{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,23]],"date-time":"2026-04-23T23:55:01Z","timestamp":1776988501848,"version":"3.51.4"},"reference-count":36,"publisher":"MDPI AG","issue":"21","license":[{"start":{"date-parts":[[2025,10,24]],"date-time":"2025-10-24T00:00:00Z","timestamp":1761264000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Program for Research of the National Association of Technical Universities\u2014GNAC ARUT 2023","award":["169"],"award-info":[{"award-number":["169"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Water"],"abstract":"<jats:p>In the hydropower sector, accurate estimation of short-term reservoir inflows is an essential element to ensure efficient and safe management of water resources. Short-term forecasting supports the optimization of energy production, prevention of uncontrolled water discharges, planning of equipment maintenance, and adaption of operational strategies. In the absence of data on topography, vegetation, and basin characteristics (required in distributed or semi-distributed models), data-driven approaches can serve as effective alternatives for inflow prediction. This study proposes a novel hybrid approach that reverses the conventional LSTM (Long Short-Term Memory)\u2014ARIMA (Autoregressive Integrated Moving Average) sequence: LSTM is first used to capture nonlinear hydrological patterns, followed by ARIMA to model residual linear trends.The model was calibrated using daily inflow data in the Izvorul Muntelui\u2013Bicaz reservoir in Romania from 2012 to 2020, tested for prediction on the day ahead in a repetitive loop of 365 days corresponding to 2021 and further evaluated through multiple seven-day forecasts randomly selected to cover all 12 months of 2021. For the tested period, the proposed model significantly outperforms the standalone LSTM, increasing the R2 from 0.93 to 0.96 and reducing RMSE from 9.74 m3\/s to 6.94 m3\/s for one-day-ahead forecasting. For multistep forecasting (84 values, randomly selected, 7 per month), the model improves R2 from 0.75 to 0.89 and lowers RMSE from 18.56 m3\/s to 12.74 m3\/s. Thus, the hybrid model offers notable improvements in multi-step forecasting by capturing both seasonal patterns and nonlinear variations in hydrological data. The approach offers a replicable data-driven solution for inflow prediction in reservoirs with limited physical data.<\/jats:p>","DOI":"10.3390\/w17213051","type":"journal-article","created":{"date-parts":[[2025,10,27]],"date-time":"2025-10-27T07:31:58Z","timestamp":1761550318000},"page":"3051","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Hybrid LSTM-ARIMA Model for Improving Multi-Step Inflow Forecasting in a Reservoir"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0009-0008-8028-5427","authenticated-orcid":false,"given":"Angela","family":"Neagoe","sequence":"first","affiliation":[{"name":"Department of Hydraulics, Hydraulic Machinery and Environmental Engineering, Faculty of Energy Engineering, National University of Science and Technology Politehnica Bucharest, 313 Splaiul Independen\u021bei, Sector 6, 060042 Bucharest, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1250-9408","authenticated-orcid":false,"given":"Eliza-Isabela","family":"Tic\u0103","sequence":"additional","affiliation":[{"name":"Department of Hydraulics, Hydraulic Machinery and Environmental Engineering, Faculty of Energy Engineering, National University of Science and Technology Politehnica Bucharest, 313 Splaiul Independen\u021bei, Sector 6, 060042 Bucharest, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5291-4694","authenticated-orcid":false,"given":"Liana-Ioana","family":"Vu\u021b\u0103","sequence":"additional","affiliation":[{"name":"Department of Hydraulics, Hydraulic Machinery and Environmental Engineering, Faculty of Energy Engineering, National University of Science and Technology Politehnica Bucharest, 313 Splaiul Independen\u021bei, Sector 6, 060042 Bucharest, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Otilia","family":"Nedelcu","sequence":"additional","affiliation":[{"name":"Department of Electronics, Telecommunication and Energy Engineering, University Valahia of T\u00e2rgovi\u0219te, 130004 T\u00e2rgovi\u0219te, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7109-7853","authenticated-orcid":false,"given":"Gabriela-Elena","family":"Dumitran","sequence":"additional","affiliation":[{"name":"Department of Hydraulics, Hydraulic Machinery and Environmental Engineering, Faculty of Energy Engineering, National University of Science and Technology Politehnica Bucharest, 313 Splaiul Independen\u021bei, Sector 6, 060042 Bucharest, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0339-1054","authenticated-orcid":false,"given":"Bogdan","family":"Popa","sequence":"additional","affiliation":[{"name":"Department of Hydraulics, Hydraulic Machinery and Environmental Engineering, Faculty of Energy Engineering, National University of Science and Technology Politehnica Bucharest, 313 Splaiul Independen\u021bei, Sector 6, 060042 Bucharest, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,10,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"19617","DOI":"10.1007\/s11356-023-25148-9","article-title":"Autoregressive models in environmental forecasting time series: A theoretical and application review","volume":"30","author":"Kaur","year":"2023","journal-title":"Environ. Sci. Pollut. Res."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Khazaeiathar, M., Hadizadeh, R., Fathollahzadeh Attar, N., and Schmalz, B. (2022). Daily Streamflow Time Series Modeling by Using a Periodic Autoregressive Model (ARMA) Based on Fuzzy Clustering. Water, 14.","DOI":"10.3390\/w14233932"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1016\/j.jher.2022.10.002","article-title":"Two-step daily reservoir inflow prediction using ARIMA-machine learning and ensemble models","volume":"45","author":"Gupta","year":"2022","journal-title":"J. Hydro-Environ. Res."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"429","DOI":"10.1016\/j.apenergy.2018.08.114","article-title":"Multi-step ahead wind speed prediction based on optimal feature extraction, long short-term memory neural network and error correction strategy","volume":"230","author":"Wang","year":"2018","journal-title":"Appl. Energy"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.egyr.2024.11.074","article-title":"Multi-step wind energy forecasting in the Mexican Isthmus using machine and deep learning","volume":"13","year":"2025","journal-title":"Energy Rep."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"122624","DOI":"10.1016\/j.apenergy.2024.122624","article-title":"Short-term wind speed forecasting using an optimized three-phase convolutional neural network fused with bidirectional long short-term memory network model","volume":"359","author":"Joseph","year":"2024","journal-title":"Appl. Energy"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"589","DOI":"10.1016\/j.enconman.2017.10.021","article-title":"Multi-step ahead wind speed forecasting using a hybrid model based on two-stage decomposition technique and AdaBoost-extreme learning machine","volume":"153","author":"Peng","year":"2017","journal-title":"Energy Convers. Manag."},{"key":"ref_8","first-page":"101889","article-title":"Day-ahead photovoltaic power generation forecasting with the HWGC-WPD-LSTM hybrid model assisted by wavelet packet decomposition and improved similar day method","volume":"61","author":"Bai","year":"2025","journal-title":"Eng. Sci. Technol. Int. J."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"9095","DOI":"10.1007\/s00521-024-09558-5","article-title":"Hybrid deep learning models for time series forecasting of solar power","volume":"36","author":"Salman","year":"2024","journal-title":"Neural Comput. Appl."},{"key":"ref_10","first-page":"102946","article-title":"A critical review of RNN and LSTM variants in hydrological time series predictions","volume":"13","author":"Waqas","year":"2024","journal-title":"Methods"},{"key":"ref_11","first-page":"1801","article-title":"Improvement of artificial neural networks to predict daily streamflow in a semi-arid area","volume":"61","author":"Zemzami","year":"2016","journal-title":"Hydrol. Sci. J."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Ghimire, S., Yaseen, Z.M., Farooque, A.A., Deo, R.C., Zhang, J., and Tao, X. (2021). Streamflow prediction using an integrated methodology based on convolutional neural network and long short-term memory networks. Sci. Rep., 11.","DOI":"10.1038\/s41598-021-96751-4"},{"key":"ref_13","first-page":"6596397","article-title":"A Review on Deep Sequential Models for Forecasting Time Series Data","volume":"2022","author":"Ahmed","year":"2022","journal-title":"Appl. Comput. Intell. Soft Comput."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"10206","DOI":"10.1007\/s11356-024-32228-x","article-title":"Comparing ARIMA and various deep learning models for long-term water quality index forecasting in Dez River, Iran","volume":"32","author":"Niknam","year":"2025","journal-title":"Environ. Sci. Pollut. Res."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Wang, W., Ma, B., Guo, X., Chen, Y., and Xu, Y. (2024). A Hybrid ARIMA-LSTM Model for Short-Term Vehicle Speed Prediction. Energies, 17.","DOI":"10.3390\/en17153736"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"113563","DOI":"10.1016\/j.knosys.2025.113563","article-title":"LSTM-ARIMA as a hybrid approach in algorithmic investment strategies","volume":"320","author":"Kashif","year":"2025","journal-title":"Knowl.-Based Syst."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Kontopoulou, V.I., Panagopoulos, A.D., Kakkos, I., and Matsopoulos, G.K. (2023). A Review of ARIMA vs. Machine Learning Approaches for Time Series Forecasting in Data Driven Networks. Future Internet, 15.","DOI":"10.3390\/fi15080255"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"68","DOI":"10.1049\/iet-its.2016.0208","article-title":"LSTM network: A deep learning approach for short-term traffic forecast","volume":"11","author":"Zhao","year":"2017","journal-title":"IET Intell. Transp. Syst."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"02006","DOI":"10.1051\/e3sconf\/202563802006","article-title":"Daily inflow forecasting in Asomata reservoir, on Aliakmon River, using Long Short-Term Memory network","volume":"638","author":"Neagoe","year":"2025","journal-title":"E3S Web Conf."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"110092","DOI":"10.1016\/j.ecolind.2023.110092","article-title":"A dynamic classification-based long short-term memory network model for daily streamflow forecasting in different climate regions","volume":"148","author":"Chu","year":"2023","journal-title":"Ecol. Indic."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Chu, H., Wang, Z., and Nie, C. (2024). Monthly Streamflow Prediction of the Source Region of the Yellow River Based on Long Short-Term Memory Considering Different Lagged Months. Water, 16.","DOI":"10.3390\/w16040593"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Dong, Z., and Zhou, Y. (2024). A Novel Hybrid Model for Financial Forecasting Based on CEEMDAN-SE and ARIMA-CNN-LSTM. Mathematics, 12.","DOI":"10.3390\/math12162434"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"4128","DOI":"10.1007\/s11356-021-15325-z","article-title":"Application of a hybrid ARIMA-LSTM model based on the SPEI for drought forecasting","volume":"29","author":"Xu","year":"2022","journal-title":"Environ. Sci. Pollut. Res."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1007\/978-3-642-41822-8_9","article-title":"Single-Step-Ahead and Multi-Step-Ahead Prediction with Evolutionary Artificial Neural Networks","volume":"Volume 8258","year":"2013","journal-title":"Lecture Notes in Computer Science"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1080\/00031305.2017.1380080","article-title":"Forecasting at scale","volume":"72","author":"Taylor","year":"2018","journal-title":"Am. Stat."},{"key":"ref_26","first-page":"1763","article-title":"Hydrologic and water quality models: Performance measures and evaluation criteria","volume":"58","author":"Moriasi","year":"2015","journal-title":"Am. Soc. Agric. Biol. Eng."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"343","DOI":"10.1111\/j.1752-1688.2005.tb03740.x","article-title":"Hydrologic modeling of the Iroquois River watershed using HSPF and SWAT","volume":"41","author":"Singh","year":"2007","journal-title":"J. Am. Water Resour. Assoc."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"282","DOI":"10.1016\/0022-1694(70)90255-6","article-title":"River flow forecasting through conceptual models: Part 1. A discussion of principles","volume":"10","author":"Nash","year":"1970","journal-title":"J. Hydrol."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"2377510","DOI":"10.1080\/08839514.2024.2377510","article-title":"Generalized Performance of LSTM in Time-Series Forecasting","volume":"38","author":"Prater","year":"2024","journal-title":"App. Artif. Intell."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"210","DOI":"10.33096\/ilkom.v16i2.2333.210-220","article-title":"Enhanced Multivariate Time Series Analysis Using LSTM: A Comparative Study of Min-Max and Z-Score Normalization Techniques","volume":"16","author":"Pranolo","year":"2024","journal-title":"Ilk. J. Ilm."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"2343","DOI":"10.5194\/hess-24-2343-2020","article-title":"Multistep-ahead daily inflow forecasting using the ERA-Interim reanalysis data set based on gradient-boosting regression trees","volume":"24","author":"Liao","year":"2020","journal-title":"Hydrol. Earth Syst. Sci."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"12854","DOI":"10.1111\/jfr3.12854","article-title":"Dongyang Han, Exploring the role of the long short-term memory model in improving multi-step ahead reservoir inflow forecasting","volume":"16","author":"Luo","year":"2023","journal-title":"J. Flood Risk Manag."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1016\/S0925-2312(01)00702-0","article-title":"Time series forecasting using a hybrid ARIMA and neural network model","volume":"50","author":"Zhang","year":"2003","journal-title":"Neurocomputing"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"83105","DOI":"10.1109\/ACCESS.2021.3085085","article-title":"Evaluation of Deep Learning Models for Multi-Step Ahead Time Series Prediction","volume":"9","author":"Chandra","year":"2021","journal-title":"IEEE Access"},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Fan, M., Lu, D., and Gangrade, S. (2025). Enhancing Multi-Step Reservoir Inflow Forecasting: A Time-Variant Encoder\u2013Decoder Approach. Geosciences, 15.","DOI":"10.3390\/geosciences15080279"},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Weekaew, J., Ditthakit, P., Kittiphattanabawon, N., and Pham, Q.B. (2024). Quartile Regression and Ensemble Models for Extreme Events of Multi-Time Step-Ahead Monthly Reservoir Inflow Forecasting. Water, 16.","DOI":"10.3390\/w16233388"}],"container-title":["Water"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-4441\/17\/21\/3051\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,27]],"date-time":"2025-10-27T07:41:45Z","timestamp":1761550905000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-4441\/17\/21\/3051"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,10,24]]},"references-count":36,"journal-issue":{"issue":"21","published-online":{"date-parts":[[2025,11]]}},"alternative-id":["w17213051"],"URL":"https:\/\/doi.org\/10.3390\/w17213051","relation":{},"ISSN":["2073-4441"],"issn-type":[{"value":"2073-4441","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,10,24]]}}}