{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,4]],"date-time":"2026-07-04T02:33:27Z","timestamp":1783132407895,"version":"3.54.6"},"reference-count":50,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2018,3,20]],"date-time":"2018-03-20T00:00:00Z","timestamp":1521504000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Recently, the Entropy Ensemble Filter (EEF) method was proposed to mitigate the computational cost of the Bootstrap AGGregatING (bagging) method. This method uses the most informative training data sets in the model ensemble rather than all ensemble members created by the conventional bagging. In this study, we evaluate, for the first time, the application of the EEF method in Neural Network (NN) modeling of El Nino-southern oscillation. Specifically, we forecast the first five principal components (PCs) of sea surface temperature monthly anomaly fields over tropical Pacific, at different lead times (from 3 to 15 months, with a three-month increment) for the period 1979\u20132017. We apply the EEF method in a multiple-linear regression (MLR) model and two NN models, one using Bayesian regularization and one Levenberg-Marquardt algorithm for training, and evaluate their performance and computational efficiency relative to the same models with conventional bagging. All models perform equally well at the lead time of 3 and 6 months, while at higher lead times, the MLR model\u2019s skill deteriorates faster than the nonlinear models. The neural network models with both bagging methods produce equally successful forecasts with the same computational efficiency. It remains to be shown whether this finding is sensitive to the dataset size.<\/jats:p>","DOI":"10.3390\/e20030207","type":"journal-article","created":{"date-parts":[[2018,3,20]],"date-time":"2018-03-20T06:57:11Z","timestamp":1521529031000},"page":"207","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Application of Entropy Ensemble Filter in Neural Network Forecasts of Tropical Pacific Sea Surface Temperatures"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4858-8686","authenticated-orcid":false,"given":"Hossein","family":"Foroozand","sequence":"first","affiliation":[{"name":"Department of Civil Engineering, University of British Columbia, Vancouver, BC V6T 1Z4, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Valentina","family":"Radi\u0107","sequence":"additional","affiliation":[{"name":"Department of Earth, Ocean and Atmospheric Sciences, University of British Columbia, Vancouver, BC V6T 1Z4, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1311-3867","authenticated-orcid":false,"given":"Steven","family":"Weijs","sequence":"additional","affiliation":[{"name":"Department of Civil Engineering, University of British Columbia, Vancouver, BC V6T 1Z4, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2018,3,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Chau, K. (2017). Use of meta-heuristic techniques in rainfall-runoff modelling. Water, 9.","DOI":"10.3390\/w9030186"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Hsieh, W.W. (2009). Machine Learning Methods in the Environmental Sciences: Neural Networks and Kernels, Cambridge University Press.","DOI":"10.1017\/CBO9780511627217"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1294","DOI":"10.1109\/TPAMI.2008.138","article-title":"Supervised learning of quantizer codebooks by information loss minimization","volume":"31","author":"Lazebnik","year":"2009","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1016\/j.cnsns.2017.04.026","article-title":"On the formulation and numerical simulation of distributed-order fractional optimal control problems","volume":"52","author":"Zaky","year":"2017","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1016\/j.enbuild.2017.07.053","article-title":"HVAC system energy optimization using an adaptive hybrid metaheuristic","volume":"152","author":"Ghahramani","year":"2017","journal-title":"Energy Build."},{"key":"ref_6","unstructured":"Foroozand, H., and Afzali, S.H. (2015, January 29\u201330). A comparative study of honey-bee mating optimization algorithm and support vector regression system approach for river discharge prediction case study: Kashkan river basin. Proceedings of the International Conference on Civil Engineering Architecture and Urban Infrastructure, Tabriz, Iran."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1253","DOI":"10.2166\/nh.2016.089","article-title":"Parameter estimation of an improved nonlinear muskingum model using a new hybrid method","volume":"48","author":"Niazkar","year":"2017","journal-title":"Hydrol. Res."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"100","DOI":"10.2166\/hydro.2017.129","article-title":"Bed material load estimation in channels using machine learning and meta-heuristic methods","volume":"20","author":"Sahraei","year":"2018","journal-title":"J. Hydroinformatics"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Nikoo, M.R., Kerachian, R., and Alizadeh, M. (2017). A fuzzy KNN-based model for significant wave height prediction in large lakes. Oceanologia.","DOI":"10.1016\/j.oceano.2017.09.003"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1016\/S0022-1694(02)00112-9","article-title":"River flow forecasting: Use of phase-space reconstruction and artificial neural networks approaches","volume":"265","author":"Sivakumar","year":"2002","journal-title":"J. Hydrol."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"04016082","DOI":"10.1061\/(ASCE)WR.1943-5452.0000741","article-title":"Nondominated sorting differential evolution algorithms for multiobjective optimization of water distribution systems","volume":"143","author":"Moosavian","year":"2017","journal-title":"J. Water Resour. Plan. Manag."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"979706","DOI":"10.1155\/2014\/979706","article-title":"Hydraulic analysis of water distribution network using shuffled complex evolution","volume":"2014","author":"Moosavian","year":"2014","journal-title":"J. Fluid."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"2179","DOI":"10.1007\/s11269-016-1281-2","article-title":"A hybrid double feedforward neural network for suspended sediment load estimation","volume":"30","author":"Chen","year":"2016","journal-title":"Water Resour. Manag."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1007\/s10661-015-4381-1","article-title":"A comparison of various artificial intelligence approaches performance for estimating suspended sediment load of river systems: A case study in United States","volume":"187","author":"Olyaie","year":"2015","journal-title":"Environ. Monit. Assess."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1656","DOI":"10.1080\/15325008.2016.1198437","article-title":"Probabilistic wind power forecasting with hybrid artificial neural networks","volume":"44","author":"Wan","year":"2016","journal-title":"Electr. Power Compon. Syst."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.chemolab.2010.10.004","article-title":"Bagging for robust Non-Linear Multivariate Calibration of Spectroscopy","volume":"105","author":"Wang","year":"2011","journal-title":"Chemom. Intell. Lab. Syst."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1007\/s00477-012-0600-2","article-title":"Quantification of the predictive uncertainty of artificial neural network based river flow forecast models","volume":"27","author":"Kasiviswanathan","year":"2013","journal-title":"Stoch. Environ. Res. Risk Assess."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"487","DOI":"10.1093\/bioinformatics\/bti1030","article-title":"Bayesian neural network approaches to ovarian cancer identification from high-resolution mass spectrometry data","volume":"21","author":"Yu","year":"2005","journal-title":"Bioinformatics"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Foroozand, H., and Weijs, S.V. (2017). Entropy ensemble filter: A modified bootstrap aggregating (Bagging) procedure to improve efficiency in ensemble model simulation. Entropy, 19.","DOI":"10.3390\/e19100520"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1016\/j.neunet.2006.01.004","article-title":"Neural network forecasts of the tropical Pacific sea surface temperatures","volume":"19","author":"Wu","year":"2006","journal-title":"Neural Netw."},{"key":"ref_21","first-page":"167239","article-title":"Forecasts of tropical Pacific sea surface temperatures by neural networks and support vector regression","volume":"2009","author":"Hsieh","year":"2009","journal-title":"Int. J. Oceanogr."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"14241","DOI":"10.1029\/97JC02905","article-title":"On the structure and evolution of ENSO-related climate variability in the tropical Pacific: Lessons from TOGA","volume":"103","author":"Wallace","year":"1998","journal-title":"J. Geophys. Res. Oceans"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1061\/(ASCE)0733-9496(2002)128:2(91)","article-title":"Economic value of long-lead streamflow forecasts for columbia river hydropower","volume":"128","author":"Hamlet","year":"2002","journal-title":"J. Water Resour. Plan. Manag."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Vu, T.M., Mishra, A.K., and Konapala, G. (2018). Information entropy suggests stronger nonlinear associations between hydro-meteorological variables and ENSO. Entropy, 20.","DOI":"10.3390\/e20010038"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1111","DOI":"10.1002\/joc.636","article-title":"Current approaches to seasonal to interannual climate predictions","volume":"21","author":"Goddard","year":"2001","journal-title":"Int. J. Climatol."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"631","DOI":"10.1175\/BAMS-D-11-00111.1","article-title":"Skill of real-time seasonal ENSO model predictions during 2002\u201311: Is our capability increasing?","volume":"93","author":"Barnston","year":"2011","journal-title":"Bull. Am. Meteorol. Soc."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Zhu, L., Jin, J., Cannon, A.J., and Hsieh, W.W. (2016, January 16\u201321). Bayesian neural networks based bootstrap aggregating for tropical cyclone tracks prediction in south China sea. Proceedings of the 23rd International Conference ICONIP, Kyoto, Japan.","DOI":"10.1007\/978-3-319-46675-0_52"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1007\/s003820050156","article-title":"Forecasting the equatorial Pacific sea surface temperatures by neural network models","volume":"13","author":"Tangang","year":"1997","journal-title":"Clim. Dyn."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"221","DOI":"10.5194\/npg-15-221-2008","article-title":"Robust nonlinear canonical correlation analysis: Application to seasonal climate forecasting","volume":"15","author":"Cannon","year":"2008","journal-title":"Nonlinear Process. Geophys."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1175\/1520-0442(2000)013<0287:SCBNNA>2.0.CO;2","article-title":"Skill comparisons between neural networks and canonical correlation analysis in predicting the equatorial Pacific sea surface temperatures","volume":"13","author":"Tang","year":"2000","journal-title":"J. Clim."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"164","DOI":"10.1090\/qam\/10666","article-title":"A method for the solution of certain non-linear problems in least squares","volume":"2","author":"Levenberg","year":"1944","journal-title":"Q. Appl. Math."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"431","DOI":"10.1137\/0111030","article-title":"An algorithm for least-squares estimation of nonlinear parameters","volume":"11","author":"Marquardt","year":"1963","journal-title":"J. Soc. Ind. Appl. Math."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1788","DOI":"10.1016\/j.jhydrol.2015.08.008","article-title":"Neural network river forecasting through baseflow separation and binary-coded swarm optimization","volume":"529","author":"Taormina","year":"2015","journal-title":"J. Hydrol."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"415","DOI":"10.1162\/neco.1992.4.3.415","article-title":"Bayesian Interpolation","volume":"4","author":"MacKay","year":"1992","journal-title":"Neural Comput."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"304","DOI":"10.1080\/00401706.2016.1142905","article-title":"A bootstrap metropolis-hastings algorithm for Bayesian analysis of big data","volume":"58","author":"Liang","year":"2016","journal-title":"Technometrics"},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Gianola, D., Weigel, K.A., Kr\u00e4mer, N., Stella, A., and Sch\u00f6n, C.C. (2014). Enhancing genome-enabled prediction by bagging genomic BLUP. PLoS ONE, 9.","DOI":"10.1371\/journal.pone.0091693"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"79","DOI":"10.4141\/cjas2013-078","article-title":"Bootstrapped neural network models for analyzing the responses of broiler chicks to dietary protein and branched chain amino acids","volume":"94","author":"Faridi","year":"2013","journal-title":"Can. J. Anim. Sci."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"720","DOI":"10.1016\/j.jprocont.2007.11.008","article-title":"A reliable multi-objective control strategy for batch processes based on bootstrap aggregated neural network models","volume":"18","author":"Mukherjee","year":"2008","journal-title":"J. Process Control"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1109\/34.655647","article-title":"Neural network-based face detection","volume":"20","author":"Rowley","year":"1998","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1002\/j.1538-7305.1948.tb01338.x","article-title":"A mathematical theory of communication","volume":"27","author":"Shannon","year":"1948","journal-title":"Bell Syst. Tech. J."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"1340","DOI":"10.1061\/(ASCE)HE.1943-5584.0000930","article-title":"Flow duration curve using entropy theory","volume":"19","author":"Singh","year":"2014","journal-title":"J. Hydrol. Eng."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1007\/BF00058655","article-title":"Bagging predictors","volume":"24","author":"Breiman","year":"1996","journal-title":"Mach. Learn."},{"key":"ref_43","unstructured":"Cover, T.M., and Thomas, J.A. (2006). Elements of Information Theory, Wiley-Interscience."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1109\/JRPROC.1949.232969","article-title":"Communication in the Presence of Noise","volume":"37","author":"Shannon","year":"1949","journal-title":"Proc. IRE"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1016\/j.jhydrol.2013.06.033","article-title":"An information-theoretical perspective on weighted ensemble forecasts","volume":"498","author":"Weijs","year":"2013","journal-title":"J. Hydrol."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"1289","DOI":"10.3390\/e15041289","article-title":"HydroZIP: How hydrological knowledge can be used to improve compression of hydrological data","volume":"15","author":"Weijs","year":"2013","journal-title":"Entropy"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1016\/j.physa.2015.08.060","article-title":"Maximum entropy spectral analysis for streamflow forecasting","volume":"442","author":"Cui","year":"2016","journal-title":"Phys. Stat. Mech. Its. Appl."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"989","DOI":"10.1109\/72.329697","article-title":"Training feedforward networks with the Marquardt algorithm","volume":"5","author":"Hagan","year":"1994","journal-title":"IEEE Trans. Neural Netw."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"553","DOI":"10.1002\/qj.828","article-title":"The ERA-interim reanalysis: Configuration and performance of the data assimilation system","volume":"137","author":"Dee","year":"2011","journal-title":"Q. J. R. Meteorol. Soc."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1037\/0033-2909.87.2.245","article-title":"Tests for comparing elements of a correlation matrix","volume":"87","author":"Steiger","year":"1980","journal-title":"Psychol. Bull."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/20\/3\/207\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T14:57:43Z","timestamp":1760194663000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/20\/3\/207"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,3,20]]},"references-count":50,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2018,3]]}},"alternative-id":["e20030207"],"URL":"https:\/\/doi.org\/10.3390\/e20030207","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,3,20]]}}}