Abstract
Streamflow forecasting holds a pivotal role in the effective management of water resources, flood control, hydropower generation, agricultural planning, and environmental conservation.
This study assessed the effectiveness of a stacked Multilayer Perceptron-Random Forest (MLP-RF) ensemble model for short- to medium-term (7 to 15 days ahead) daily streamflow forecasts in the UK. The stacked model combines MLP and RF, enhancing generalization by capturing complex nonlinear relationships and robustness to noisy data. Stacking reduces bias and variance by aggregating predictions and addressing differing sources of bias and variance in MLP and RF. Furthermore, this ensemble model is computationally inexpensive. The study also examined the impact of different meta-learner algorithms, Elastic Net (EN), Isotonic Regression (IR), Pace Regression (PR), and Radial Basis Function (RBF) Neural Networks, on model performance.
For 1-day ahead forecasts, all models performed well (Kling Gupta efficiency, KGE, from 0.921 to 0.985, mean absolute percentage error, MAPE, from 3.59 to 13.02%), with minimal impact from the choice of meta-learner. At 7-day ahead forecasts, satisfactory results were obtained (KGE from 0.876 to 0.963, MAPE from 11.53 to 24.55%), while at the 15-day horizon, accuracy remained reasonable (KGE from 0.82 to 0.961, MAPE from 18.31 to 34.38%). The RBF meta-learner generally led to more accurate predictions, particularly affecting low and peak flow rates. RBF consistently outperformed in predicting low flow rates, while EN excelled in predicting flood flow rates in many cases. For estimating total discharged water volume, all models exhibited low relative error (< 0.08).
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Data availability
Data from the National River Flow Archive, which is the primary archive of daily river flows for the United Kingdom, were used in the creation of this manuscript. Data are available at the following website: https://nrfa.ceh.ac.uk.
References
Adnan RM, Jaafari A, Mohanavelu A, Kisi O, Elbeltagi A (2021) Novel ensemble forecasting of streamflow using locally weighted learning algorithm. Sustainability 13(11):5877
Babel MS, Gupta AD, Nayak DK (2005) A model for optimal allocation of water to competing demands. Water Resour Manage 19:693–712
Bender M, Simonovic S (1994) Time-series modeling for long-range stream-flow forecasting. J Water Resour Plan Manag 120(6):857–870
Best MJ, Chakravarti N (1990) Active set algorithms for isotonic regression; a unifying framework. Math Program 47(1–3):425–439
Beven KJ (2011) Rainfall-runoff modelling: the primer. Wiley
Breiman L (2001) Random forests. Mach Learn 45(1):5–32
Breiman L, Friedman JH, Olshen RA, Stone CJ (2017) Classification and regression trees. Routledge
Chang FJ, Chen PA, Lu YR, Huang E, Chang KY (2014) Real-time multi-step-ahead water level forecasting by recurrent neural networks for urban flood control. J Hydrol 517:836–846
Cheng M, Fang F, Kinouchi T, Navon IM, Pain CC (2020) Long lead-time daily and monthly streamflow forecasting using machine learning methods. J Hydrol 590:125376
Dawadi S, Ahmad S (2012) Changing climatic conditions in the Colorado River Basin: implications for water resources management. J Hydrol 430:127–141
Di Nunno F, de Marinis G, Granata F (2023) Short-term forecasts of streamflow in the UK based on a novel hybrid artificial intelligence algorithm. Sci Rep 13(1):7036
Edossa DC, Babel MS (2011) Application of ANN-based streamflow forecasting model for agricultural water management in the Awash River Basin, Ethiopia. Water Resour Manage 25:1759–1773
Elbeltagi A, Di Nunno F, Kushwaha NL, de Marinis G, Granata F (2022) River flow rate prediction in the Des Moines watershed (Iowa, USA): a machine learning approach. Stoch Env Res Risk Assess, 1–21
Ghimire S, Yaseen ZM, Farooque AA, Deo RC, Zhang J, Tao X (2021) Streamflow prediction using an integrated methodology based on convolutional neural network and long short-term memory networks. Sci Rep 11(1):17497
Granata F, Di Nunno F (2021) Forecasting evapotranspiration in different climates using ensembles of recurrent neural networks. Agric Water Manage 255:107040
Granata F, Di Nunno F (2023) Neuroforecasting of daily streamflows in the UK for short-and medium-term horizons: a novel insight. J Hydrol, 129888
Granata F, Di Nunno F, de Marinis G (2022) Stacked machine learning algorithms and bidirectional long short-term memory networks for multi-step ahead streamflow forecasting: a comparative study. J Hydrol 613:128431
Granata F, Di Nunno F, de Marinis G (2024) Advanced evapotranspiration forecasting in Central Italy: stacked MLP-RF algorithm and correlated Nystrom views with feature selection strategies. Comput Electron Agric 220:108887
Kişi Ö (2007) Streamflow forecasting using different artificial neural network algorithms. J Hydrol Eng 12(5):532–539
Lee DG, Ahn KH (2021) A stacking ensemble model for hydrological post-processing to improve streamflow forecasts at medium-range timescales over South Korea. J Hydrol 600:126681
Li FF, Wang ZY, Qiu J (2019) Long-term streamflow forecasting using artificial neural network based on preprocessing technique. J Forecast 38(3):192–206
Liu J, Yuan X, Zeng J, Jiao Y, Li Y, Zhong L, & Yao, L (2022) Ensemble streamflow forecasting over a cascade reservoir catchment with integrated hydrometeorological modeling and machine learning. Hydrology andearth system sciences, 26(2):265–278
Noori N, Kalin L (2016) Coupling SWAT and ANN models for enhanced daily streamflow prediction. J Hydrol 533:141–151
Nourani V, Baghanam AH, Adamowski J, Kisi O (2014) Applications of hybrid wavelet–artificial intelligence models in hydrology: a review. J Hydrol 514:358–377
Papacharalampous G, Tyralis H, Koutsoyiannis D (2019) Comparison of stochastic and machine learning methods for multi-step ahead forecasting of hydrological processes. Stoch Env Res Risk Assess 33(2):481–514
Park J, Sandberg IW (1991) Universal approximation using radial-basis-function networks. Neural Comput 3(2):246–257
Rasouli K, Hsieh WW, Cannon AJ (2012) Daily streamflow forecasting by machine learning methods with weather and climate inputs. J Hydrol 414:284–293
Saraiva SV, de Oliveira Carvalho F, Santos CAG, Barreto LC, Freire PKDMM (2021). Daily streamflow forecasting in Sobradinho Reservoir using machine learning models coupled with wavelet transform and bootstrap**. Appl Soft Comput 102:107081
Snoek J, Larochelle H, Adams RP (2012) Practical bayesian optimization of machine learning algorithms. Adv Neural Inf Process Syst 25
Sofi MS, Bhat SU, Rashid I, Kuniyal JC (2020) The natural flow regime: a master variable for maintaining river ecosystem health. Ecohydrology 13(8):e2247
Sun W, Wang Y, Wang G, Cui X, Yu J, Zuo D, Xu Z (2017) Physically based distributed hydrological model calibration based on a short period of streamflow data: case studies in four Chinese basins. Hydrol Earth Syst Sci 21(1):251–265
Tyralis H, Papacharalampous G, Langousis A (2021) Super ensemble learning for daily streamflow forecasting: large-scale demonstration and comparison with multiple machine learning algorithms. Neural Comput Appl 33(8):3053–3068
Wang Y, Witten IH (1999) Pace Regression. (Working paper 99/12). University of Waikato, Department of Computer Science, Hamilton, New Zealand
Werritty A (2002) Living with uncertainty: climate change, river flows and water resource management in Scotland. Sci Total Environ 294(1–3):29–40
**ang Z, Yan J, Demir I (2020) A rainfall-runoff model with LSTM‐based sequence‐to‐sequence learning. Water Resour Res 56(1):e2019WR025326
Xu W, Zhang C, Peng Y, Fu G, Zhou H (2014) A two stage B ayesian stochastic optimization model for cascaded hydropower systems considering varying uncertainty of flow forecasts. Water Resour Res 50(12):9267–9286
Yaseen ZM, El-Shafie A, Jaafar O, Afan HA, Sayl KN (2015) Artificial intelligence based models for stream-flow forecasting: 2000–2015. J Hydrol 530:829–844
Zhu S, Di Nunno F, Ptak M, Sojka M, Granata F (2023) A novel optimized model based on NARX networks for predicting thermal anomalies in Polish lakes during heatwaves, with special reference to the 2018 heatwave. Sci Total Environ 905:167121
Zou H, Hastie T (2005) Regularization and variable selection via the elastic net. J Royal Stat Society: Ser B (Statistical Methodology) 67(2):301–320
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The authors have no relevant financial or non-financial interests to disclose. The authors have no competing interests to declare that are relevant to the content of this article. All authors certify that they have no affiliations with or involvement in any organization or entity with any financial interest or non-financial interest in the subject matter or materials discussed in this manuscript. The authors have no financial or proprietary interests in any material discussed in this article.
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F.G. conceptualized this research and developed the forecasting models. F.G and F.D.N. collected the data, analyzed the results, validated them, inferred insights, and wrote the manuscript.
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Granata, F., Di Nunno, F. Forecasting short- and medium-term streamflow using stacked ensemble models and different meta-learners. Stoch Environ Res Risk Assess (2024). https://doi.org/10.1007/s00477-024-02760-w
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DOI: https://doi.org/10.1007/s00477-024-02760-w