Long tide gauge time series are essential for coastal monitoring, port management, and sea level studies, but are often affected by data gaps due to instrumental and operational failures. These gaps hinder reliable analysis and long-term environmental assessment. This study proposes a Long Short-Term Memory (LSTM)-based framework for reconstructing missing data in tide gauge records from the Gulf of Guinea. Three data structuring strategies are designed to address gaps of varying lengths. The proposed model achieves strong performance, with RMSE ≈ 0.05 m, MAPE < 5%, and R2 ≈ 0.96. The reconstructed series are validated using harmonic analysis, demonstrating accurate preservation of tidal dynamics. Additional evaluation through tidal constituent analysis confirms the reliability of the reconstructed data. Results further indicate that the Gulf of Guinea is characterized by an asymmetrical semi-diurnal tidal regime, consistent with existing literature.
References
[1]
Chang, J.Y. and Feng, S.J. (2022) A Constitutive Model for Geosynthetic Interfaces Considering Nonlinear Softening Behavior. Computers and Geotechnics, 143, Article 104633. https://doi.org/10.1016/j.compgeo.2022.104633
[2]
Del-Rosal-Salido, J., Folgueras, P., Bermúdez, M., Ortega-Sánchez, M. and Losada, M.á. (2021) Flood Management Challenges in Transitional Environments: Assessing the Effects of Sea-Level Rise on Compound Flooding in the 21st Century. Coastal Engineering, 167, Article 103872. https://doi.org/10.1016/j.coastaleng.2021.103872
[3]
Intergovernmental Panel on Climate Change (2007) Changements Climatiques. Cambridge University Press.
[4]
Intergovernmental Panel on Climate Change (2014) Summary for Policymakers. In: Climate Change 2013: The Physical Science Basis, Cambridge University Press, 1-30.
[5]
Intergovernmental Panel on Climate Change (2014) Technical Summary. In: Climate Change 2013: The Physical Science Basis, Cambridge University Press, 31-116.
[6]
Daron, J., Macadam, I., Kanamaru, H., Cinco, T., Katzfey, J., Scannell, C., et al. (2018) Providing Future Climate Projections Using Multiple Models and Methods: Insights from the Philippines. Climatic Change, 148, 187-203. https://doi.org/10.1007/s10584-018-2183-5
[7]
Ricart, S., Gandolfi, C. and Castelletti, A. (2023) Climate Change Awareness, Perceived Impacts, and Adaptation from Farmers’ Experience and Behavior: A Triple-Loop Review. Regional Environmental Change, 23, Article No. 82. https://doi.org/10.1007/s10113-023-02078-3
[8]
Pappas, C., Papalexiou, S.M. and Koutsoyiannis, D. (2014) A Quick Gap Filling of Missing Hydrometeorological Data. Journal of Geophysical Research: Atmospheres, 119, 9290-9300. https://doi.org/10.1002/2014jd021633
[9]
Douglas, B.C. (1991) Global Sea Level Rise. Journal of Geophysical Research: Oceans, 96, 6981-6992. https://doi.org/10.1029/91jc00064
[10]
Pouvreau, N. (2008) Trois cents ans de mesures marégraphiques en France: Outils, méthodes et tendances des composantes du niveau de la mer au port de Brest.
[11]
Gouriou, T. (2012) Evolution des composantes du niveau marin à partir d’observations in Situ: Application aux marégraphes du littoral fran？ais. La Rochelle.
[12]
Woodworth, P., Aman, A. and Aarup, T. (2007) Sea Level Monitoring in Africa. African Journal of Marine Science, 29, 321-330. https://doi.org/10.2989/ajms.2007.29.3.2.332
[13]
Fossi Fotsi, Y., Pouvreau, N., Brenon, I., Onguene, R. and Etame, J. (2019) Temporal (1948–2012) and Dynamic Evolution of the Wouri Estuary Coastline within the Gulf of Guinea. Journal of Marine Science and Engineering, 7, Article 343. https://doi.org/10.3390/jmse7100343
[14]
Djeumeni Noubissie, L., Birol, F., Onguene, R., Léger, F., Ni？o, F. and Dzonde Naoussi, R. (2023) Virtual Coastal Altimetry Tide Gauges along the West African Coast. Estuarine, Coastal and Shelf Science, 296, Article 108600. https://doi.org/10.1016/j.ecss.2023.108600
[15]
Bleidorn, M.T., Pinto, W.D.P., Schmidt, I.M., Mendon？a, A.S.F. and Reis, J.A.T.D. (2022) Methodological Approaches for Imputing Missing Data into Monthly Flows Series. Ambiente e Agua—An Interdisciplinary Journal of Applied Science, 17, 1-27. https://doi.org/10.4136/ambi-agua.2795
[16]
Fang, C. and Wang, C. (2020) Time Series Data Imputation: A Survey on Deep Learning Approaches. http://arxiv.org/abs/2011.11347
[17]
Tzoumpas, K., Estrada, A., Miraglio, P. and Zambelli, P. (2023) A Data Filling Methodology for Time Series Based on CNN and (Bi)LSTM Neural Networks. http://arxiv.org/abs/2204.09994
[18]
Li, J., Wan, H. and Shang, S. (2020) Comparison of Interpolation Methods for Mapping Layered Soil Particle-Size Fractions and Texture in an Arid Oasis. Catena, 190, Article 104514. https://doi.org/10.1016/j.catena.2020.104514
[19]
Kumar, R. and Baskar, S. (2018) Hybrid BSQI-WENO Based Numerical Scheme for Hyperbolic Conservation Laws.
[20]
Janbain, I., Deloffre, J., Jardani, A., Vu, M.T. and Massei, N. (2023) Use of Long Short-Term Memory Network (LSTM) in the Reconstruction of Missing Water Level Data in the River Seine. Hydrological Sciences Journal, 68, 1372-1390. https://doi.org/10.1080/02626667.2023.2221791
[21]
Moffat, A.M., Papale, D., Reichstein, M., Hollinger, D.Y., Richardson, A.D., Barr, A.G., et al. (2007) Comprehensive Comparison of Gap-Filling Techniques for Eddy Covariance Net Carbon Fluxes. Agricultural and Forest Meteorology, 147, 209-232. https://doi.org/10.1016/j.agrformet.2007.08.011
[22]
Afrifa-Yamoah, E., Mueller, U.A., Taylor, S.M. and Fisher, A.J. (2020) Missing Data Imputation of High-Resolution Temporal Climate Time Series Data. Meteorological Applications, 27, e1873. https://doi.org/10.1002/met.1873
[23]
Londhe, S.N. and Panchang, V. (2007) Correlation of Wave Data from Buoy Networks. Estuarine, Coastal and Shelf Science, 74, 481-492. https://doi.org/10.1016/j.ecss.2007.05.003
[24]
Zamani, A., Solomatine, D., Azimian, A. and Heemink, A. (2008) Learning from Data for Wind-Wave Forecasting. Ocean Engineering, 35, 953-962. https://doi.org/10.1016/j.oceaneng.2008.03.007
[25]
J？rges, C., Berkenbrink, C. and Stumpe, B. (2021) Prediction and Reconstruction of Ocean Wave Heights Based on Bathymetric Data Using LSTM Neural Networks. Ocean Engineering, 232, Article 109046. https://doi.org/10.1016/j.oceaneng.2021.109046
[26]
Minuzzi, F.C. and Farina, L. (2023) A Deep Learning Approach to Predict Significant Wave Height Using Long Short-Term Memory. Ocean Modelling, 181, Article 102151. https://doi.org/10.1016/j.ocemod.2022.102151
[27]
Primo de Siqueira, B.V. and Paiva, A.D.M. (2021) Using Neural Network to Improve Sea Level Prediction along the Southeastern Brazilian Coast. Ocean Modelling, 168, Article 101898. https://doi.org/10.1016/j.ocemod.2021.101898
[28]
Kumar, N.K., Savitha, R. and Mamun, A.A. (2017) Regional Ocean Wave Height Prediction Using Sequential Learning Neural Networks. Ocean Engineering, 129, 605-612. https://doi.org/10.1016/j.oceaneng.2016.10.033
[29]
Kumar, A., Dwivedi, S., Rajak, D.R. and Pandey, A.C. (2018) Impact of Air-Sea Forcings on the Southern Ocean Sea Ice Variability around the Indian Antarctic Stations. Polar Science, 18, 197-212. https://doi.org/10.1016/j.polar.2018.05.005
[30]
Stefanakos, C.N., Schinas, O. and Eidnes, G. (2014) Application of Fuzzy Time Series Techniques in Wind and Wave Data Forecasting. Volume 4B: Structures, Safety and Reliability, San Francisco, 8-13 June 2014, V04BT02A046. https://doi.org/10.1115/omae2014-24612
[31]
LeCun, Y., Bengio, Y. and Hinton, G. (2015) Deep Learning. Nature, 521, 436-444. https://doi.org/10.1038/nature14539
[32]
Medina, J.R. and Serrano-Hidalgo, O. (2006) Discussion of “Predictions of Missing Wave Data by Recurrent Neuronets” by Can Elmar Balas, Levent Ko？, and Lale Balas. Journal of Waterway, Port, Coastal, and Ocean Engineering, 132, 71-72. https://doi.org/10.1061/(asce)0733-950x(2006)132:1(71)
[33]
Hochreiter, S. and Schmidhuber, J. (1997) Long Short-Term Memory. Neural Computation, 9, 1735-1780. https://doi.org/10.1162/neco.1997.9.8.1735
[34]
Graves, A., Jaitly, N. and Mohamed, A. (2013) Hybrid Speech Recognition with Deep Bidirectional LSTM. 2013 IEEE Workshop on Automatic Speech Recognition and Understanding, Olomouc, 8-12 December 2013, 273-278. https://doi.org/10.1109/asru.2013.6707742
[35]
Wu, Y.H., Schuster, M., Chen, Z.F., et al. (2016) Google’s Neural Machine Translation System: Bridging the Gap between Human and Machine Translation. https://doi.org/10.48550/arXiv.1609.08144
[36]
Ryu, K., Shin, N.Y., Kim, D.H. and Nam, Y. (2019) Synthesizing T1 Weighted MPRAGE Image from Multi Echo GRE Images via Deep Neural Network. MagneticResonanceImaging, 64, 13-20. https://doi.org/10.1016/j.mri.2019.04.002
[37]
Kim, H.Y. and Won, C.H. (2018) Forecasting the Volatility of Stock Price Index: A Hybrid Model Integrating LSTM with Multiple Garch-Type Models. Expert Systems with Applications, 103, 25-37. https://doi.org/10.1016/j.eswa.2018.03.002
[38]
Liu, H., Mi, X. and Li, Y. (2018) Wind Speed Forecasting Method Based on Deep Learning Strategy Using Empirical Wavelet Transform, Long Short Term Memory Neural Network and Elman Neural Network. Energy Conversion and Management, 156, 498-514. https://doi.org/10.1016/j.enconman.2017.11.053
[39]
Sarkar, P.P., Janardhan, P. and Roy, P. (2020) Prediction of Sea Surface Temperatures Using Deep Learning Neural Networks. SN Applied Sciences, 2, Article 1458. https://doi.org/10.1007/s42452-020-03239-3
[40]
Singla, P., Duhan, M. and Saroha, S. (2022) An Ensemble Method to Forecast 24-H Ahead Solar Irradiance Using Wavelet Decomposition and BiLSTM Deep Learning Network. EarthScienceInformatics, 15, 291-306. https://doi.org/10.1007/s12145-021-00723-1
[41]
Abhishek, K., Singh, M.P., Ghosh, S. and Anand, A. (2012) Weather Forecasting Model Using Artificial Neural Network. ProcediaTechnology, 4, 311-318. https://doi.org/10.1016/j.protcy.2012.05.047
[42]
Lee, E.J., Kim, K. and Park, J.H. (2022) Reconstruction of Long-Term Sea-Level Data Gaps of Tide Gauge Records Using a Neural Network Operator. FrontiersinMarineScience, 9, Article 1037697. https://doi.org/10.3389/fmars.2022.1037697
[43]
Janbain, I., Jardani, A., Deloffre, J. and Massei, N. (2023) Deep Learning Approaches for Numerical Modeling and Historical Reconstruction of Water Quality Parameters in Lower Seine. Water, 15, Article 1773. https://doi.org/10.3390/w15091773
[44]
Caldwell, J.D., Lindsay, L., Giannini, V., Vurgaftman, I., Reinecke, T.L., Maier, S.A., et al. (2015) Low-Loss, Infrared and Terahertz Nanophotonics Using Surface Phonon Polaritons. Nanophotonics, 4, 44-68. https://doi.org/10.1515/nanoph-2014-0003
[45]
Onguene, R., Pemha, E., Lyard, F., Du-Penhoat, Y., Nkoue, G., Duhaut, T., et al. (2015) Overview of Tide Characteristics in Cameroon Coastal Areas Using Recent Observations. Open Journal of Marine Science, 5, 81-98. https://doi.org/10.4236/ojms.2015.51008
[46]
Fossi Fotsi, Y., Brenon, I., Pouvreau, N., Ferret, Y., Latapy, A., Onguene, R., et al. (2023) Exploring Tidal Dynamics in the Wouri Estuary, Cameroon. Continental Shelf Research, 259, Article 104982. https://doi.org/10.1016/j.csr.2023.104982
[47]
Rozenberg, G., B？ck, T. and Kok, J.N. (2010) Handbook of Natural Computing. Springer.
[48]
Montavon, G., Samek, W. and Müller, K. (2018) Methods for Interpreting and Understanding Deep Neural Networks. Digital Signal Processing, 73, 1-15. https://doi.org/10.1016/j.dsp.2017.10.011
[49]
Büyük？ahin, ü.？. and Ertekin, ？. (2019) Improving Forecasting Accuracy of Time Series Data Using a New ARIMA-ANN Hybrid Method and Empirical Mode Decomposition. Neurocomputing, 361, 151-163. https://doi.org/10.1016/j.neucom.2019.05.099
[50]
Aichouri, I., Hani, A., Bougherira, N., Djabri, L., Chaffai, H. and Lallahem, S. (2015) River Flow Model Using Artificial Neural Networks. Energy Procedia, 74, 1007-1014. https://doi.org/10.1016/j.egypro.2015.07.832
[51]
Tang, J., Liu, F., Zhang, W., Ke, R. and Zou, Y. (2018) Lane-Changes Prediction Based on Adaptive Fuzzy Neural Network. Expert Systems with Applications, 91, 452-463. https://doi.org/10.1016/j.eswa.2017.09.025
[52]
McCulloch, W.S. and Pitts, W. (1943) A Logical Calculus of the Ideas Immanent in Nervous Activity. The Bulletin of Mathematical Biophysics, 5, 115-133. https://doi.org/10.1007/bf02478259
[53]
Rumelhart, D.E., Hinton, G.E. and Williams, R.J. (1986) Learning Representations by Back-Propagating Errors. Nature, 323, 533-536. https://doi.org/10.1038/323533a0
[54]
Bengio, Y., Simard, P. and Frasconi, P. (1994) Learning Long-Term Dependencies with Gradient Descent Is Difficult. IEEE Transactions on Neural Networks, 5, 157-166. https://doi.org/10.1109/72.279181
[55]
Kingma, D.P. and Ba, J. (2014) Adam: A Method for Stochastic Optimization. https://doi.org/10.48550/arXiv.1412.6980
[56]
Sagheer, A. and Kotb, M. (2019) Time Series Forecasting of Petroleum Production Using Deep LSTM Recurrent Networks. Neurocomputing, 323, 203-213. https://doi.org/10.1016/j.neucom.2018.09.082
[57]
van der Walt, S., Colbert, S.C. and Varoquaux, G. (2011) The Numpy Array: A Structure for Efficient Numerical Computation. Computing in Science & Engineering, 13, 22-30. https://doi.org/10.1109/mcse.2011.37
[58]
Vu, M.T., Jardani, A., Massei, N. and Fournier, M. (2021) Reconstruction of Missing Groundwater Level Data by Using Long Short-Term Memory (LSTM) Deep Neural Network. Journal of Hydrology, 597, Article 125776. https://doi.org/10.1016/j.jhydrol.2020.125776
[59]
Kilinc, O. and Uysal, I. (2018) GAR: An Efficient and Scalable Graph-Based Activity Regularization for Semi-Supervised Learning. Neurocomputing, 296, 46-54. https://doi.org/10.1016/j.neucom.2018.03.028
[60]
Kampffmeyer, M., L？kse, S., Bianchi, F.M., Livi, L., Salberg, A. and Jenssen, R. (2019) Deep Divergence-Based Approach to Clustering. Neural Networks, 113, 91-101. https://doi.org/10.1016/j.neunet.2019.01.015
[61]
Bergstra, J., Bardenet, R., Bengio, Y. and Kégl, B. (2011) Algorithms for Hyper-Parameter Optimization. https://proceedings.neurips.cc/paper_files/paper/2011/hash/86e8f7ab32cfd12577bc2619bc635690-Abstract.html
[62]
Snoek, J., Larochelle, H. and Adams, R.P. (2012) Practical Bayesian Optimization of Machine Learning Algorithms. https://proceedings.neurips.cc/paper_files/paper/2012/hash/05311655a15b75fab86956663e1819cd-Abstract.html
[63]
Brochu, E., Cora, V.M. and de Freitas, N. (2010) A Tutorial on Bayesian Optimization of Expensive Cost Functions, with Application to Active User Modeling and Hierarchical Reinforcement Learning. https://arxiv.org/abs/1012.2599
[64]
Pawlowicz, R., Beardsley, B. and Lentz, S. (2002) Classical Tidal Harmonic Analysis Including Error Estimates in MATLAB Using T_Tide. Computers&Geosciences, 28, 929-937. https://doi.org/10.1016/s0098-3004(02)00013-4
[65]
Simon, B. (2007) La marée océanique c？tière. In: Collection Synthèses, Institut océanographique, 105-123.
[66]
Tranchant, Y.T., Testut, L., Chupin, C., Ballu, V. and Bonnefond, P. (2021) Near-Coast Tide Model Validation Using GNSS Unmanned Surface Vehicle (USV), a Case Study in the Pertuis Charentais (France). Remote Sensing, 13, Article 2886.
[67]
Yang, C.H., Wu, C.H., Hsieh, C.M., et al. (2021) Deep Learning for Imputation and Forecasting Tidal Level. IEEEJournalofOceanicEngineering, 46, 1261-1271. https://doi.org/10.1109/joe.2021.3073931
[68]
Bai, S., Kolter, J.Z. and Koltun, V. (2018) An Empirical Evaluation of Generic Convolutional and Recurrent Networks for Sequence Modeling. https://doi.org/10.48550/ARXIV.1803.01271
[69]
Zhang, Q., Wang, H., Dong, J., Zhong, G. and Sun, X. (2017) Prediction of Sea Surface Temperature Using Long Short-Term Memory. IEEEGeoscienceandRemoteSensingLetters, 14, 1745-1749. https://doi.org/10.1109/lgrs.2017.2733548
[70]
Pugh, D. and Woodworth, P.L. (2014) Tidal Analysis and Prediction. In: Sea-Level Science: Understanding Tides, Surges, Tsunamis and Mean Sea-Level Changes, Cambridge University Press, 60-96.
[71]
Xu, S., Dai, D., Cui, X., Yin, X., Jiang, S., Pan, H., et al. (2023) A Deep Learning Approach to Predict Sea Surface Temperature Based on Multiple Modes. Ocean Modelling, 181, Article 102158. https://doi.org/10.1016/j.ocemod.2022.102158
[72]
Fang, K., Kifer, D., Lawson, K., Feng, D. and Shen, C. (2022) The Data Synergy Effects of Time-Series Deep Learning Models in Hydrology. Water Resources Research, 58, e2021WR029583. https://doi.org/10.1029/2021wr029583
