Meteorological Time Series Interpolation: A Literature Review of Classical, Machine Learning and Deep Learning Approaches
DOI:
https://doi.org/10.61467/2007.1558.2027.v18i1.1516Keywords:
Meteorological time series, interpolation, missing data, imputation, neural networks, deep learning, forecasting climate data, Series temporales meteorológicas, redes neuronales, aprendizaje profundo, predicción de datos climáticosAbstract
Meteorological time series are frequently affected by missing observations caused by sensor failures, communication problems, maintenance activities, or data acquisition errors. Subsequent analyses, including forecasting, climate monitoring, hydrological assessment, and environmental decision-making, may therefore be biased or weakened. In this review, interpolation methods for meteorological time series are reviewed, including classical, statistical, machine learning, and deep learning approaches. Emphasis is placed on the distinction between prediction and interpolation, since both tasks are often treated as equivalent. The literature is also organized according to reconstruction strategy, including recursive, bidirectional, probabilistic or generative, and hybrid or evolutionary approaches. Current challenges, evaluation practices, open gaps, and future trends for meteorological data reconstruction are discussed.
Spanish-language metadata / Metadatos en español
Título en español:
Interpolación de series temporales meteorológicas: una revisión de la literatura sobre enfoques clásicos, de aprendizaje automático y aprendizaje profundo
Resumen:
Las series temporales meteorológicas se ven afectadas con frecuencia por observaciones faltantes causadas por fallos de sensores, problemas de comunicación, actividades de mantenimiento o errores en la adquisición de datos. En consecuencia, los análisis posteriores, incluidos la predicción, la monitorización climática, la evaluación hidrológica y la toma de decisiones ambientales, pueden presentar sesgos o verse comprometidos.
En esta revisión se examinan los métodos de interpolación aplicados a series temporales meteorológicas, incluidos los enfoques clásicos, estadísticos, de aprendizaje automático y de aprendizaje profundo. Se hace especial hincapié en la distinción entre predicción e interpolación, dado que ambas tareas se tratan con frecuencia como equivalentes. La literatura también se organiza según la estrategia de reconstrucción empleada, incluidos los enfoques recursivos, bidireccionales, probabilísticos o generativos, e híbridos o evolutivos.
Asimismo, se analizan los desafíos actuales, las prácticas de evaluación, las brechas de investigación existentes y las tendencias futuras en la reconstrucción de datos meteorológicos.
Palabras Claves:
Series temporales meteorológicas, interpolación, datos faltantes, imputación, redes neuronales, aprendizaje profundo, predicción de datos climáticos.
Smart citations:
SciteAI.
Dimensions.
Open Alex.
References
Ahmed, N. K., Atiya, A. F., El Gayar, N., & El-Shishiny, H. (2010). An empirical comparison of machine learning models for time series forecasting. Econometric Reviews, 29(5–6), 594–621. https://doi.org/10.1080/07474938.2010.481556
Ben Taieb, S., Bontempi, G., Atiya, A. F., & Sorjamaa, A. (2012). A review and comparison of strategies for multi-step ahead time series forecasting based on the NN5 forecasting competition. Expert Systems with Applications, 39(8), 7067–7083. https://doi.org/10.1016/j.eswa.2012.01.039
Bontempi, G., Ben Taieb, S., & Le Borgne, Y.-A. (2013). Machine learning strategies for time series forecasting. In M.-A. Aufaure & E. Zimányi (Eds.), Business intelligence: Second European Summer School, eBISS 2012, Brussels, Belgium, July 15–21, 2012, tutorial lectures (pp. 62–77). Springer. https://doi.org/10.1007/978-3-642-36318-4_3
Breiman, L. (2001). Random forests. Machine Learning, 45, 5–32. https://doi.org/10.1023/A:1010933404324
Cao, W., Wang, D., Li, J., Zhou, H., Li, L., & Li, Y. (2018). BRITS: Bidirectional recurrent imputation for time series. Advances in Neural Information Processing Systems, 31.
Che, Z., Purushotham, S., Cho, K., Sontag, D., & Liu, Y. (2018). Recurrent neural networks for multivariate time series with missing values. Scientific Reports, 8, Article 6085. https://doi.org/10.1038/s41598-018-24271-9
Chen, Y., Kopp, G. A., & Surry, D. (2002). Interpolation of wind-induced pressure time series with an artificial neural network. Journal of Wind Engineering and Industrial Aerodynamics, 90(6), 589–615. https://doi.org/10.1016/S0167-6105(02)00155-1
Cho, K., van Merriënboer, B., Gulcehre, C., Bahdanau, D., Bougares, F., Schwenk, H., & Bengio, Y. (2014). Learning phrase representations using RNN encoder–decoder for statistical machine translation. In Proceedings of the 2014 Conference on Empirical Methods in Natural Language Processing (EMNLP) (pp. 1724–1734). Association for Computational Linguistics. https://doi.org/10.3115/v1/D14-1179
Cressie, N. (1990). The origins of kriging. Mathematical Geology, 22(3), 239–252. https://doi.org/10.1007/BF00889887
De Gooijer, J. G., & Hyndman, R. J. (2006). 25 years of time series forecasting. International Journal of Forecasting, 22(3), 443–473. https://doi.org/10.1016/j.ijforecast.2006.01.001
Du, W., Côté, D., & Liu, Y. (2023). SAITS: Self-attention-based imputation for time series. Expert Systems with Applications, 219, Article 119619. https://doi.org/10.1016/j.eswa.2023.119619
Fang, C., & Wang, C. (2020). Time series data imputation: A survey on deep learning approaches [Preprint]. arXiv. https://doi.org/10.48550/arXiv.2011.11347
Floreano, D., Dürr, P., & Mattiussi, C. (2008). Neuroevolution: From architectures to learning. Evolutionary Intelligence, 1(1), 47–62. https://doi.org/10.1007/s12065-007-0002-4
Fortuin, V., Baranchuk, D., Raetsch, G., & Mandt, S. (2020). GP-VAE: Deep probabilistic time series imputation. In Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics (Vol. 108, pp. 1651–1661). PMLR.
Gardner, M. W., & Dorling, S. R. (1998). Artificial neural networks (the multilayer perceptron)—A review of applications in the atmospheric sciences. Atmospheric Environment, 32(14–15), 2627–2636. https://doi.org/10.1016/S1352-2310(97)00447-0
Goodfellow, I., Bengio, Y., & Courville, A. (2016). Deep learning. MIT Press.
Haylock, M. R., Hofstra, N., Klein Tank, A. M. G., Klok, E. J., Jones, P. D., & New, M. (2008). A European daily high-resolution gridded data set of surface temperature and precipitation for 1950–2006. Journal of Geophysical Research: Atmospheres, 113, Article D20119. https://doi.org/10.1029/2008JD010201
Hochreiter, S., & Schmidhuber, J. (1997). Long short-term memory. Neural Computation, 9(8), 1735–1780. https://doi.org/10.1162/neco.1997.9.8.1735
Hocke, K., & Kämpfer, N. (2009). Gap filling and noise reduction of unevenly sampled data by means of the Lomb-Scargle periodogram. Atmospheric Chemistry and Physics, 9, 4197–4206. https://doi.org/10.5194/acp-9-4197-2009
Hofstra, N., Haylock, M., New, M., Jones, P. D., & Frei, C. (2008). Comparison of six methods for the interpolation of daily, European climate data. Journal of Geophysical Research: Atmospheres, 113, Article D21110. https://doi.org/10.1029/2008JD010100
Junninen, H., Niska, H., Tuppurainen, K., Ruuskanen, J., & Kolehmainen, M. (2004). Methods for imputation of missing values in air quality data sets. Atmospheric Environment, 38(18), 2895–2907. https://doi.org/10.1016/j.atmosenv.2004.02.026
Kalman, R. E. (1960). A new approach to linear filtering and prediction problems. Journal of Basic Engineering, 82(1), 35–45. https://doi.org/10.1115/1.3662552
Kazijevs, M., & Samad, M. D. (2023). Deep imputation of missing values in time series health data: A review with benchmarking. Journal of Biomedical Informatics, 144, Article 104440. https://doi.org/10.1016/j.jbi.2023.104440
Kondrashov, D., & Ghil, M. (2006). Spatio-temporal filling of missing points in geophysical data sets. Nonlinear Processes in Geophysics, 13, 151–159. https://doi.org/10.5194/npg-13-151-2006
Lepot, M., Aubin, J.-B., & Clemens, F. H. L. R. (2017). Interpolation in time series: An introductive overview of existing methods, their performance criteria and uncertainty assessment. Water, 9(10), Article 796. https://doi.org/10.3390/w9100796
Li, J., & Heap, A. D. (2014). Spatial interpolation methods applied in the environmental sciences: A review. Environmental Modelling & Software, 53, 173–189. https://doi.org/10.1016/j.envsoft.2013.12.008
Liu, Y., Yu, R., Zheng, S., Zhan, E., & Yue, Y. (2019). NAOMI: Non-autoregressive multiresolution sequence imputation [Preprint]. arXiv. https://doi.org/10.48550/arXiv.1901.10946
Liu, Y., Hu, T., Zhang, H., Wu, H., Wang, S., Ma, L., & Long, M. (2024). iTransformer: Inverted transformers are effective for time series forecasting. In The Twelfth International Conference on Learning Representations.
Matheron, G. (1963). Principles of geostatistics. Economic Geology, 58(8), 1246–1266. https://doi.org/10.2113/gsecongeo.58.8.1246
Miikkulainen, R., Liang, J., Meyerson, E., Rawal, A., Fink, D., Francon, O., Raju, B., Shahrzad, H., Navruzyan, A., Duffy, N., & Hodjat, B. (2019). Evolving deep neural networks. In R. Kozma, C. Alippi, Y. Choe, & F. C. Morabito (Eds.), Artificial intelligence in the age of neural networks and brain computing (pp. 293–312). Academic Press. https://doi.org/10.1016/B978-0-12-815480-9.00015-3
Mitra, R., McGough, S. F., Chakraborti, T., Holmes, C., Copping, R., Hagenbuch, N., Biedermann, S., Noonan, J., Lehmann, B., Shenvi, A., Doan, X. V., Leslie, D., Bianconi, G., Sanchez-Garcia, R., Davies, A., Mackintosh, M., Andrinopoulou, E.-R., Basiri, A., Harbron, C., & MacArthur, B. D. (2023). Learning from data with structured missingness. Nature Machine Intelligence, 5, 13–23. https://doi.org/10.1038/s42256-022-00596-z
Moritz, S., & Bartz-Beielstein, T. (2017). imputeTS: Time series missing value imputation in R. The R Journal, 9(1), 207–218. https://doi.org/10.32614/RJ-2017-009
Musial, J. P., Verstraete, M. M., & Gobron, N. (2011). Technical note: Comparing the effectiveness of recent algorithms to fill and smooth incomplete and noisy time series. Atmospheric Chemistry and Physics, 11, 7905–7923. https://doi.org/10.5194/acp-11-7905-2011
Nie, Y., Nguyen, N. H., Sinthong, P., & Kalagnanam, J. (2023). A time series is worth 64 words: Long-term forecasting with transformers. In The Eleventh International Conference on Learning Representations.
Rasmussen, C. E., & Williams, C. K. I. (2006). Gaussian processes for machine learning. MIT Press.
Real, E., Aggarwal, A., Huang, Y., & Le, Q. V. (2019). Regularized evolution for image classifier architecture search. Proceedings of the AAAI Conference on Artificial Intelligence, 33(1), 4780–4789. https://doi.org/10.1609/aaai.v33i01.33014780
Rubin, D. B. (1976). Inference and missing data. Biometrika, 63(3), 581–592. https://doi.org/10.1093/biomet/63.3.581
Rudin, C. (2019). Stop explaining black box machine learning models for high stakes decisions and use interpretable models instead. Nature Machine Intelligence, 1, 206–215. https://doi.org/10.1038/s42256-019-0048-x
Schafer, J. L., & Graham, J. W. (2002). Missing data: Our view of the state of the art. Psychological Methods, 7(2), 147–177. https://doi.org/10.1037/1082-989X.7.2.147
Shumway, R. H., & Stoffer, D. S. (1982). An approach to time series smoothing and forecasting using the EM algorithm. Journal of Time Series Analysis, 3(4), 253–264. https://doi.org/10.1111/j.1467-9892.1982.tb00349.x
Smola, A. J., & Schölkopf, B. (2004). A tutorial on support vector regression. Statistics and Computing, 14(3), 199–222. https://doi.org/10.1023/B:STCO.0000035301.49549.88
Stanley, K. O., & Miikkulainen, R. (2002). Evolving neural networks through augmenting topologies. Evolutionary Computation, 10(2), 99–127. https://doi.org/10.1162/106365602320169811
Stanley, K. O., Clune, J., Lehman, J., & Miikkulainen, R. (2019). Designing neural networks through neuroevolution. Nature Machine Intelligence, 1, 24–35. https://doi.org/10.1038/s42256-018-0006-z
Stekhoven, D. J., & Bühlmann, P. (2012). MissForest—Non-parametric missing value imputation for mixed-type data. Bioinformatics, 28(1), 112–118. https://doi.org/10.1093/bioinformatics/btr597
Tashiro, Y., Song, J., Song, Y., & Ermon, S. (2021). CSDI: Conditional score-based diffusion models for probabilistic time series imputation. Advances in Neural Information Processing Systems, 34, 24804–24816.
Troyanskaya, O., Cantor, M., Sherlock, G., Brown, P., Hastie, T., Tibshirani, R., Botstein, D., & Altman, R. B. (2001). Missing value estimation methods for DNA microarrays. Bioinformatics, 17(6), 520–525. https://doi.org/10.1093/bioinformatics/17.6.520
Vaswani, A., Shazeer, N., Parmar, N., Uszkoreit, J., Jones, L., Gomez, A. N., Kaiser, Ł., & Polosukhin, I. (2017). Attention is all you need. Advances in Neural Information Processing Systems, 30, 5998–6008.
Wang, J., Du, W., Yang, Y., Qian, L., Cao, W., Zhang, K., Wang, W., Liang, Y., & Wen, Q. (2025). Deep learning for multivariate time series imputation: A survey. In Proceedings of the Thirty-Fourth International Joint Conference on Artificial Intelligence (pp. 10696–10704). https://doi.org/10.24963/ijcai.2025/1187
White, I. R., Royston, P., & Wood, A. M. (2011). Multiple imputation using chained equations: Issues and guidance for practice. Statistics in Medicine, 30(4), 377–399. https://doi.org/10.1002/sim.4067
Whitley, D., Starkweather, T., & Bogart, C. (1990). Genetic algorithms and neural networks: Optimizing connections and connectivity. Parallel Computing, 14(3), 347–361. https://doi.org/10.1016/0167-8191(90)90086-O
Wu, H., Xu, J., Wang, J., & Long, M. (2021). Autoformer: Decomposition transformers with auto-correlation for long-term series forecasting [Preprint]. arXiv. https://doi.org/10.48550/arXiv.2106.13008
Wu, H., Hu, T., Liu, Y., Zhou, H., Wang, J., & Long, M. (2023). TimesNet: Temporal 2D-variation modeling for general time series analysis. In The Eleventh International Conference on Learning Representations.
Yao, X. (1999). Evolving artificial neural networks. Proceedings of the IEEE, 87(9), 1423–1447. https://doi.org/10.1109/5.784219
Yao, X., & Liu, Y. (1997). A new evolutionary system for evolving artificial neural networks. IEEE Transactions on Neural Networks, 8(3), 694–713. https://doi.org/10.1109/72.572107
Yoon, J., Jordon, J., & van der Schaar, M. (2018). GAIN: Missing data imputation using generative adversarial nets. In Proceedings of the 35th International Conference on Machine Learning (Vol. 80, pp. 5689–5698). PMLR.
Zhang, G., Patuwo, B. E., & Hu, M. Y. (1998). Forecasting with artificial neural networks: The state of the art. International Journal of Forecasting, 14(1), 35–62. https://doi.org/10.1016/S0169-2070(97)00044-7
Zhou, H., Zhang, S., Peng, J., Zhang, S., Li, J., Xiong, H., & Zhang, W. (2021). Informer: Beyond efficient transformer for long sequence time-series forecasting. Proceedings of the AAAI Conference on Artificial Intelligence, 35(12), 11106–11115. https://doi.org/10.1609/aaai.v35i12.17325
Žukovič, M., & Hristopulos, D. T. (2008). Environmental time series interpolation based on Spartan random processes. Atmospheric Environment, 42(33), 7669–7678. https://doi.org/10.1016/j.atmosenv.2008.05.062
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2026 International Journal of Combinatorial Optimization Problems and Informatics
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
