respectively (Parkinson and Cavalieri 2008 ). The Arctic sea ice is more sensitive to climate change than the Antarctic sea ice (Shokr and Ye 2023 ). As defined by Meier et al. ( 2007 ), the Arctic is divided into 14 regions. As the entire Arctic region has experienced melting since the 1970s, these regions have shown a strong negative trend. A maximum negative slope is observed for the Kara and Barents Seas, Baffin Bay, Bering Sea and Greenland Sea (Parkinson and Cavalieri 2008 ) (Fig. 1 ). While the Antarctic regions showed a positive trend until 2014, the regional changes during the decline were very different. A steep negative trend was observed for all regions except the Indian Ocean and a few parts of the Ross Sea (Eayrs et al. 2021 ), resulting in an overall negative trend (Fig. 2 ). The Arctic SIE is closely monitored because it affects weather patterns and has economic impacts, such as opening new summer marine routes between the Atlantic and Pacific Oceans through the Northwest Passage (Somanathan et al. 2009 ) and Northeast Passage (Mou et al. 2020 ). This affects the Northern Hemisphere population in several ways. Although the Antarctic SIE does not have the same effect on the global economy or population, its melting plays a crucial role in global ocean circulation and climate patterns. Melting Antarctic ice is also expected to influence temperature, sea level and storm frequency in multiple regions, especially within the Southern Hemisphere. SIE forecasting is important for daily marine activities as well as research for future climate modeling. The Arctic has always been a center of study, and very few models have been applied for Antarctic forecasting. The statistical models developed for prediction were based on the interaction of sea ice with atmospheric or oceanic conditions and sea ice variables such as thickness and concentration (Guemas et al. 2014 ; Lindsay et al. 2008 ). Global coupled models (GCMs) are based on a similar concept for ice prediction. However, these methods are computationally expensive, and their accuracy depends largely on the initial ice state (Blanchard-Wrigglesworth et al. 2011 ). The advancement of machine learning as a branch of artificial intelligence has provided the computational capability to remember, learn and predict data. Notably, techniques such as regression have enabled sea ice prediction without the need for additional predictors. Linear regression was first applied by Drobot and Maslanik ( 2002 ) for the prediction of Beaufort Sea ice. Gregory et al. ( 2020 ) applied Gaussian regression to forecast the SIEs of nine Arctic regions surrounding the North Pole. Horvath et al. ( 2020 ) used a Bayesian logistic regression model for September SIE forecasting in the Arctic. These models showed better prediction accuracy than did the previously built statistical models. The recent evolution of deep learning models such as recurrent neural networks (RNNs), including long short-term memory (LSTM) networks and gated recurrent units (GRUs), has made time series forecasting even more efficient. An LSTM architecture was applied for the Arctic (Chi and Kim 2017 ), and it outperformed traditional statistical models. Wei et al. ( 2022 ) introduced an LSTM architecture with an attention layer to further improve the forecasting accuracy. A hybrid CNN + LSTM was introduced by Liu et al. ( 2021 ) for forecasting Arctic SIEs at longer time scales. Although these models were developed primarily for the Arctic, they may not operate in the case of the Antarctic SIE. Furthermore, the accuracy of the SIE forecasting model is primarily determined by the time series plot peaks and troughs, which represent the periods of maximum and minimum melting, respectively. The proposed methods take advantage of the Arctic and Antarctic regional SIE time-series properties to accurately predict ice extent over a longer time scale, particularly during the highest and lowest melting periods. To the best of current knowledge, the proposed work is the first to use a bidirectional LSTM architecture for regional Arctic and Antarctic SIE prediction. The bidirectional model performed better than the standalone LSTM model. The presented models have demonstrated improved prediction over a longer time range. 2. Materials and Methods 2.1 Dataset and Preprocessing The NSIDC sea ice index data are used for the study. The dataset has monthly SIE values from 1979 to 2023 for both the southern and the northern hemispheres. The 5 Arctic regions used for the analysis are the Barents Sea, Baffin Bay, Bering Sea, Greenland Sea and Kara Sea (Fig. 3). These regions experienced noticeable melting and played a vital role in the Northeast and Northwest Passages. The Barents and Bering Seas are of economic importance owing to widespread fishing and other maritime activities. The 5 Antarctic regions are the Pacific Ocean, Indian Ocean, Bell-Amundsen Sea, Weddell Sea and Ross Sea (Fig. 4). The Bell-Amundsen Sea and the Ross Sea are regions of concern due to the recent increase in ice melting. Here, the monthly SIE values are used for training and testing the models because the errors from daily extent values are averaged, assisting better long-term forecasting. The dataset is divided into 80:20:20 partitions for training, validation and testing. A sliding window approach with a window size of 12 and a lead time of up to 12 months is used for all the LSTM models. As shown in Fig. 5 , the prediction at any time-step \(t\) will be derived from the SIE values of the past 12 months. This allows the model to capture long-term dependencies eventually assisting better forecasts, especially for the regions with high seasonal variability. 2.2 Time Series Forecasting Time series forecasting is the process of evaluating sequential data to extract meaningful statistics and predict future outcomes based on patterns in the data (Albeladi et al. 2023 ). It has various applications in multiple domains and aims to predict near-future values (Vijayakumar et al. 2022 ). In particular, SIE forecasting is vital for climate studies, route navigation, resource exploration and future infrastructure planning in polar regions. Time-series analysis is used to understand the data pattern and identify underlying problems. On the other hand, time-series forecasting is used for predicting the future values of the data. Several statistical models, such as multiple regression, ARIMA (autoregressive integrated moving average) and SARIMA (seasonal ARIMA), are implemented for time series forecasting. However, these models are linear in their predictions (Zhang 2003 ), leading to limited flexibility and difficulty in handling nonstationary data. A class of nonlinear models, including neural networks, was developed to address the drawbacks of linear models. In particular, recurrent neural networks (RNNs), which use a feedback loop of recurrent cells, have shown better prediction accuracy than linear models (Hewamalage et al. 2021 ). LSTM and gated recurrent units (GRUs) are RNNs that can handle large, complex, nonstationary time-series data. 2.3 Standalone and bidirectional LSTMs The RNN encounters a ‘vanishing gradient problem’ where gradients diminish as they backpropagate through time. The LSTM architecture was first explained by Hochreiter and Schmidhuber ( 1997 ) to solve the backpropagation problems of RNNs while enabling long-term remembering capabilities. Typically, an LSTM cell contains four layers, including three sigmoid functions and one hyperbolic tan function, which act as activation functions (Fig. 6 ). The cell state ( \({C}_{t}\) ) flows the information through a cell, and the hidden state ( \({ℎ}_{t}\) ) is the output of the current cell. LSTM controls the flow and loss of information using three gates (red boxes). The forget gate decides which information to discard from previous cells, the input gate adds new information from the current cell to the cell state, and the output gate decides the output of the current cell. Let \({x}_{t}\) and \({ℎ}_{t-1}\) denote the input and the previous cell hidden state respectively. Then, the output of each LSTM gate is as follows: $${f}_{t}=\sigma \left({x}_{t}\ast {u}_{f}+{ℎ}_{t-1}\ast {w}_{f}\right) \left(1\right)$$ $$\stackrel{-}{{C}_{t}}=\text{t}\text{a}\text{n}\text{h}\left({x}_{t}\ast {u}_{c}+{ℎ}_{t-1}{\ast w}_{c}\right) \left(2\right)$$ $${I}_{t}=\sigma \left({x}_{t}\ast {u}_{i}+{ℎ}_{t-1}\ast {w}_{i}\right) \left(3\right)$$ $${O}_{t}=\sigma \left({x}_{t}\ast {u}_{o}+{ℎ}_{t-1}\ast {w}_{o}\right) \left(4\right)$$ Here \(\left({u}_{f},{u}_{c},{u}_{i},{u}_{o}\right)\) and \(\left({w}_{f},{w}_{c},{w}_{i},{w}_{o}\right)\) are all weight metrics. The cell state \({C}_{t}\) and hidden state \({ℎ}_{t}\) for the next cell are as follows: $${C}_{t}={f}_{t}\ast {C}_{t-1}+\stackrel{-}{{C}_{t}}\ast {I}_{t} \left(5\right)$$ $${ℎ}_{t}={O}_{t}\ast \text{t}\text{a}\text{n}\text{h}\left({C}_{t}\right) \left(6\right)$$ While the standalone (unidirectional) LSTM processes the input sequence in a single direction, the bidirectional LSTM works in both directions: forward processing (from the start to the end) and backward processing (from the end to the start) for the same sequence (Fig. 7 ). The outputs of these two processing layers are concatenated at each time step, resulting in a combined output that captures the bidirectional context. The simultaneous input sequence processing from two directions improves the model's flexibility in learning complex patterns and reduces information loss. 2.4 ConvLSTM The convolution LSTM model uses CNNs as the initial layers to capture patterns and relevant features of the time-series data. CNNs are capable of processing multidimensional data. The core components of a CNN architecture are convolutional and pooling layers. The convolutional layer extracts features using a set of filters (kernels), while the pooling layer downsamples these features, reducing the number of dimensions. Consider an input at the \({l}^{tℎ}\) convolutional layer of size \({H}^{l}\times {W}^{l}\times {D}^{l}\) and let f represent the kernels used, each of size \(H\times W\times {D}^{l}\) . Then, the convolution process can be expressed mathematically as $${y}_{{i}^{l+1},{j}^{l+1},{d}^{l}}=\sum _{i=0}^{H}\sum _{j=0}^{W}\sum _{d=0}^{{D}^{l}}{f}_{i,j,{d}^{l}}\times {x}_{{i}^{l+1}+i,{j}^{l+1}+j,{d}^{l}}^{l} \left(7\right)$$ The pooling layer operates independently on \({x}^{l}\) channels. It divides each channel into subregions of size \(H\times W\) . Then, a pooling operator maps each subregion to a single number, thus reducing the dimensions. A max pooling operator, which maps the subregion to its maximum value, was used in this study. Mathematically, max pooling can be expressed as $${y}_{{i}^{l+1},{j}^{l+1},d}=\text{m}\text{a}\text{x} {x}_{{i}^{l+1}\times H+i,{j}^{l+1}\times W+j.d}^{l} \left(8\right)$$ As shown in Fig. 8 , the architecture used in this study has a convolutional layer with 64 filters followed by a pooling layer. The output of the CNN will be passed to the LSTM with 32 units followed by a normalization layer which ensures training stability. The final output is produced by a fully connected (dense) layer. These models were trained with a batchwise processing approach and compiled using an Adam optimizer with a learning rate of 0.0001. During BPTT (back propagation through time), Adam will optimize parameters and minimize the loss function for the entire sequence. Adaptive moment estimation (Adam) is a better choice for time-series forecasting models because it has a minimum memory requirement because it computes first-order gradients only (Kingma and Ba 2014 ) 2.5 Evaluation Metrics The performance of the three models is evaluated using standard accuracy metrics: root mean square error (RMSE) and mean absolute error (MAE). These metrics are widely used for measuring the performance of time series forecasting models (Aijaz and Agarwal 2020 ). The RMSE indicates the overall error that occurred during forecasting, while the MAE measures the absolute deviation of the predicted values from the original data (Adhikari and Agrawal 2013 ). \({SIE}^{observed}\) is the true value of the ice extent, and \({SIE}^{predicted}\) is the extent value predicted by the model. The RMSE penalizes large errors, while the MAE penalizes all errors regardless of their magnitude. $$\text{R}\text{M}\text{S}\text{E} = \sqrt{\frac{1}{\text{N}} \sum _{\text{i}=1}^{\text{N}}{\left({SIE}_{i}^{observed}- {SIE}_{i}^{predicted}\right)}^{2}} \left(9\right)$$ $$\text{M}\text{A}\text{E} = \frac{1}{\text{N}} \sum _{\text{i}=1}^{\text{N}}\left|{SIE}_{i}^{observed}- {SIE}_{i}^{predicted}\right| \left(10\right)$$ 3. Results and Discussion 3.1 Forecasting the Arctic SIE The RMSE scores of CNN + LSTM, bidirectional LSTM (Bidir LSTM) and the standalone LSTM at different lead times are shown in Fig. 9 . The CNN + LSTM is the best-performing model at lower lead times across all regions. However, as the lead time increases, the error scores tend to fluctuate. This fluctuation in forecasting efficiency can be linked to the climatic dynamics and variability of the respective regions. Climate patterns and ocean currents can make LSTM models more difficult to predict at longer lead months. The wind direction significantly impacts the SIE (Brown and Arrigo 2012 ). It influences the sea surface temperature (SST) and determines the movement of sea ice, eventually causing compression or divergence. The SST in the Bering Sea was generally greater than that in the other 4 regions. This is due to the proximity of the Bering Sea to the Pacific Ocean, which brings relatively warm winds northward through ocean currents. It also experiences strong winds and frequent storms due to the Aleutian low-pressure system. The deepening of the Aleutian Low and increased penetration of warmer Pacific streams after the mid-1970s resulted in the gradual warming of the Bering Sea (Wang et al. 2005 ). This shift in climatic patterns greatly affects the SIE and its forecasting. The high variability of the Bering Sea leads to fluctuations in the forecasting efficiency of CNN + LSTM. The bidirectional LSTM, on the other hand, has shown stable RMSE scores throughout the lead times and slightly improved performance compared with CNN + LSTM at higher lead times. Table 1 shows the average error scores of the three models across the 12-month lead period. Table 1 RMSE and MAE scores of Arctic regions averaged over a 12-month lead time for the three models used in the study. Regions CNN+LSTM Bidirectional (Bidir) LSTM Standalone LSTM RMSE MAE RMSE MAE RMSE MAE Bering Sea 0.016 0.095 0.015 0.086 0.168 0.136 Barents Sea 0.090 0.731 0.094 0.074 0.105 0.086 Baffin Bay 0.060 0.046 0.060 0.046 0.064 0.051 Kara Sea 0.129 0.091 0.129 0.091 0.153 0.119 Greenland Sea 0.095 0.079 0.086 0.066 0.101 0.079 The Barents Sea is comparatively more stable than the Bering Sea. Due to its proximity to the Arctic Ocean, the northern part of the Barents Sea is permanently covered by ice (Hunt and Megrey 2005 ). However, it has contributed the most to Arctic sea ice loss. A large part of Arctic sea ice loss can be traced back to the missing Barents Sea winter ice (Smedsrud et al. 2013 ). The influence of warmer Atlantic water has warmed the Barents Sea, resulting in a large volume of sea ice melting yearly. The Barents Sea is expected to be completely ice-free by 2050 if the warming continues. Hence, these recent climatic developments in the past few decades have increased variability in the winter and summer ice cover of the Barents Sea, eventually affecting forecasting. In summer, there is a significant north‒south temperature gradient. CNN + LSTM predicts the Barents Sea SIE more efficiently than does Bidir and standalone LSTM. It is interesting to note that Baffin Bay showed minimum errors at the initial lead months using the CNN + LSTM model. A possible reason could be the reduced susceptibility to the influence of complex ocean currents compared to regions such as the Barents and Kara Seas (Chen et al. 2023 ). Baffin Bay is a relatively enclosed water body, which simplifies the region's SIE forecasting. Its climatic stability has resulted in the almost equal performance of both hybrid models. The above table shows that the CNN + LSTM and bidirectional LSTM models perform equally well in Baffin Bay and the Kara Sea. During the winter, the Kara Sea’s sea ice experiences significant expansion, and by February and March, almost the entire sea is covered under the ice. The Kara Sea has high summer sea ice variability, and winter sea ice is also affected by strong winds and storms. This may lead to fluctuations in the performance of CNN + LSTM and bidirectional LSTM, as seen in the above regions. The Greenland Sea has also shown high sea ice variability over the past few decades. Similar to the Barents Sea, the influence of warmer Atlantic water has warmed the Greenland Sea. This process is subject to a significant feedback mechanism that accelerates ice melting. This instability is observed in the performance of the three models at higher lead times. Although all the models achieved significant rise and fall in the error scores, the bidirectional LSTM model noticeably outperformed the CNN + LSTM and standalone LSTM models for the Greenland Sea. 3.2 Forecasting the Antarctic SIE The RMSE vs. lead time plots for the Antarctic regions are shown in Fig. 10 . The Antarctic climate plays a major role in SIE forecasting. Like in Arctic regions, global warming is now also affecting the Antarctic climate, eventually leading to ice melting. The climate of the Bell-Amundsen Sea is influenced by circumpolar westerlies, resulting in strong winds in the region. The region is consistently frigid throughout the year, and the winter is marked by strong winds and sea ice drifting. Ice movement and formation are also influenced by the Antarctic Circumpolar Current (ACC). However, the change in ocean currents due to the warming of deep ocean water has triggered basal melting in the region, making the Bell-Amundsen Sea one of the most affected Antarctic regions. The sea ice distribution between the Antarctic Peninsula and the Ross Sea is affected by El Niño and La Niña phases (Turner et al. 2015 ), where the former leads to a less dynamic environment allowing sea ice to extend further northward, and the latter results in increased sea ice advection leading to potentially less sea ice cover. Rapid melting of Ross Sea sea ice is observed throughout the spring (Smith et al. 2012 ). The sea ice dynamics related to the El Niño Southern Oscillation (ENSO) also affect the Pacific Ocean SIE. These events account for the high seasonal variability in the Bellingshausen-Amundsen Sea, the Ross Sea and the Pacific Ocean, eventually leading to comparatively higher error scores in forecasting among the Antarctic regions. Table 2 shows the average error scores across the 12-month lead period for five Antarctic regions. Overall, the CNN + LSTM model performed better than did the other two models for the Bell-Amundsen Sea; however, a rather unexpected outcome was observed with the standalone LSTM model, where it outperformed the hybrid models for longer lead months. The CNN + LSTM showed minimum average error scores for the Ross Sea, and Bidir LSTM outperformed in Pacific Ocean SIE forecasting. Table 2 RMSE and MAE scores of Antarctic regions averaged over a 12-month lead time for the three models used in the study. Regions CNN+LSTM Bidirectional (Bidir) LSTM Standalone LSTM RMSE MAE RMSE MAE RMSE MAE Bell-Amundsen Sea 0.090 0.072 0.091 0.074 0.097 0.080 Indian Ocean 0.059 0.049 0.056 0.046 0.058 0.047 Pacific Ocean 0.067 0.053 0.065 0.052 0.070 0.056 Ross Sea 0.082 0.061 0.084 0.063 0.102 0.083 Weddell Sea 0.060 0.048 0.057 0.047 0.073 0.057 The Indian Ocean is a relatively more stable region with no direct effects of ENSO, leading to minimum error scores. The limited fluctuations in the Indian Ocean and the Weddell Sea enable the model to predict values closer to the original SIE values. Bidir LSTM showed a noticeably improved performance compared with the other two models for comparatively stable regions such as the Indian Ocean and the Weddell Sea. 4. Conclusion Considering the significance of sea ice in the operation of polar maritime routes, climate regulation, sea level rise and global ocean circulation, the precise forecasting of Sea Ice Extent (SIE) is crucial. Particularly, regional SIE forecasting will enable better understanding and planning given the importance and unique climatic conditions of each region surrounding the Arctic and the Antarctic. The development of deep neural networks, especially the RNN, showed improved SIE forecasting capability. Long Short-Term Memory (LSTM), a type of RNN, allows efficient forecasting of complex, non-linear time series data. LSTM uses a feedback loop to remember past values and predict the future value a few time steps ahead. This study explores the potential of employing hybrid LSTM models (CNN+LSTM and bidirectional LSTM) for SIE forecasting of 5 Arctic and Antarctic regions. RMSE and MAE were used to compare the models’ performance for a lead time of up to 12 months. The hybrid models outperform standalone LSTM for SIE forecasting, even at longer lead months. Overall, the CNN+LSTM and bidirectional LSTM models show similar performances across all Arctic regions in the study. However, their performance at specific lead times is heavily influenced by the climatic conditions of each region. Throughout the entire lead period, bidirectional LSTM tends to maintain stable performance, while the error scores of CNN+LSTM tend to fluctuate, especially for unstable seas. A similar trend was observed for the Antarctic regions, where hybrid models showed noticeable improvement over the standalone LSTM. This study demonstrates the effectiveness of bidirectional LSTM in forecasting the extent of Antarctic sea ice over extended lead times. Despite this progress, there are limitations in the current hybrid models that require attention. For instance, the RMSE of the CNN+LSTM model fluctuates as the lead time increases, which can be addressed in future research by integrating climatic and atmospheric variables to enhance stability. Additionally, the efficiency of bidirectional LSTM for shorter lead times could be improved by incorporating more dynamic factors. Future studies will also include Arctic regions not covered in this analysis. Overall, the proposed models offer significant advancements in precise SIE forecasting, benefiting climatology research and facilitating economic planning in polar regions. Declarations Availability and requirements Funding: No funding was received for conducting this study. Financial interests: The author has no competing interests to declare that are relevant to the content of this article. Data availability: The NSIDC dataset used in the study is available at the link https://nsidc.org/data/g02135/versions/3 Code availability: The source code and the required files can be downloaded from the link https://github.com/Spandan2308/Sea-Ice-Extent-forecasting-using-hybrid-LSTM Competing interests: The author declare no competing interests. Author Contribution The entire study was performed by Spandan Sureja including background research, coding, manuscript writing, formatting and review. References Adhikari R, Agrawal RK (2013) An Introductory Study on Time Series Modeling and Forecasting. LAP Lambert Academic Publishing Aijaz I, Agarwal P (2020) A Study on Time Series Forecasting using Hybridization of Time Series Models and Neural Networks. Recent Advances in Computer Science and Communications 13:827–832. https://doi.org/10.2174/1573401315666190619112842 Albeladi K, Zafar B, Mueen A (2023) Time Series Forecasting using LSTM and ARIMA. International Journal of Advanced Computer Science and Applications 14. https://doi.org/10.14569/ijacsa.2023.0140133 Blanchard-Wrigglesworth E, Armour KC, Bitz CM, DeWeaver E (2011) Persistence and Inherent Predictability of Arctic Sea Ice in a GCM Ensemble and Observations. Journal of Climate 24:231–250. https://doi.org/10.1175/2010jcli3775.1 Brown ZW, Arrigo KR (2012) Contrasting trends in sea ice and primary production in the Bering Sea and Arctic Ocean. ICES Journal of Marine Science 69:1180–1193. https://doi.org/10.1093/icesjms/fss113 Chen S, Li K, Fu H, Wu YC, Huang Y (2023) Sea Ice Extent Prediction with Machine Learning Methods and Subregional Analysis in the Arctic. Atmosphere 14:1023. https://doi.org/10.3390/atmos14061023 Chi J, Kim H (2017) Prediction of Arctic Sea Ice Concentration Using a Fully Data Driven Deep Neural Network. Remote Sensing 9:1305. https://doi.org/10.3390/rs9121305 Drobot SD, Maslanik JA (2002) A practical method for long‐range forecasting of ice severity in the Beaufort Sea. Geophysical Research Letters 29. https://doi.org/10.1029/2001gl014173 Eayrs C, Li X, Raphael MN, Holland DM (2021) Rapid decline in Antarctic sea ice in recent years hints at future change. Nature Geoscience 14:460–464. https://doi.org/10.1038/s41561-021-00768-3 Gregory W, Tsamados M, Stroeve J, Sollich P (2020) Regional September Sea Ice Forecasting with Complex Networks and Gaussian Processes. Weather and Forecasting 35:793–806. https://doi.org/10.1175/waf-d-19-0107.1 Guemas V, Blanchard‐Wrigglesworth E, Chevallier M, Day JJ, Déqué M, Doblas‐Reyes FJ, Fučkar NS, Germe A, Hawkins E, Keeley S, Koenigk T, Salas y Mélia D, Tietsche S (2014) A review on Arctic sea‐ice predictability and prediction on seasonal to decadal time‐scales. Quarterly Journal of the Royal Meteorological Society 142:546–561. https://doi.org/10.1002/qj.2401 Hewamalage H, Bergmeir C, Bandara K (2021) Recurrent Neural Networks for Time Series Forecasting: Current status and future directions. International Journal of Forecasting 37:388–427. https://doi.org/10.1016/j.ijforecast.2020.06.008 Hochreiter S, Schmidhuber J (1997) Long Short-Term Memory. Neural Computation 9:1735–1780. https://doi.org/10.1162/neco.1997.9.8.1735 Horvath S, Stroeve J, Rajagopalan B, Kleiber W (2020) A Bayesian Logistic Regression for Probabilistic Forecasts of the Minimum September Arctic Sea Ice Cover. Earth and Space Science 7. https://doi.org/10.1029/2020ea001176 Hunt GL, Megrey BA (2005) Comparison of the biophysical and trophic characteristics of the Bering and Barents Seas. ICES Journal of Marine Science 62:1245–1255. https://doi.org/10.1016/j.icesjms.2005.04.008 Kingma DP, Ba J (2014) Adam: A method for stochastic optimization. arXiv (Cornell University). https://doi.org/10.48550/arxiv.1412.6980 Lindsay RW, Zhang J, Schweiger AJ, Steele MA (2008) Seasonal predictions of ice extent in the Arctic Ocean. Journal of Geophysical Research: Oceans 113. https://doi.org/10.1029/2007jc004259 Liu Y, Bogaardt L, Attema J, Hazeleger W (2021) Extended Range Arctic Sea Ice Forecast with Convolutional Long-Short Term Memory Networks. Monthly Weather Review. https://doi.org/10.1175/mwr-d-20-0113.1 Meier WN, Stroeve J, Fetterer F (2007) Whither Arctic sea ice? A clear signal of decline regionally, seasonally and extending beyond the satellite record. Annals of Glaciology 46:428–434. https://doi.org/10.3189/172756407782871170 Mou N, Li J, Sun S, Yang T, Zhang L, Zhang H, Liu W (2020) The impact of opening the Arctic Northeast Passage on the global maritime transportation network pattern using AIS data. Arabian Journal of Geosciences 13. https://doi.org/10.1007/s12517-020-05432-5 Parkinson CL (2019) A 40-y record reveals gradual Antarctic sea ice increases followed by decreases at rates far exceeding the rates seen in the Arctic. Proceedings of the National Academy of Sciences 116:14414–14423. https://doi.org/10.1073/pnas.1906556116 Parkinson CL, Cavalieri DJ (2008) Arctic sea ice variability and trends, 1979–2006. Journal of Geophysical Research: Oceans 113. https://doi.org/10.1029/2007jc004558 Parkinson CL, Cavalieri DJ (2012) Antarctic sea ice variability and trends, 1979–2010. The Cryosphere 6:871–880. https://doi.org/10.5194/tc-6-871-2012 Screen JA, Simmonds I (2010) The central role of diminishing sea ice in recent Arctic temperature amplification. Nature 464:1334–1337. https://doi.org/10.1038/nature09051 Serreze MC, Meier WN (2018) The Arctic’s sea ice cover: trends, variability, predictability, and comparisons to the Antarctic. Annals of the New York Academy of Sciences 1436:36–53. https://doi.org/10.1111/nyas.13856 Shokr M, Ye Y (2023) Why Does Arctic Sea Ice Respond More Evidently than Antarctic Sea Ice to Climate Change? Ocean-Land-Atmosphere Research 2. https://doi.org/10.34133/olar.0006 Smedsrud LH, Esau I, Ingvaldsen RB, Eldevik T, Haugan PM, Li C, Lien VS, Olsen A, Omar AM, Otterå OH, Risebrobakken B, Sandø AB, Semenov VA, Sorokina SA (2013) THE ROLE OF THE BARENTS SEA IN THE ARCTIC CLIMATE SYSTEM. Reviews of Geophysics 51:415–449. https://doi.org/10.1002/rog.20017 Smith W, Sedwick P, Arrigo K, Ainley D, Orsi A (2012) The Ross Sea in a Sea of Change. Oceanography 25:90–103. https://doi.org/10.5670/oceanog.2012.80 Somanathan S, Flynn P, Szymanski J (2009) The Northwest Passage: A simulation. Transportation Research Part A: Policy and Practice 43:127–135. https://doi.org/10.1016/j.tra.2008.08.001 Turner J, Hosking JS, Bracegirdle TJ, Marshall GJ, Phillips T (2015) Recent changes in Antarctic Sea Ice. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 373:20140163. https://doi.org/10.1098/rsta.2014.0163 Vijayakumar V, Domanic G, Ummar S, Afsal M (2022) FeRM Model for Time Series Forecasting. https://doi.org/10.21203/rs.3.rs-2010849/v2 Vinnikov KY, Robock A, Stouffer RJ, Walsh JE, Parkinson CL, Cavalieri DJ, Mitchell JFB, Garrett D, Zakharov VF (1999) Global Warming and Northern Hemisphere Sea Ice Extent. Science 286:1934–1937. https://doi.org/10.1126/science.286.5446.1934 Walsh J (2013) Melting Ice: What is Happening to Arctic Sea Ice, and What Does It Mean for Us? Oceanography 26. https://doi.org/10.5670/oceanog.2013.19 Wang M, Overland JE, Percival DB, Mofjeld HO (2005) Change in the Arctic influence on Bering Sea climate during the twentieth century. International Journal of Climatology 26:531–539. https://doi.org/10.1002/joc.1278 Wei J, Hang R, Luo J-J (2022) Prediction of Pan-Arctic Sea Ice Using Attention-Based LSTM Neural Networks. Frontiers in Marine Science 9. https://doi.org/10.3389/fmars.2022.860403 Zhang GP (2003) Time series forecasting using a hybrid ARIMA and neural network model. Neurocomputing 50:159–175. https://doi.org/10.1016/s0925-2312(01)00702-0 Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4316516","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":311337420,"identity":"c3473ba7-01a4-4bc3-953b-139f3d67490d","order_by":0,"name":"Spandan Sureja","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABB0lEQVRIiWNgGAWjYLACHhhDgsEGSDI2HiBFSxpISwMJWhgYDoNJvFrkZzc/e/Cm5g6D/Izchw8sas7brW0/DLSlxiYalxaDO8fMDecce8ZgcCPd2EDi2O3kbWcSgVqOpeU24NIikWAmzcN2GMhIY5OQYLudbHYAqIWx4TBOLfIz0r9J8/w7DGSksf+Q+Hcu2ez8Q/xaGG7kmEnztgF9fSONjUGy7YCd2Q0CthjcOVMmObfvMI/BmWfMEpJ9yQlmN4C2JODxi/zs9m0Sb74dlpNvT2P8LPHNzt7sfPrDBx9qbHA7TAJCgaOGGchJBKtMwKUcSQsYMH5gYLDHp3gUjIJRMApGJgAAPcNgV9XlApsAAAAASUVORK5CYII=","orcid":"","institution":"Gujarat Technological University","correspondingAuthor":true,"prefix":"","firstName":"Spandan","middleName":"","lastName":"Sureja","suffix":""}],"badges":[],"createdAt":"2024-04-24 08:15:16","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-4316516/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4316516/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":57910056,"identity":"d9e2f7c4-6ee9-4450-82b1-672378e043af","added_by":"auto","created_at":"2024-06-07 10:39:00","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":363912,"visible":true,"origin":"","legend":"\u003cp\u003eTime-series plots of the SIE from 1979 to 2023 for five Arctic regions along with a quadratic regression trend line\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-4316516/v1/95c461a65b0ca132d4b9dcac.png"},{"id":57911381,"identity":"7630f536-3f95-4ed2-84a3-5923cadd6597","added_by":"auto","created_at":"2024-06-07 10:55:00","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":375971,"visible":true,"origin":"","legend":"\u003cp\u003eTime-series plots of the SIE from 1979 to 2023 for five Antarctic regions along with a quadratic regression trend line\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-4316516/v1/22fc1a6e0d5d5a433d296d8a.png"},{"id":57910876,"identity":"e29e6415-3521-4d03-a904-ecb929b50839","added_by":"auto","created_at":"2024-06-07 10:47:00","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":184400,"visible":true,"origin":"","legend":"\u003cp\u003eThe Arctic regions used in study\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-4316516/v1/7e72a2e51045bd515cbc42bf.png"},{"id":57910872,"identity":"0b06d45f-ecc7-4cbf-a940-aa2ba2c48ee8","added_by":"auto","created_at":"2024-06-07 10:47:00","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":91105,"visible":true,"origin":"","legend":"\u003cp\u003eThe Antarctic regions used in study\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-4316516/v1/f1e712481452f5b2f5a23913.png"},{"id":57910052,"identity":"4ac3396f-f2ee-4fdc-abf4-c5b2765c154f","added_by":"auto","created_at":"2024-06-07 10:39:00","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":42583,"visible":true,"origin":"","legend":"\u003cp\u003ePrediction using a sliding window of size 12. The red box shows a window while the blue box represents the target value\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-4316516/v1/d85afbd22e0673434768dcfc.png"},{"id":57912029,"identity":"2d02c620-c15e-4917-b800-ec936f295fd9","added_by":"auto","created_at":"2024-06-07 11:03:00","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":77718,"visible":true,"origin":"","legend":"\u003cp\u003eA single LSTM cell with three gates\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-4316516/v1/e5e1ef1037bee9ecd308bbe2.png"},{"id":57912028,"identity":"23c58827-2deb-40e4-a996-3cdd2d29a2b1","added_by":"auto","created_at":"2024-06-07 11:03:00","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":97510,"visible":true,"origin":"","legend":"\u003cp\u003eA bidirectional LSTM with forward and backward processing layers\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-4316516/v1/72c380949cf5181f4ecad353.png"},{"id":57910058,"identity":"d7b667ad-6a3a-4ce6-9c28-d03434af7981","added_by":"auto","created_at":"2024-06-07 10:39:00","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":72896,"visible":true,"origin":"","legend":"\u003cp\u003eA CNN+LSTM architecture used in the study\u003c/p\u003e","description":"","filename":"8.png","url":"https://assets-eu.researchsquare.com/files/rs-4316516/v1/0595b379b27e3cd924ea0a14.png"},{"id":57910877,"identity":"d3e995ac-fa84-426c-a8fc-da0b015dfdf6","added_by":"auto","created_at":"2024-06-07 10:47:00","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":171290,"visible":true,"origin":"","legend":"\u003cp\u003eRMSE vs Lead Time plots for five Arctic regions\u003c/p\u003e","description":"","filename":"9.png","url":"https://assets-eu.researchsquare.com/files/rs-4316516/v1/2cefc8ca84b1fa415b87bf25.png"},{"id":57910060,"identity":"4302bffb-994b-44e0-93b8-23a8e0877ed0","added_by":"auto","created_at":"2024-06-07 10:39:01","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":171524,"visible":true,"origin":"","legend":"\u003cp\u003eRMSE vs Lead Time plots for five Antarctic regions\u003c/p\u003e","description":"","filename":"10.png","url":"https://assets-eu.researchsquare.com/files/rs-4316516/v1/b3cab5e16438b5e9f3783a66.png"},{"id":57912600,"identity":"27ff1fdd-27eb-43b4-9bab-7b7013e6c290","added_by":"auto","created_at":"2024-06-07 11:11:02","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2166255,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4316516/v1/154ad33b-a1d3-4e6e-b1b9-9b1ad70ddce2.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Arctic and Antarctic Sea Ice Extent Forecasting using hybrid LSTM Techniques","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eThe increase in greenhouse gases, which has resulted in an increase in global temperature, has eventually caused notable changes in polar regions. The Arctic ice cover is declining at an accelerated rate, along with a significant reduction in its thickness (Walsh \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2013\u003c/span\u003e). Over the past few decades, an increase in the near-surface air temperature called the 'Arctic Amplification' has been observed (Screen and Simmonds \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2010\u003c/span\u003e). This temperature increase and continuous melting have led to a feedback mechanism in the Arctic. This will result in additional ice melting. The Arctic is expected to be 'seasonally ice-free' once all layers of its multilayered ice are lost (Serreze and Meier \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2018\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eOn the other hand, in contrast to its gradual increase in ice cover since the 1970s, Antarctica experienced a remarkable decline between 2014 and 2017. Over these four years, the reduction in the extent of Antarctic sea ice exceeded the total Arctic sea ice loss observed in the four decades from 1979 to 2018 (Parkinson \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). However, after 2017, several recoveries were noted, but they have yet to reach the peak achieved in 2014, indicating a decreasing trend. The reason behind the irregular pattern of Antarctic ice remains a subject of debate.\u003c/p\u003e \u003cp\u003eThe sea ice extent (SIE) is defined as the area of the ocean with a minimum of 15% ice concentration (Vinnikov et al. \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e1999\u003c/span\u003e). The reduction in the SIE commonly occurs during the summer because of melting, followed by a rise in the SIE during the winter due to ice formation. The Antarctic SIE follows a seasonal pattern, with February as the month of minimum coverage and September as the month of maximum coverage (Parkinson and Cavalieri \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2012\u003c/span\u003e). Similarly, for the Arctic extent, March and September are the months with the maximum and minimum coverage, respectively (Parkinson and Cavalieri \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2008\u003c/span\u003e). The Arctic sea ice is more sensitive to climate change than the Antarctic sea ice (Shokr and Ye \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2023\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eAs defined by Meier et al. (\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2007\u003c/span\u003e), the Arctic is divided into 14 regions. As the entire Arctic region has experienced melting since the 1970s, these regions have shown a strong negative trend. A maximum negative slope is observed for the Kara and Barents Seas, Baffin Bay, Bering Sea and Greenland Sea (Parkinson and Cavalieri \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2008\u003c/span\u003e) (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). While the Antarctic regions showed a positive trend until 2014, the regional changes during the decline were very different. A steep negative trend was observed for all regions except the Indian Ocean and a few parts of the Ross Sea (Eayrs et al. \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2021\u003c/span\u003e), resulting in an overall negative trend (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe Arctic SIE is closely monitored because it affects weather patterns and has economic impacts, such as opening new summer marine routes between the Atlantic and Pacific Oceans through the Northwest Passage (Somanathan et al. \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2009\u003c/span\u003e) and Northeast Passage (Mou et al. \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). This affects the Northern Hemisphere population in several ways. Although the Antarctic SIE does not have the same effect on the global economy or population, its melting plays a crucial role in global ocean circulation and climate patterns. Melting Antarctic ice is also expected to influence temperature, sea level and storm frequency in multiple regions, especially within the Southern Hemisphere.\u003c/p\u003e \u003cp\u003eSIE forecasting is important for daily marine activities as well as research for future climate modeling. The Arctic has always been a center of study, and very few models have been applied for Antarctic forecasting. The statistical models developed for prediction were based on the interaction of sea ice with atmospheric or oceanic conditions and sea ice variables such as thickness and concentration (Guemas et al. \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2014\u003c/span\u003e; Lindsay et al. \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2008\u003c/span\u003e). Global coupled models (GCMs) are based on a similar concept for ice prediction. However, these methods are computationally expensive, and their accuracy depends largely on the initial ice state (Blanchard-Wrigglesworth et al. \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2011\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThe advancement of machine learning as a branch of artificial intelligence has provided the computational capability to remember, learn and predict data. Notably, techniques such as regression have enabled sea ice prediction without the need for additional predictors. Linear regression was first applied by Drobot and Maslanik (\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2002\u003c/span\u003e) for the prediction of Beaufort Sea ice. Gregory et al. (\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2020\u003c/span\u003e) applied Gaussian regression to forecast the SIEs of nine Arctic regions surrounding the North Pole. Horvath et al. (\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2020\u003c/span\u003e) used a Bayesian logistic regression model for September SIE forecasting in the Arctic. These models showed better prediction accuracy than did the previously built statistical models. The recent evolution of deep learning models such as recurrent neural networks (RNNs), including long short-term memory (LSTM) networks and gated recurrent units (GRUs), has made time series forecasting even more efficient. An LSTM architecture was applied for the Arctic (Chi and Kim \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2017\u003c/span\u003e), and it outperformed traditional statistical models. Wei et al. (\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2022\u003c/span\u003e) introduced an LSTM architecture with an attention layer to further improve the forecasting accuracy. A hybrid CNN\u0026thinsp;+\u0026thinsp;LSTM was introduced by Liu et al. (\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2021\u003c/span\u003e) for forecasting Arctic SIEs at longer time scales.\u003c/p\u003e \u003cp\u003eAlthough these models were developed primarily for the Arctic, they may not operate in the case of the Antarctic SIE. Furthermore, the accuracy of the SIE forecasting model is primarily determined by the time series plot peaks and troughs, which represent the periods of maximum and minimum melting, respectively. The proposed methods take advantage of the Arctic and Antarctic regional SIE time-series properties to accurately predict ice extent over a longer time scale, particularly during the highest and lowest melting periods. To the best of current knowledge, the proposed work is the first to use a bidirectional LSTM architecture for regional Arctic and Antarctic SIE prediction. The bidirectional model performed better than the standalone LSTM model. The presented models have demonstrated improved prediction over a longer time range.\u003c/p\u003e"},{"header":"2. Materials and Methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\n \u003ch2\u003e2.1 Dataset and Preprocessing\u003c/h2\u003e\n \u003cp\u003eThe NSIDC sea ice index data are used for the study. The dataset has monthly SIE values from 1979 to 2023 for both the southern and the northern hemispheres. The 5 Arctic regions used for the analysis are the Barents Sea, Baffin Bay, Bering Sea, Greenland Sea and Kara Sea (Fig. 3). These regions experienced noticeable melting and played a vital role in the Northeast and Northwest Passages. The Barents and Bering Seas are of economic importance owing to widespread fishing and other maritime activities. The 5 Antarctic regions are the Pacific Ocean, Indian Ocean, Bell-Amundsen Sea, Weddell Sea and Ross Sea (Fig. 4). The Bell-Amundsen Sea and the Ross Sea are regions of concern due to the recent increase in ice melting. Here, the monthly SIE values are used for training and testing the models because the errors from daily extent values are averaged, assisting better long-term forecasting.\u003c/p\u003e\n \u003cp\u003eThe dataset is divided into 80:20:20 partitions for training, validation and testing. A sliding window approach with a window size of 12 and a lead time of up to 12 months is used for all the LSTM models. As shown in Fig. \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e, the prediction at any time-step \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(t\\)\u003c/span\u003e\u003c/span\u003e will be derived from the SIE values of the past 12 months. This allows the model to capture long-term dependencies eventually assisting better forecasts, especially for the regions with high seasonal variability.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e\n \u003ch2\u003e2.2 Time Series Forecasting\u003c/h2\u003e\n \u003cp\u003eTime series forecasting is the process of evaluating sequential data to extract meaningful statistics and predict future outcomes based on patterns in the data (Albeladi et al. \u003cspan class=\"CitationRef\"\u003e2023\u003c/span\u003e). It has various applications in multiple domains and aims to predict near-future values (Vijayakumar et al. \u003cspan class=\"CitationRef\"\u003e2022\u003c/span\u003e). In particular, SIE forecasting is vital for climate studies, route navigation, resource exploration and future infrastructure planning in polar regions. Time-series analysis is used to understand the data pattern and identify underlying problems. On the other hand, time-series forecasting is used for predicting the future values of the data. Several statistical models, such as multiple regression, ARIMA (autoregressive integrated moving average) and SARIMA (seasonal ARIMA), are implemented for time series forecasting. However, these models are linear in their predictions (Zhang \u003cspan class=\"CitationRef\"\u003e2003\u003c/span\u003e), leading to limited flexibility and difficulty in handling nonstationary data. A class of nonlinear models, including neural networks, was developed to address the drawbacks of linear models. In particular, recurrent neural networks (RNNs), which use a feedback loop of recurrent cells, have shown better prediction accuracy than linear models (Hewamalage et al. \u003cspan class=\"CitationRef\"\u003e2021\u003c/span\u003e). LSTM and gated recurrent units (GRUs) are RNNs that can handle large, complex, nonstationary time-series data.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec5\" class=\"Section2\"\u003e\n \u003ch2\u003e2.3 Standalone and bidirectional LSTMs\u003c/h2\u003e\n \u003cp\u003eThe RNN encounters a \u0026lsquo;vanishing gradient problem\u0026rsquo; where gradients diminish as they backpropagate through time. The LSTM architecture was first explained by Hochreiter and Schmidhuber (\u003cspan class=\"CitationRef\"\u003e1997\u003c/span\u003e) to solve the backpropagation problems of RNNs while enabling long-term remembering capabilities. Typically, an LSTM cell contains four layers, including three sigmoid functions and one hyperbolic tan function, which act as activation functions (Fig. \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e). The cell state (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({C}_{t}\\)\u003c/span\u003e\u003c/span\u003e) flows the information through a cell, and the hidden state (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({ℎ}_{t}\\)\u003c/span\u003e\u003c/span\u003e) is the output of the current cell. LSTM controls the flow and loss of information using three gates (red boxes). The forget gate decides which information to discard from previous cells, the input gate adds new information from the current cell to the cell state, and the output gate decides the output of the current cell.\u003c/p\u003e\n \u003cp\u003eLet \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({x}_{t}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({ℎ}_{t-1}\\)\u003c/span\u003e\u003c/span\u003e denote the input and the previous cell hidden state respectively. Then, the output of each LSTM gate is as follows:\u003c/p\u003e\n \u003cdiv id=\"Equa\" class=\"Equation\"\u003e\n \u003cdiv class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e$${f}_{t}=\\sigma \\left({x}_{t}\\ast {u}_{f}+{ℎ}_{t-1}\\ast {w}_{f}\\right) \\left(1\\right)$$\u003c/div\u003e\n \u003c/div\u003e\n \u003cdiv id=\"Equb\" class=\"Equation\"\u003e\n \u003cdiv class=\"mathdisplay\" id=\"FileID_Equb\" name=\"EquationSource\"\u003e$$\\stackrel{-}{{C}_{t}}=\\text{t}\\text{a}\\text{n}\\text{h}\\left({x}_{t}\\ast {u}_{c}+{ℎ}_{t-1}{\\ast w}_{c}\\right) \\left(2\\right)$$\u003c/div\u003e\n \u003c/div\u003e\n \u003cdiv id=\"Equc\" class=\"Equation\"\u003e\n \u003cdiv class=\"mathdisplay\" id=\"FileID_Equc\" name=\"EquationSource\"\u003e$${I}_{t}=\\sigma \\left({x}_{t}\\ast {u}_{i}+{ℎ}_{t-1}\\ast {w}_{i}\\right) \\left(3\\right)$$\u003c/div\u003e\n \u003c/div\u003e\n \u003cdiv id=\"Equd\" class=\"Equation\"\u003e\n \u003cdiv class=\"mathdisplay\" id=\"FileID_Equd\" name=\"EquationSource\"\u003e$${O}_{t}=\\sigma \\left({x}_{t}\\ast {u}_{o}+{ℎ}_{t-1}\\ast {w}_{o}\\right) \\left(4\\right)$$\u003c/div\u003e\n \u003c/div\u003e\n \u003cp\u003eHere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\left({u}_{f},{u}_{c},{u}_{i},{u}_{o}\\right)\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\left({w}_{f},{w}_{c},{w}_{i},{w}_{o}\\right)\\)\u003c/span\u003e\u003c/span\u003e are all weight metrics. The cell state \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({C}_{t}\\)\u003c/span\u003e\u003c/span\u003e and hidden state \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({ℎ}_{t}\\)\u003c/span\u003e\u003c/span\u003e for the next cell are as follows:\u003c/p\u003e\n \u003cdiv id=\"Eque\" class=\"Equation\"\u003e\n \u003cdiv class=\"mathdisplay\" id=\"FileID_Eque\" name=\"EquationSource\"\u003e$${C}_{t}={f}_{t}\\ast {C}_{t-1}+\\stackrel{-}{{C}_{t}}\\ast {I}_{t} \\left(5\\right)$$\u003c/div\u003e\n \u003c/div\u003e\n \u003cdiv id=\"Equf\" class=\"Equation\"\u003e\n \u003cdiv class=\"mathdisplay\" id=\"FileID_Equf\" name=\"EquationSource\"\u003e$${ℎ}_{t}={O}_{t}\\ast \\text{t}\\text{a}\\text{n}\\text{h}\\left({C}_{t}\\right) \\left(6\\right)$$\u003c/div\u003e\n \u003c/div\u003e\n \u003cp\u003eWhile the standalone (unidirectional) LSTM processes the input sequence in a single direction, the bidirectional LSTM works in both directions: forward processing (from the start to the end) and backward processing (from the end to the start) for the same sequence (Fig. \u003cspan class=\"InternalRef\"\u003e7\u003c/span\u003e). The outputs of these two processing layers are concatenated at each time step, resulting in a combined output that captures the bidirectional context. The simultaneous input sequence processing from two directions improves the model\u0026apos;s flexibility in learning complex patterns and reduces information loss.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec6\" class=\"Section2\"\u003e\n \u003ch2\u003e2.4 ConvLSTM\u003c/h2\u003e\n \u003cp\u003eThe convolution LSTM model uses CNNs as the initial layers to capture patterns and relevant features of the time-series data. CNNs are capable of processing multidimensional data. The core components of a CNN architecture are convolutional and pooling layers. The convolutional layer extracts features using a set of filters (kernels), while the pooling layer downsamples these features, reducing the number of dimensions. Consider an input at the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({l}^{tℎ}\\)\u003c/span\u003e\u003c/span\u003e convolutional layer of size \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({H}^{l}\\times {W}^{l}\\times {D}^{l}\\)\u003c/span\u003e\u003c/span\u003e and let \u003cem\u003ef\u003c/em\u003e represent the kernels used, each of size \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(H\\times W\\times {D}^{l}\\)\u003c/span\u003e\u003c/span\u003e. Then, the convolution process can be expressed mathematically as\u003c/p\u003e\n \u003cdiv id=\"Equg\" class=\"Equation\"\u003e\n \u003cdiv class=\"mathdisplay\" id=\"FileID_Equg\" name=\"EquationSource\"\u003e$${y}_{{i}^{l+1},{j}^{l+1},{d}^{l}}=\\sum _{i=0}^{H}\\sum _{j=0}^{W}\\sum _{d=0}^{{D}^{l}}{f}_{i,j,{d}^{l}}\\times {x}_{{i}^{l+1}+i,{j}^{l+1}+j,{d}^{l}}^{l} \\left(7\\right)$$\u003c/div\u003e\n \u003c/div\u003e\n \u003cp\u003eThe pooling layer operates independently on \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({x}^{l}\\)\u003c/span\u003e\u003c/span\u003e channels. It divides each channel into subregions of size \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(H\\times W\\)\u003c/span\u003e\u003c/span\u003e. Then, a pooling operator maps each subregion to a single number, thus reducing the dimensions. A max pooling operator, which maps the subregion to its maximum value, was used in this study. Mathematically, max pooling can be expressed as\u003c/p\u003e\n \u003cdiv id=\"Equh\" class=\"Equation\"\u003e\n \u003cdiv class=\"mathdisplay\" id=\"FileID_Equh\" name=\"EquationSource\"\u003e$${y}_{{i}^{l+1},{j}^{l+1},d}=\\text{m}\\text{a}\\text{x} {x}_{{i}^{l+1}\\times H+i,{j}^{l+1}\\times W+j.d}^{l} \\left(8\\right)$$\u003c/div\u003e\u003c/div\u003e\u003cp\u003eAs shown in Fig. \u003cspan class=\"InternalRef\"\u003e8\u003c/span\u003e, the architecture used in this study has a convolutional layer with 64 filters followed by a pooling layer. The output of the CNN will be passed to the LSTM with 32 units followed by a normalization layer which ensures training stability. The final output is produced by a fully connected (dense) layer.\u003c/p\u003e\u003cp\u003eThese models were trained with a batchwise processing approach and compiled using an Adam optimizer with a learning rate of 0.0001. During BPTT (back propagation through time), Adam will optimize parameters and minimize the loss function for the entire sequence. Adaptive moment estimation (Adam) is a better choice for time-series forecasting models because it has a minimum memory requirement because it computes first-order gradients only (Kingma and Ba \u003cspan class=\"CitationRef\"\u003e2014\u003c/span\u003e)\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec7\" class=\"Section2\"\u003e\u003ch2\u003e2.5 Evaluation Metrics\u003c/h2\u003e\u003cp\u003eThe performance of the three models is evaluated using standard accuracy metrics: root mean square error (RMSE) and mean absolute error (MAE). These metrics are widely used for measuring the performance of time series forecasting models (Aijaz and Agarwal \u003cspan class=\"CitationRef\"\u003e2020\u003c/span\u003e). The RMSE indicates the overall error that occurred during forecasting, while the MAE measures the absolute deviation of the predicted values from the original data (Adhikari and Agrawal \u003cspan class=\"CitationRef\"\u003e2013\u003c/span\u003e). \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({SIE}^{observed}\\)\u003c/span\u003e\u003c/span\u003e is the true value of the ice extent, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({SIE}^{predicted}\\)\u003c/span\u003e\u003c/span\u003e is the extent value predicted by the model. The RMSE penalizes large errors, while the MAE penalizes all errors regardless of their magnitude.\u003c/p\u003e\u003cdiv id=\"Equi\" class=\"Equation\"\u003e\u003cdiv class=\"mathdisplay\" id=\"FileID_Equi\" name=\"EquationSource\"\u003e$$\\text{R}\\text{M}\\text{S}\\text{E} = \\sqrt{\\frac{1}{\\text{N}} \\sum _{\\text{i}=1}^{\\text{N}}{\\left({SIE}_{i}^{observed}- {SIE}_{i}^{predicted}\\right)}^{2}} \\left(9\\right)$$\u003c/div\u003e\n \u003c/div\u003e\n \u003cdiv id=\"Equj\" class=\"Equation\"\u003e\n \u003cdiv class=\"mathdisplay\" id=\"FileID_Equj\" name=\"EquationSource\"\u003e$$\\text{M}\\text{A}\\text{E} = \\frac{1}{\\text{N}} \\sum _{\\text{i}=1}^{\\text{N}}\\left|{SIE}_{i}^{observed}- {SIE}_{i}^{predicted}\\right| \\left(10\\right)$$\u003c/div\u003e\n \u003c/div\u003e\n\u003c/div\u003e"},{"header":"3. Results and Discussion","content":"\u003cdiv id=\"Sec9\" class=\"Section2\"\u003e\n \u003ch2\u003e3.1 Forecasting the Arctic SIE\u003c/h2\u003e\n \u003cp\u003eThe RMSE scores of CNN\u0026thinsp;+\u0026thinsp;LSTM, bidirectional LSTM (Bidir LSTM) and the standalone LSTM at different lead times are shown in Fig. \u003cspan class=\"InternalRef\"\u003e9\u003c/span\u003e. The CNN\u0026thinsp;+\u0026thinsp;LSTM is the best-performing model at lower lead times across all regions. However, as the lead time increases, the error scores tend to fluctuate. This fluctuation in forecasting efficiency can be linked to the climatic dynamics and variability of the respective regions. Climate patterns and ocean currents can make LSTM models more difficult to predict at longer lead months. The wind direction significantly impacts the SIE (Brown and Arrigo \u003cspan class=\"CitationRef\"\u003e2012\u003c/span\u003e). It influences the sea surface temperature (SST) and determines the movement of sea ice, eventually causing compression or divergence.\u003c/p\u003e\n \u003cp\u003eThe SST in the Bering Sea was generally greater than that in the other 4 regions. This is due to the proximity of the Bering Sea to the Pacific Ocean, which brings relatively warm winds northward through ocean currents. It also experiences strong winds and frequent storms due to the Aleutian low-pressure system. The deepening of the Aleutian Low and increased penetration of warmer Pacific streams after the mid-1970s resulted in the gradual warming of the Bering Sea (Wang et al. \u003cspan class=\"CitationRef\"\u003e2005\u003c/span\u003e). This shift in climatic patterns greatly affects the SIE and its forecasting. The high variability of the Bering Sea leads to fluctuations in the forecasting efficiency of CNN\u0026thinsp;+\u0026thinsp;LSTM. The bidirectional LSTM, on the other hand, has shown stable RMSE scores throughout the lead times and slightly improved performance compared with CNN\u0026thinsp;+\u0026thinsp;LSTM at higher lead times. Table \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e shows the average error scores of the three models across the 12-month lead period.\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003eTable\u0026nbsp;\u003c/strong\u003e\u003cstrong\u003e1\u003c/strong\u003e RMSE and MAE scores of Arctic regions averaged over a 12-month lead time for the three models used in the study.\u003c/p\u003e\n \u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\" width=\"99%\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd width=\"21.649484536082475%\" rowspan=\"2\"\u003e\n \u003cp\u003eRegions\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"22.68041237113402%\" colspan=\"2\"\u003e\n \u003cp\u003eCNN+LSTM\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"28.8659793814433%\" colspan=\"2\"\u003e\n \u003cp\u003eBidirectional (Bidir) LSTM\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"26.804123711340207%\" colspan=\"2\"\u003e\n \u003cp\u003eStandalone LSTM\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"15.789473684210526%\"\u003e\n \u003cp\u003eRMSE\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.157894736842104%\"\u003e\n \u003cp\u003eMAE\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"19.736842105263158%\"\u003e\n \u003cp\u003eRMSE\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"17.105263157894736%\"\u003e\n \u003cp\u003eMAE\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.42105263157895%\"\u003e\n \u003cp\u003eRMSE\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"15.789473684210526%\"\u003e\n \u003cp\u003eMAE\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"21.649484536082475%\"\u003e\n \u003cp\u003eBering Sea\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.371134020618557%\"\u003e\n \u003cp\u003e0.016\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"10.309278350515465%\"\u003e\n \u003cp\u003e0.095\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"15.463917525773196%\"\u003e\n \u003cp\u003e0.015\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.402061855670103%\"\u003e\n \u003cp\u003e0.086\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.43298969072165%\"\u003e\n \u003cp\u003e0.168\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.371134020618557%\"\u003e\n \u003cp\u003e0.136\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"21.649484536082475%\"\u003e\n \u003cp\u003eBarents Sea\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.371134020618557%\"\u003e\n \u003cp\u003e0.090\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"10.309278350515465%\"\u003e\n \u003cp\u003e0.731\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"15.463917525773196%\"\u003e\n \u003cp\u003e0.094\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.402061855670103%\"\u003e\n \u003cp\u003e0.074\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.43298969072165%\"\u003e\n \u003cp\u003e0.105\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.371134020618557%\"\u003e\n \u003cp\u003e0.086\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"21.649484536082475%\"\u003e\n \u003cp\u003eBaffin Bay\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.371134020618557%\"\u003e\n \u003cp\u003e0.060\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"10.309278350515465%\"\u003e\n \u003cp\u003e0.046\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"15.463917525773196%\"\u003e\n \u003cp\u003e0.060\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.402061855670103%\"\u003e\n \u003cp\u003e0.046\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.43298969072165%\"\u003e\n \u003cp\u003e0.064\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.371134020618557%\"\u003e\n \u003cp\u003e0.051\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"21.649484536082475%\"\u003e\n \u003cp\u003eKara Sea\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.371134020618557%\"\u003e\n \u003cp\u003e0.129\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"10.309278350515465%\"\u003e\n \u003cp\u003e0.091\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"15.463917525773196%\"\u003e\n \u003cp\u003e0.129\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.402061855670103%\"\u003e\n \u003cp\u003e0.091\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.43298969072165%\"\u003e\n \u003cp\u003e0.153\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.371134020618557%\"\u003e\n \u003cp\u003e0.119\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"21.649484536082475%\"\u003e\n \u003cp\u003eGreenland Sea\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.371134020618557%\"\u003e\n \u003cp\u003e0.095\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"10.309278350515465%\"\u003e\n \u003cp\u003e0.079\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"15.463917525773196%\"\u003e\n \u003cp\u003e0.086\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.402061855670103%\"\u003e\n \u003cp\u003e0.066\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.43298969072165%\"\u003e\n \u003cp\u003e0.101\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.371134020618557%\"\u003e\n \u003cp\u003e0.079\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003cp\u003eThe Barents Sea is comparatively more stable than the Bering Sea. Due to its proximity to the Arctic Ocean, the northern part of the Barents Sea is permanently covered by ice (Hunt and Megrey \u003cspan class=\"CitationRef\"\u003e2005\u003c/span\u003e). However, it has contributed the most to Arctic sea ice loss. A large part of Arctic sea ice loss can be traced back to the missing Barents Sea winter ice (Smedsrud et al. \u003cspan class=\"CitationRef\"\u003e2013\u003c/span\u003e). The influence of warmer Atlantic water has warmed the Barents Sea, resulting in a large volume of sea ice melting yearly. The Barents Sea is expected to be completely ice-free by 2050 if the warming continues. Hence, these recent climatic developments in the past few decades have increased variability in the winter and summer ice cover of the Barents Sea, eventually affecting forecasting. In summer, there is a significant north‒south temperature gradient. CNN\u0026thinsp;+\u0026thinsp;LSTM predicts the Barents Sea SIE more efficiently than does Bidir and standalone LSTM.\u003c/p\u003e\n \u003cp\u003eIt is interesting to note that Baffin Bay showed minimum errors at the initial lead months using the CNN\u0026thinsp;+\u0026thinsp;LSTM model. A possible reason could be the reduced susceptibility to the influence of complex ocean currents compared to regions such as the Barents and Kara Seas (Chen et al. \u003cspan class=\"CitationRef\"\u003e2023\u003c/span\u003e). Baffin Bay is a relatively enclosed water body, which simplifies the region\u0026apos;s SIE forecasting. Its climatic stability has resulted in the almost equal performance of both hybrid models. The above table shows that the CNN\u0026thinsp;+\u0026thinsp;LSTM and bidirectional LSTM models perform equally well in Baffin Bay and the Kara Sea. During the winter, the Kara Sea\u0026rsquo;s sea ice experiences significant expansion, and by February and March, almost the entire sea is covered under the ice. The Kara Sea has high summer sea ice variability, and winter sea ice is also affected by strong winds and storms. This may lead to fluctuations in the performance of CNN\u0026thinsp;+\u0026thinsp;LSTM and bidirectional LSTM, as seen in the above regions.\u003c/p\u003e\n \u003cp\u003eThe Greenland Sea has also shown high sea ice variability over the past few decades. Similar to the Barents Sea, the influence of warmer Atlantic water has warmed the Greenland Sea. This process is subject to a significant feedback mechanism that accelerates ice melting. This instability is observed in the performance of the three models at higher lead times. Although all the models achieved significant rise and fall in the error scores, the bidirectional LSTM model noticeably outperformed the CNN\u0026thinsp;+\u0026thinsp;LSTM and standalone LSTM models for the Greenland Sea.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec10\" class=\"Section2\"\u003e\n \u003ch2\u003e3.2 Forecasting the Antarctic SIE\u003c/h2\u003e\n \u003cp\u003eThe RMSE vs. lead time plots for the Antarctic regions are shown in Fig. \u003cspan class=\"InternalRef\"\u003e10\u003c/span\u003e. The Antarctic climate plays a major role in SIE forecasting. Like in Arctic regions, global warming is now also affecting the Antarctic climate, eventually leading to ice melting. The climate of the Bell-Amundsen Sea is influenced by circumpolar westerlies, resulting in strong winds in the region. The region is consistently frigid throughout the year, and the winter is marked by strong winds and sea ice drifting. Ice movement and formation are also influenced by the Antarctic Circumpolar Current (ACC). However, the change in ocean currents due to the warming of deep ocean water has triggered basal melting in the region, making the Bell-Amundsen Sea one of the most affected Antarctic regions.\u003c/p\u003e\n \u003cp\u003eThe sea ice distribution between the Antarctic Peninsula and the Ross Sea is affected by El Ni\u0026ntilde;o and La Ni\u0026ntilde;a phases (Turner et al. \u003cspan class=\"CitationRef\"\u003e2015\u003c/span\u003e), where the former leads to a less dynamic environment allowing sea ice to extend further northward, and the latter results in increased sea ice advection leading to potentially less sea ice cover. Rapid melting of Ross Sea sea ice is observed throughout the spring (Smith et al. \u003cspan class=\"CitationRef\"\u003e2012\u003c/span\u003e). The sea ice dynamics related to the El Ni\u0026ntilde;o Southern Oscillation (ENSO) also affect the Pacific Ocean SIE. These events account for the high seasonal variability in the Bellingshausen-Amundsen Sea, the Ross Sea and the Pacific Ocean, eventually leading to comparatively higher error scores in forecasting among the Antarctic regions.\u003c/p\u003e\n \u003cp\u003eTable \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e shows the average error scores across the 12-month lead period for five Antarctic regions. Overall, the CNN\u0026thinsp;+\u0026thinsp;LSTM model performed better than did the other two models for the Bell-Amundsen Sea; however, a rather unexpected outcome was observed with the standalone LSTM model, where it outperformed the hybrid models for longer lead months. The CNN\u0026thinsp;+\u0026thinsp;LSTM showed minimum average error scores for the Ross Sea, and Bidir LSTM outperformed in Pacific Ocean SIE forecasting.\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003eTable\u0026nbsp;\u003c/strong\u003e\u003cstrong\u003e2\u003c/strong\u003e RMSE and MAE scores of Antarctic regions averaged over a 12-month lead time for the three models used in the study.\u003c/p\u003e\n \u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\" width=\"99%\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd width=\"24.742268041237114%\" rowspan=\"2\"\u003e\n \u003cp\u003eRegions\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"19.587628865979383%\" colspan=\"2\"\u003e\n \u003cp\u003eCNN+LSTM\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"32.98969072164948%\" colspan=\"2\"\u003e\n \u003cp\u003eBidirectional (Bidir) LSTM\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"22.68041237113402%\" colspan=\"2\"\u003e\n \u003cp\u003eStandalone LSTM\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"13.698630136986301%\"\u003e\n \u003cp\u003eRMSE\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.32876712328767%\"\u003e\n \u003cp\u003eMAE\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"23.28767123287671%\"\u003e\n \u003cp\u003eRMSE\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"20.54794520547945%\"\u003e\n \u003cp\u003eMAE\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"16.438356164383563%\"\u003e\n \u003cp\u003eRMSE\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.698630136986301%\"\u003e\n \u003cp\u003eMAE\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"24.742268041237114%\"\u003e\n \u003cp\u003eBell-Amundsen Sea\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"10.309278350515465%\"\u003e\n \u003cp\u003e0.090\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.278350515463918%\"\u003e\n \u003cp\u003e0.072\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"17.52577319587629%\"\u003e\n \u003cp\u003e0.091\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"15.463917525773196%\"\u003e\n \u003cp\u003e0.074\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.371134020618557%\"\u003e\n \u003cp\u003e0.097\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"10.309278350515465%\"\u003e\n \u003cp\u003e0.080\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"24.742268041237114%\"\u003e\n \u003cp\u003eIndian Ocean\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"10.309278350515465%\"\u003e\n \u003cp\u003e0.059\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.278350515463918%\"\u003e\n \u003cp\u003e0.049\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"17.52577319587629%\"\u003e\n \u003cp\u003e0.056\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"15.463917525773196%\"\u003e\n \u003cp\u003e0.046\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.371134020618557%\"\u003e\n \u003cp\u003e0.058\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"10.309278350515465%\"\u003e\n \u003cp\u003e0.047\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"24.742268041237114%\"\u003e\n \u003cp\u003ePacific Ocean\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"10.309278350515465%\"\u003e\n \u003cp\u003e0.067\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.278350515463918%\"\u003e\n \u003cp\u003e0.053\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"17.52577319587629%\"\u003e\n \u003cp\u003e0.065\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"15.463917525773196%\"\u003e\n \u003cp\u003e0.052\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.371134020618557%\"\u003e\n \u003cp\u003e0.070\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"10.309278350515465%\"\u003e\n \u003cp\u003e0.056\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"24.742268041237114%\"\u003e\n \u003cp\u003eRoss Sea\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"10.309278350515465%\"\u003e\n \u003cp\u003e0.082\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.278350515463918%\"\u003e\n \u003cp\u003e0.061\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"17.52577319587629%\"\u003e\n \u003cp\u003e0.084\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"15.463917525773196%\"\u003e\n \u003cp\u003e0.063\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.371134020618557%\"\u003e\n \u003cp\u003e0.102\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"10.309278350515465%\"\u003e\n \u003cp\u003e0.083\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"24.742268041237114%\"\u003e\n \u003cp\u003eWeddell Sea\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"10.309278350515465%\"\u003e\n \u003cp\u003e0.060\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.278350515463918%\"\u003e\n \u003cp\u003e0.048\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"17.52577319587629%\"\u003e\n \u003cp\u003e0.057\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"15.463917525773196%\"\u003e\n \u003cp\u003e0.047\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.371134020618557%\"\u003e\n \u003cp\u003e0.073\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"10.309278350515465%\"\u003e\n \u003cp\u003e0.057\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003cp\u003eThe Indian Ocean is a relatively more stable region with no direct effects of ENSO, leading to minimum error scores. The limited fluctuations in the Indian Ocean and the Weddell Sea enable the model to predict values closer to the original SIE values. Bidir LSTM showed a noticeably improved performance compared with the other two models for comparatively stable regions such as the Indian Ocean and the Weddell Sea.\u003c/p\u003e\n\u003c/div\u003e"},{"header":"4. Conclusion","content":"\u003cp\u003eConsidering the significance of sea ice in the operation of polar maritime routes, climate regulation, sea level rise and global ocean circulation, the precise forecasting of Sea Ice Extent (SIE) is crucial. Particularly, regional SIE forecasting will enable better understanding and planning given the importance and unique climatic conditions of each region surrounding the Arctic and the Antarctic. The development of deep neural networks, especially the RNN, showed improved SIE forecasting capability. Long Short-Term Memory (LSTM), a type of RNN, allows efficient forecasting of complex, non-linear time series data. LSTM uses a feedback loop to remember past values and predict the future value a few time steps ahead. This study explores the potential of employing hybrid LSTM models (CNN+LSTM and bidirectional LSTM) for SIE forecasting of 5 Arctic and Antarctic regions. RMSE and MAE were used to compare the models’ performance for a lead time of up to 12 months.\u003c/p\u003e\n\u003cp\u003eThe hybrid models outperform standalone LSTM for SIE forecasting, even at longer lead months. Overall, the CNN+LSTM and bidirectional LSTM models show similar performances across all Arctic regions in the study. However, their performance at specific lead times is heavily influenced by the climatic conditions of each region. Throughout the entire lead period, bidirectional LSTM tends to maintain stable performance, while the error scores of CNN+LSTM tend to fluctuate, especially for unstable seas. A similar trend was observed for the Antarctic regions, where hybrid models showed noticeable improvement over the standalone LSTM.\u003c/p\u003e\n\u003cp\u003eThis study demonstrates the effectiveness of bidirectional LSTM in forecasting the extent of Antarctic sea ice over extended lead times. Despite this progress, there are limitations in the current hybrid models that require attention. For instance, the RMSE of the CNN+LSTM model fluctuates as the lead time increases, which can be addressed in future research by integrating climatic and atmospheric variables to enhance stability. Additionally, the efficiency of bidirectional LSTM for shorter lead times could be improved by incorporating more dynamic factors. Future studies will also include Arctic regions not covered in this analysis. Overall, the proposed models offer significant advancements in precise SIE forecasting, benefiting climatology research and facilitating economic planning in polar regions.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAvailability and requirements\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding:\u0026nbsp;\u003c/strong\u003eNo funding was received for conducting this study.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFinancial interests:\u003c/strong\u003e The author has no competing interests to declare that are relevant to the content of this article.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData availability:\u0026nbsp;\u003c/strong\u003eThe NSIDC dataset used in the study is available at the link https://nsidc.org/data/g02135/versions/3\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCode availability:\u0026nbsp;\u003c/strong\u003eThe source code and the required files can be downloaded from the link https://github.com/Spandan2308/Sea-Ice-Extent-forecasting-using-hybrid-LSTM\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting interests:\u0026nbsp;\u003c/strong\u003eThe author declare no competing interests.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthor Contribution\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe entire study was performed by Spandan Sureja including background research, coding, manuscript writing, formatting and review.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n \u003cli\u003eAdhikari R, Agrawal RK (2013) An Introductory Study on Time Series Modeling and Forecasting. LAP Lambert Academic Publishing\u003c/li\u003e\n \u003cli\u003eAijaz I, Agarwal P (2020) A Study on Time Series Forecasting using Hybridization of Time Series Models and Neural Networks. Recent Advances in Computer Science and Communications 13:827\u0026ndash;832. https://doi.org/10.2174/1573401315666190619112842\u003c/li\u003e\n \u003cli\u003eAlbeladi K, Zafar B, Mueen A (2023) Time Series Forecasting using LSTM and ARIMA. International Journal of Advanced Computer Science and Applications 14. https://doi.org/10.14569/ijacsa.2023.0140133\u003c/li\u003e\n \u003cli\u003eBlanchard-Wrigglesworth E, Armour KC, Bitz CM, DeWeaver E (2011) Persistence and Inherent Predictability of Arctic Sea Ice in a GCM Ensemble and Observations. Journal of Climate 24:231\u0026ndash;250. https://doi.org/10.1175/2010jcli3775.1\u003c/li\u003e\n \u003cli\u003eBrown ZW, Arrigo KR (2012) Contrasting trends in sea ice and primary production in the Bering Sea and Arctic Ocean. ICES Journal of Marine Science 69:1180\u0026ndash;1193. https://doi.org/10.1093/icesjms/fss113\u003c/li\u003e\n \u003cli\u003eChen S, Li K, Fu H, Wu YC, Huang Y (2023) Sea Ice Extent Prediction with Machine Learning Methods and Subregional Analysis in the Arctic. Atmosphere 14:1023. https://doi.org/10.3390/atmos14061023\u003c/li\u003e\n \u003cli\u003eChi J, Kim H (2017) Prediction of Arctic Sea Ice Concentration Using a Fully Data Driven Deep Neural Network. Remote Sensing 9:1305. https://doi.org/10.3390/rs9121305\u003c/li\u003e\n \u003cli\u003eDrobot SD, Maslanik JA (2002) A practical method for long‐range forecasting of ice severity in the Beaufort Sea. Geophysical Research Letters 29. https://doi.org/10.1029/2001gl014173\u003c/li\u003e\n \u003cli\u003eEayrs C, Li X, Raphael MN, Holland DM (2021) Rapid decline in Antarctic sea ice in recent years hints at future change. Nature Geoscience 14:460\u0026ndash;464. https://doi.org/10.1038/s41561-021-00768-3\u003c/li\u003e\n \u003cli\u003eGregory W, Tsamados M, Stroeve J, Sollich P (2020) Regional September Sea Ice Forecasting with Complex Networks and Gaussian Processes. Weather and Forecasting 35:793\u0026ndash;806. https://doi.org/10.1175/waf-d-19-0107.1\u003c/li\u003e\n \u003cli\u003eGuemas V, Blanchard‐Wrigglesworth E, Chevallier M, Day JJ, D\u0026eacute;qu\u0026eacute; M, Doblas‐Reyes FJ, Fučkar NS, Germe A, Hawkins E, Keeley S, Koenigk T, Salas y M\u0026eacute;lia D, Tietsche S (2014) A review on Arctic sea‐ice predictability and prediction on seasonal to decadal time‐scales. Quarterly Journal of the Royal Meteorological Society 142:546\u0026ndash;561. https://doi.org/10.1002/qj.2401\u003c/li\u003e\n \u003cli\u003eHewamalage H, Bergmeir C, Bandara K (2021) Recurrent Neural Networks for Time Series Forecasting: Current status and future directions. International Journal of Forecasting 37:388\u0026ndash;427. https://doi.org/10.1016/j.ijforecast.2020.06.008\u003c/li\u003e\n \u003cli\u003eHochreiter S, Schmidhuber J (1997) Long Short-Term Memory. Neural Computation 9:1735\u0026ndash;1780. https://doi.org/10.1162/neco.1997.9.8.1735\u003c/li\u003e\n \u003cli\u003eHorvath S, Stroeve J, Rajagopalan B, Kleiber W (2020) A Bayesian Logistic Regression for Probabilistic Forecasts of the Minimum September Arctic Sea Ice Cover. Earth and Space Science 7. https://doi.org/10.1029/2020ea001176\u003c/li\u003e\n \u003cli\u003eHunt GL, Megrey BA (2005) Comparison of the biophysical and trophic characteristics of the Bering and Barents Seas. ICES Journal of Marine Science 62:1245\u0026ndash;1255. https://doi.org/10.1016/j.icesjms.2005.04.008\u003c/li\u003e\n \u003cli\u003eKingma DP, Ba J (2014) Adam: A method for stochastic optimization. arXiv (Cornell University). https://doi.org/10.48550/arxiv.1412.6980\u003c/li\u003e\n \u003cli\u003eLindsay RW, Zhang J, Schweiger AJ, Steele MA (2008) Seasonal predictions of ice extent in the Arctic Ocean. Journal of Geophysical Research: Oceans 113. https://doi.org/10.1029/2007jc004259\u003c/li\u003e\n \u003cli\u003eLiu Y, Bogaardt L, Attema J, Hazeleger W (2021) Extended Range Arctic Sea Ice Forecast with Convolutional Long-Short Term Memory Networks. Monthly Weather Review. https://doi.org/10.1175/mwr-d-20-0113.1\u003c/li\u003e\n \u003cli\u003eMeier WN, Stroeve J, Fetterer F (2007) Whither Arctic sea ice? A clear signal of decline regionally, seasonally and extending beyond the satellite record. Annals of Glaciology 46:428\u0026ndash;434. https://doi.org/10.3189/172756407782871170\u003c/li\u003e\n \u003cli\u003eMou N, Li J, Sun S, Yang T, Zhang L, Zhang H, Liu W (2020) The impact of opening the Arctic Northeast Passage on the global maritime transportation network pattern using AIS data. Arabian Journal of Geosciences 13. https://doi.org/10.1007/s12517-020-05432-5\u003c/li\u003e\n \u003cli\u003eParkinson CL (2019) A 40-y record reveals gradual Antarctic sea ice increases followed by decreases at rates far exceeding the rates seen in the Arctic. Proceedings of the National Academy of Sciences 116:14414\u0026ndash;14423. https://doi.org/10.1073/pnas.1906556116\u003c/li\u003e\n \u003cli\u003eParkinson CL, Cavalieri DJ (2008) Arctic sea ice variability and trends, 1979\u0026ndash;2006. Journal of Geophysical Research: Oceans 113. https://doi.org/10.1029/2007jc004558\u003c/li\u003e\n \u003cli\u003eParkinson CL, Cavalieri DJ (2012) Antarctic sea ice variability and trends, 1979\u0026ndash;2010. The Cryosphere 6:871\u0026ndash;880. https://doi.org/10.5194/tc-6-871-2012\u003c/li\u003e\n \u003cli\u003eScreen JA, Simmonds I (2010) The central role of diminishing sea ice in recent Arctic temperature amplification. Nature 464:1334\u0026ndash;1337. https://doi.org/10.1038/nature09051\u003c/li\u003e\n \u003cli\u003eSerreze MC, Meier WN (2018) The Arctic\u0026rsquo;s sea ice cover: trends, variability, predictability, and comparisons to the Antarctic. Annals of the New York Academy of Sciences 1436:36\u0026ndash;53. https://doi.org/10.1111/nyas.13856\u003c/li\u003e\n \u003cli\u003eShokr M, Ye Y (2023) Why Does Arctic Sea Ice Respond More Evidently than Antarctic Sea Ice to Climate Change? Ocean-Land-Atmosphere Research 2. https://doi.org/10.34133/olar.0006\u003c/li\u003e\n \u003cli\u003eSmedsrud LH, Esau I, Ingvaldsen RB, Eldevik T, Haugan PM, Li C, Lien VS, Olsen A, Omar AM, Otter\u0026aring; OH, Risebrobakken B, Sand\u0026oslash; AB, Semenov VA, Sorokina SA (2013) THE ROLE OF THE BARENTS SEA IN THE ARCTIC CLIMATE SYSTEM. Reviews of Geophysics 51:415\u0026ndash;449. https://doi.org/10.1002/rog.20017\u003c/li\u003e\n \u003cli\u003eSmith W, Sedwick P, Arrigo K, Ainley D, Orsi A (2012) The Ross Sea in a Sea of Change. Oceanography 25:90\u0026ndash;103. https://doi.org/10.5670/oceanog.2012.80\u003c/li\u003e\n \u003cli\u003eSomanathan S, Flynn P, Szymanski J (2009) The Northwest Passage: A simulation. Transportation Research Part A: Policy and Practice 43:127\u0026ndash;135. https://doi.org/10.1016/j.tra.2008.08.001\u003c/li\u003e\n \u003cli\u003eTurner J, Hosking JS, Bracegirdle TJ, Marshall GJ, Phillips T (2015) Recent changes in Antarctic Sea Ice. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 373:20140163. https://doi.org/10.1098/rsta.2014.0163\u003c/li\u003e\n \u003cli\u003eVijayakumar V, Domanic G, Ummar S, Afsal M (2022) FeRM Model for Time Series Forecasting. https://doi.org/10.21203/rs.3.rs-2010849/v2\u003c/li\u003e\n \u003cli\u003eVinnikov KY, Robock A, Stouffer RJ, Walsh JE, Parkinson CL, Cavalieri DJ, Mitchell JFB, Garrett D, Zakharov VF (1999) Global Warming and Northern Hemisphere Sea Ice Extent. Science 286:1934\u0026ndash;1937. https://doi.org/10.1126/science.286.5446.1934\u003c/li\u003e\n \u003cli\u003eWalsh J (2013) Melting Ice: What is Happening to Arctic Sea Ice, and What Does It Mean for Us? Oceanography 26. https://doi.org/10.5670/oceanog.2013.19\u003c/li\u003e\n \u003cli\u003eWang M, Overland JE, Percival DB, Mofjeld HO (2005) Change in the Arctic influence on Bering Sea climate during the twentieth century. International Journal of Climatology 26:531\u0026ndash;539. https://doi.org/10.1002/joc.1278\u003c/li\u003e\n \u003cli\u003eWei J, Hang R, Luo J-J (2022) Prediction of Pan-Arctic Sea Ice Using Attention-Based LSTM Neural Networks. Frontiers in Marine Science 9. https://doi.org/10.3389/fmars.2022.860403\u003c/li\u003e\n \u003cli\u003eZhang GP (2003) Time series forecasting using a hybrid ARIMA and neural network model. Neurocomputing 50:159\u0026ndash;175. https://doi.org/10.1016/s0925-2312(01)00702-0\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":true,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Sea ice extent, time series forecasting, long short-term memory (LSTM), bidirectional long short-term memory (LSTM), Arctic SIE, Antarctic SIE ","lastPublishedDoi":"10.21203/rs.3.rs-4316516/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4316516/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eRecent changes in global climate patterns have triggered the melting of polar sea ice, especially in Arctic regions. A decrease in the extent of sea ice is observed at a much faster rate than previously expected. The Antarctic region, on the other hand, has shown a stable sea ice pattern throughout the last few decades. However, the southern polar region is not completely unaffected. Recent studies of the Bellingshausen and Amundsen Seas have shown a downward trend in sea ice. The extent of sea ice is crucial for regulating global climate patterns, ocean circulation and human activities, including shipping and fishing. Hence, forecasting sea ice extent is vital for global economy planning and climatology studies. In this paper, time-series forecasting of 5 Antarctic and Arctic regions is evaluated using a hybrid convolutional long short-term memory (ConvLSTM) and a bidirectional long short-term memory (LSTM) and compared with a standalone long short-term memory (LSTM). This study uses regional sea ice extent data rather than considering the extent across entire hemispheres. Evaluation metrics such as the root mean squared error (RMSE) and mean absolute error (MAE) are used to compare the performances of the models. With lower RMSE scores across all lead times, the proposed hybrid models show better performance in regional sea ice forecasting than does the standalone LSTM. The study also indicated that the climatic conditions of a particular region play a crucial role in forecasting efficiency, especially at longer lead times.\u003c/p\u003e","manuscriptTitle":"Arctic and Antarctic Sea Ice Extent Forecasting using hybrid LSTM Techniques","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-06-07 10:38:55","doi":"10.21203/rs.3.rs-4316516/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"82a7f2e9-f8ca-4b09-885b-bddf6f925453","owner":[],"postedDate":"June 7th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2024-06-07T10:38:56+00:00","versionOfRecord":[],"versionCreatedAt":"2024-06-07 10:38:55","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-4316516","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4316516","identity":"rs-4316516","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}