{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T14:43:21Z","timestamp":1777560201964,"version":"3.51.4"},"reference-count":33,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2022,12,12]],"date-time":"2022-12-12T00:00:00Z","timestamp":1670803200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["2021YFC3101600"],"award-info":[{"award-number":["2021YFC3101600"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Information"],"abstract":"<jats:p>The multi-model ensemble (MME) forecast for meteorological elements has been proved many times to be more skillful than the single model. It improves the forecast quality by integrating multiple sets of numerical forecast results with different spatial-temporal characteristics. Currently, the main numerical forecast results present a grid structure formed by longitude and latitude lines in space and a special two-dimensional time structure in time, namely the initial time and the lead time, compared with the traditional one-dimensional time. These characteristics mean that many MME methods have limitations in further improving forecast quality. Focusing on this problem, we propose a deep MME forecast method that suits the special structure. At spatial level, our model uses window self-attention and shifted window attention to aggregate information. At temporal level, we propose a recurrent like neural network with rolling structure (Roll-RLNN) which is more suitable for two-dimensional time structure that widely exists in the institutions of numerical weather prediction (NWP) with running service. In this paper, we test the MME forecast for sea level pressure as the forecast characteristics of the essential meteorological element vary clearly across institutions, and the results show that our model structure is effective and can make significant forecast improvements.<\/jats:p>","DOI":"10.3390\/info13120577","type":"journal-article","created":{"date-parts":[[2022,12,13]],"date-time":"2022-12-13T03:32:32Z","timestamp":1670902352000},"page":"577","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["SWAR: A Deep Multi-Model Ensemble Forecast Method with Spatial Grid and 2-D Time Structure Adaptability for Sea Level Pressure"],"prefix":"10.3390","volume":"13","author":[{"given":"Jingyun","family":"Zhang","sequence":"first","affiliation":[{"name":"Department of Computer Engineering and Science, Shanghai University, Shanghai 200444, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lingyu","family":"Xu","sequence":"additional","affiliation":[{"name":"Department of Computer Engineering and Science, Shanghai University, Shanghai 200444, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Baogang","family":"Jin","sequence":"additional","affiliation":[{"name":"Beijing Institute of Applied Meteorology, Beijing 100029, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,12,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"781","DOI":"10.1007\/BF02918678","article-title":"Ensemble forecast: A new approach to uncertainty and predictability","volume":"22","author":"Zhu","year":"2005","journal-title":"Adv. Atmos. Sci."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"432160","DOI":"10.1155\/2010\/432160","article-title":"Beating the Uncertainties: Ensemble Forecasting and Ensemble-Based Data Assimilation in Modern Numerical Weather Prediction","volume":"2010","author":"Zhang","year":"2010","journal-title":"Adv. Meteorol."},{"key":"ref_3","first-page":"234","article-title":"The rationale behind the success of multi-model ensembles in seasonal forecasting\u2014II. Calibration and combination","volume":"57","author":"Hagedorn","year":"2005","journal-title":"Tellus Ser. A-Dyn. Meteorol. Oceanol."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1002\/qj.210","article-title":"Can multi-model combination really enhance the prediction skill of probabilistic ensemble forecasts?","volume":"134","author":"Weigel","year":"2008","journal-title":"Q. J. R. Meteorol. Soc."},{"key":"ref_5","unstructured":"Deconinck, W. (2019). Development of Atlas, a flexible data structure framework. arXiv."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"336","DOI":"10.1002\/2015RG000513","article-title":"A review of multimodel superensemble forecasting for weather, seasonal climate, and hurricanes","volume":"54","author":"Krishnamurti","year":"2016","journal-title":"Rev. Geophys."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1007\/s13351-012-0104-5","article-title":"A comparison of three kinds of multimodel ensemble forecast techniques based on the TIGGE data","volume":"26","author":"Zhi","year":"2012","journal-title":"Acta Meteorol. Sin."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"2375","DOI":"10.1175\/MWR-D-15-0260.1","article-title":"Calibrated Ensemble Forecasts Using Quantile Regression Forests and Ensemble Model Output Statistics","volume":"144","author":"Taillardat","year":"2016","journal-title":"Mon. Weather Rev."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.gloplacha.2011.08.006","article-title":"Multi-model ensemble projections in temperature and precipitation extremes of the Tibetan Plateau in the 21st century","volume":"80\u201381","author":"Yang","year":"2012","journal-title":"Glob. Planet Chang."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Wang, K., Zheng, X., Wang, G., Liu, D., and Cui, N. (2020). A Multi-Model Ensemble Approach for Gold Mineral Prospectivity Mapping: A Case Study on the Beishan Region, Western China. Minerals, 126.","DOI":"10.3390\/min10121126"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"372","DOI":"10.1016\/j.asoc.2014.02.002","article-title":"Support vector machine applications in the field of hydrology: A review","volume":"19","author":"Raghavendra","year":"2014","journal-title":"Appl. Soft Comput. J."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Abuella, M., and Chowdhury, B. (2017, January 23\u201326). Random forest ensemble of support vector regression models for solar power forecasting. Proceedings of the 2017 IEEE Power & Energy Society Innovative Smart Grid Technologies Conference (ISGT), Washington, DC, USA.","DOI":"10.1109\/ISGT.2017.8086027"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"4891","DOI":"10.1002\/joc.5705","article-title":"Using multi-model ensembles of CMIP5 global climate models to reproduce observed monthly rainfall and temperature with machine learning methods in Australia","volume":"38","author":"Wang","year":"2018","journal-title":"Int. J. Climatol."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"467","DOI":"10.1002\/joc.5188","article-title":"Non-stationary bias correction of monthly CMIP5 temperature projections over China using a residual-based bagging tree model","volume":"38","author":"Tao","year":"2018","journal-title":"Int. J. Climatol."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"12616","DOI":"10.1029\/2018GL080704","article-title":"Toward Data-Driven Weather and Climate Forecasting: Approximating a Simple General Circulation Model With Deep Learning","volume":"45","author":"Scher","year":"2018","journal-title":"Geophys. Res. Lett."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1002\/met.254","article-title":"Multi-model ensemble (MME) prediction of rainfall using neural networks during monsoon season in India","volume":"19","author":"Kumar","year":"2012","journal-title":"Mereorol. Appl."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Kim, J., Kim, K., Cho, J., Kang, Y.Q., Yoon, H.-J., and Lee, Y.-W. (2019). Satellite-Based Prediction of Arctic Sea Ice Concentration Using a Deep Neural Network with Multi-Model Ensemble. Remote Sens., 11.","DOI":"10.3390\/rs11010019"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"127221","DOI":"10.1016\/j.jhydrol.2021.127221","article-title":"Hydrologic multi-model ensemble predictions using variational Bayesian deep learning","volume":"604","author":"Li","year":"2022","journal-title":"J. Hydrol."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"20200092","DOI":"10.1098\/rsta.2020.0092","article-title":"Deep learning for post-processing ensemble weather forecasts","volume":"379","author":"Yao","year":"2021","journal-title":"Philos. Trans. R. Soc. A"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"e2032","DOI":"10.1002\/met.2032","article-title":"Deep learning-based precipitation bias correction approach for Yin\u2013He global spectral model","volume":"28","author":"Hu","year":"2021","journal-title":"Mereorol. Appl."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Wang, X., He, X., Cao, Y., Liu, M., and Chua, T.-S. (2019, January 4\u20138). KGAT: Knowledge Graph Attention Network for Recommendation. Proceedings of the 25th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, Anchorage, AK, USA.","DOI":"10.1145\/3292500.3330989"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Qin, Y., Song, D., Cheng, H., Cheng, W., Jiang, G., and Cottrell, G.W. (2017, January 19\u201325). A Dual-Stage Attention-Based Recurrent Neural Network for Time Series Prediction. Proceedings of the 26th International Joint Conference on Artificial Intelligence, Melbourne, VIC, Australia.","DOI":"10.24963\/ijcai.2017\/366"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"178","DOI":"10.1016\/j.patrec.2021.01.036","article-title":"SmaAt-UNet: Precipitation Nowcasting Using a Small Attention-UNet Architecture","volume":"145","author":"Trebing","year":"2021","journal-title":"Pattern Recogn. Lett."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Sperber, M., Niehues, J., Neubig, G., St\u00fcker, S., and Waibel, A. (2018). Self-Attentional Acoustic Models. arXiv.","DOI":"10.21437\/Interspeech.2018-1910"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Li, X., Zhong, Z., Wu, J., Yang, Y., Lin, Z., and Liu, H. (2019, January 4\u20138). Expectation-Maximization Attention Networks for Semantic Segmentation. Proceedings of the 2019 IEEE\/CVF International Conference on Computer Vision (ICCV), Anchorage, AK, USA.","DOI":"10.1109\/ICCV.2019.00926"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1109\/JBHI.2020.2986926","article-title":"Multi-Scale Self-Guided Attention for Medical Image Segmentation","volume":"25","author":"Sinha","year":"2021","journal-title":"IEEE J. Biomed. Health Inform."},{"key":"ref_27","unstructured":"Beltagy, I., Fischer, P., Peters, M.E., and Cohan, A. (2020). Longformer: The Long-Document Transformer. arXiv."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1016\/j.neucom.2019.09.024","article-title":"A Window-Based Self-Attention approach for sentence encoding","volume":"375","author":"Huang","year":"2020","journal-title":"Neurocomputing"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Liu, Z., Lin, Y., Cao, Y., Hu, H., Wei, Y., Zhang, Z., Lin, S., and Guo, B. (November, January 27). Swin Transformer: Hierarchical Vision Transformer using Shifted Windows. Proceedings of the 2021 IEEE\/CVF International Conference on Computer Vision (ICCV), Seoul, Republic of Korea.","DOI":"10.1109\/ICCV48922.2021.00986"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"377","DOI":"10.3390\/meteorology1040024","article-title":"Initial-Value vs. Model-Induced Forecast Error: A New Perspective","volume":"1","author":"Jankov","year":"2022","journal-title":"Meteorology"},{"key":"ref_31","unstructured":"ECMWF (2022, November 03). Public Datasets. Available online: https:\/\/apps.ecmwf.int\/datasets\/."},{"key":"ref_32","unstructured":"Shi, X., Chen, Z., Wang, H., Yeung, D.-Y., Wong, W., and Woo, W. (2015, January 7\u201312). Convolutional LSTM Network: A Machine Learning Approach for Precipitation Nowcasting. Proceedings of the 28th International Conference on Neural Information Processing Systems (NIPS), Montreal, QC, Canada."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Ronneberger, O., Fischer, P., and Brox, T. (2015). U-Net: Convolutional Networks for Biomedical Image Segmentation. arXiv.","DOI":"10.1007\/978-3-319-24574-4_28"}],"container-title":["Information"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2078-2489\/13\/12\/577\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:39:49Z","timestamp":1760146789000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2078-2489\/13\/12\/577"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,12,12]]},"references-count":33,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2022,12]]}},"alternative-id":["info13120577"],"URL":"https:\/\/doi.org\/10.3390\/info13120577","relation":{},"ISSN":["2078-2489"],"issn-type":[{"value":"2078-2489","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,12,12]]}}}