Abstract
Reference evapotranspiration (ET0) is a crucial element for deriving irrigation scheduling of major crops. Thus, precise projection of ET0 is essential for better management of scarce water resources in many parts of the globe. This study evaluates the potential of a Hierarchical Fuzzy System (HFS) optimized by Particle Swarm Optimization (PSO) algorithm (PSO-HFS) to predict daily ET0. The meteorological variables and estimated ET0 (using FAO-56 Penman–Monteith equation) were employed as inputs and outputs, respectively, for the PSO-HFS model. The prediction accuracy of PSO-HFS was compared with that of a Fuzzy Inference System (FIS), M5 Model Tree (M5Tree), and a Regression Tree (RT) model. Ranking of the models was performed using the concept of Shannon’s Entropy that accounts for a set of performance evaluation indices. Results revealed that the PSO-HFS model performed better (with Entropy weight = 0.93) than the benchmark models (Entropy weights of 0.77, 0.74, and 0.90 for the FIS, RT, and M5Tree, respectively). Furthermore, the generalization capabilities of the proposed models were evaluated using the dataset from a test station. Generalization performances revealed that the models performed equally well with the unseen test dataset and that the PSO-HFS model provided superior performance (with R = 0.93, RMSE = 0.59 mm d−1 and IOA = 0.94) while the RT model (with R = 0.82, RMSE = 0.90 mm d−1, and IOA = 0.83) exhibited the worst performance for the test dataset. The overall results imply that the PSO-HFS model could effectively be utilized to model ET0 quite efficiently and accurately.
Similar content being viewed by others
Availability of Data and Material
Datasets and other materials are available with the authors, and may be accessible at any time upon request.
Code Availability
MATLAB codes are available with the first author.
References
Alavi SA, Rahimikhoob A (2016) A simple model for determining reference evapotranspiration using NOAA satellite data: A case study. Environ Process 3:479–493. https://doi.org/10.1007/s40710-016-0141-7
Alizamir M, Kisi O, Muhammad Adnan R, Kuriqi A (2020) Modelling reference evapotranspiration by combining neuro-fuzzy and evolutionary strategies. Acta Geophys 68:1113–1126. https://doi.org/10.1007/s11600-020-00446-9
Allen RG, Pereira LS, Raes D, Smith M (1998) Crop evapotranspiration—guidelines for computing crop water requirements. FAO Irrig Drain Pap No 56, Rome
Azad A, Saeed F, Hadi S et al (2021) Approaches for optimizing the performance of adaptive neuro-fuzzy inference system and least-squares support vector machine in precipitation modeling. J Hydrol Eng 26:4021010. https://doi.org/10.1061/(ASCE)HE.1943-5584.0002069
Azad A, Kashi H, Farzin S et al (2019a) Novel approaches for air temperature prediction: Comparison of four hybrid evolutionary fuzzy models. Meteorol Appl 27. https://doi.org/10.1002/met.1817
Azad A, Manoochehri M, Kashi H et al (2019b) Comparative evaluation of intelligent algorithms to improve adaptive neuro-fuzzy inference system performance in precipitation modelling. J Hydrol 571:214–224
Azad A, Karami H, Farzin S et al (2018a) Prediction of water quality parameters using ANFIS optimized by intelligence algorithms (Case Study: Gorganrood River). KSCE J Civ Eng 22:2206–2213. https://doi.org/10.1007/s12205-017-1703-6
Azad A, Farzin S, Kashi H et al (2018b) Prediction of river flow using hybrid neuro-fuzzy models. Arab J Geosci 11:718. https://doi.org/10.1007/s12517-018-4079-0
Bhattacharya B, Solomatine DP (2005) Neural networks and M5 model trees in modelling water level–discharge relationship. Neurocomputing 63:381–396. https://doi.org/10.1016/j.neucom.2004.04.016
Breiman L, Friedman JH, Olshen RA, Stone CJ (1984) Classification and regression trees. Wadsworth International, CA, USA
Chen H, Huang JJ, McBean E (2020) Partitioning of daily evapotranspiration using a modified shuttleworth-wallace model, random Forest and support vector regression, for a cabbage farmland. Agric Water Manag 228:105923. https://doi.org/10.1016/j.agwat.2019.105923
Chia MY, Huang YF, Koo CH (2020) Support vector machine enhanced empirical reference evapotranspiration estimation with limited meteorological parameters. Comput Electron Agric 175:105577. https://doi.org/10.1016/j.compag.2020.105577
Elkatoury A, Alazba AA, Mossad A (2020) Estimating evapotranspiration using coupled remote sensing and three SEB models in an arid region. Environ Process 7:109–133. https://doi.org/10.1007/s40710-019-00410-w
Ferreira LB, da Cunha FF (2020) New approach to estimate daily reference evapotranspiration based on hourly temperature and relative humidity using machine learning and deep learning. Agric Water Manag 234:106113. https://doi.org/10.1016/j.agwat.2020.106113
Ferreira LB, da Cunha FF, de Oliveira RA, Fernandes Filho EI (2019) Estimation of reference evapotranspiration in Brazil with limited meteorological data using ANN and SVM – A new approach. J Hydrol 572:556–570. https://doi.org/10.1016/j.jhydrol.2019.03.028
Francone FD (2001) Owner’s manual: Fast genetic programming based on AIMLearning technology
Gocić M, Amiri MA (2021) Reference evapotranspiration prediction using neural networks and optimum time lags. Water Resour Manag 35:1913–1926. https://doi.org/10.1007/s11269-021-02820-8
Gupta HV, Sorooshian S, Yapo PO (1999) Status of automatic calibration for hydrologic models: Comparison with multilevel expert calibration. J Hydrol Eng 4:135–143. https://doi.org/10.1061/(ASCE)1084-0699(1999)4:2(135)
Han D, Cluckie ID, Karbassioun D et al (2002) River flow modelling using fuzzy decision trees. Water Resour Manag 16:431–445. https://doi.org/10.1023/A:1022251422280
Heinemann AB, Oort PAV, Fernandes DS, Maia A (2012) Sensitivity of APSIM/ORYZA model due to estimation errors in solar radiation. Bragantia 71:572–582
Jang J-SR, Sun C-T, Mizutani E (1997) Neuro-fuzzy and soft computing: A computational approach to learning and machine intelligence. Prentice-Hall, Upper Saddle River, New Jersey
Jekabsons G (2016) M5PrimeLab: M5’ regression tree, model tree, and tree ensemble toolbox for Matlab/Octave
Karbasi M (2018) Forecasting of multi-step ahead reference evapotranspiration using wavelet- Gaussian process regression model. Water Resour Manag 32:1035–1052. https://doi.org/10.1007/s11269-017-1853-9
Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Proceedings of ICNN’95 - International Conference on Neural Networks (vol. 4), pp 1942–1948
Kisi O, Azad A, Kashi H et al (2019) Modeling groundwater quality parameters using hybrid neuro-fuzzy methods. Water Resour Manag 33:847–861. https://doi.org/10.1007/s11269-018-2147-6
Kisi O, Alizamir M, Zounemat-Kermani M (2017) Modeling groundwater fluctuations by three different evolutionary neural network techniques using hydroclimatic data. Nat Hazards 87. https://doi.org/10.1007/s11069-017-2767-9
Kisi O (2016) Modeling reference evapotranspiration using three different heuristic regression approaches. Agric Water Manag 169:162–172. https://doi.org/10.1016/j.agwat.2016.02.026
Kisi O, Zounemat-Kermani M (2014) Comparison of two different adaptive neuro-fuzzy inference systems in modelling daily reference evapotranspiration. Water Resour Manag 28:2655–2675. https://doi.org/10.1007/s11269-014-0632-0
Kord M, Moghaddam AA (2014) Spatial analysis of Ardabil plain aquifer potable groundwater using fuzzy logic. J King Saud Univ-Sci 26:129–140. https://doi.org/10.1016/j.jksus.2013.09.004
Krzywinski M, Altman N (2017) Classification and regression trees. Nat Methods 14:757–758. https://doi.org/10.1038/nmeth.4370
Kumar M, Raghuwanshi SN, Singh R et al (2002) Estimating evapotranspiration using artificial neural network. J Irrig Drain Eng 128:224–233. https://doi.org/10.1061/(ASCE)0733-9437(2002)128:4(224)
Li M-F, Tang X-P, Wu W, Liu H-B (2013) General models for estimating daily global solar radiation for different solar radiation zones in mainland China. Energy Convers Manag 70:139–148. https://doi.org/10.1016/j.enconman.2013.03.004
Liu SM, Xu ZW, Zhu ZL, et al (2013) Measurements of evapotranspiration from eddy-covariance systems and large aperture scintillometers in the Hai River Basin, China. J Hydrol 487:24–38. https://doi.org/10.1016/j.jhydrol.2013.02.025
Martí P, González-Altozano P, López-Urrea R et al (2015) Modeling reference evapotranspiration with calculated targets. Assessment and implications. Agric Water Manag 149:81–90. https://doi.org/10.1016/j.agwat.2014.10.028
Mathworks (2021) Technical documentation. In: Fuzzy trees. https://au.mathworks.com/help/fuzzy/fuzzy-trees.html. Accessed 5 May 2021
Mohammadi B, Mehdizadeh S (2020) Modeling daily reference evapotranspiration via a novel approach based on support vector regression coupled with whale optimization algorithm. Agric Water Manag 237:106145. https://doi.org/10.1016/j.agwat.2020.106145
Müller J, Piché R (2011) Mixture surrogate models based on Dempster-Shafer theory for global optimization problems. J Glob Optim 51:79–104. https://doi.org/10.1007/s10898-010-9620-y
Petković B, Petković D, Kuzman B et al (2020) Neuro-fuzzy estimation of reference crop evapotranspiration by neuro fuzzy logic based on weather conditions. Comput Electron Agric 173:105358. https://doi.org/10.1016/j.compag.2020.105358
Proias G, Gravalos I, Papageorgiou E et al (2020) Forecasting reference evapotranspiration using time lagged recurrent neural network. WSEAS Trans Environ Dev 16:699–707. https://doi.org/10.37394/232015.2020.16.72
Quinlan JR (1992) Learning with continuous classes. In: Proceedings of Australian Joint Conference on Artificial Intelligence. Hobart 16–18 November, pp 343–348
Rankin J, Fayek AR, Meade G et al (2008) Initial metrics and pilot program results for measuring the performance of the Canadian construction industry. Can J Civ Eng 35:894–907. https://doi.org/10.1139/L08-018
Reis MM, da Silva AJ, Junior JZ et al (2019) Empirical and learning machine approaches to estimating reference evapotranspiration based on temperature data. Comput Electron Agric 165:104937. https://doi.org/10.1016/j.compag.2019.104937
Roy DK (2021) Long short-term memory networks to predict one-step ahead reference evapotranspiration in a subtropical climatic zone. Environ Process 8:911–941. https://doi.org/10.1007/s40710-021-00512-4
Roy DK, Lal A, Sarker KK et al (2021) Optimization algorithms as training approaches for prediction of reference evapotranspiration using adaptive neuro fuzzy inference system. Agric Water Manag 255:107003. https://doi.org/10.1016/j.agwat.2021.107003
Roy DK, Barzegar R, Quilty J, Adamowski J (2020) Using ensembles of adaptive neuro-fuzzy inference system and optimization algorithms to predict reference evapotranspiration in subtropical climatic zones. J Hydrol 591:125509. https://doi.org/10.1016/j.jhydrol.2020.125509
Roy DK, Datta B (2019) An ensemble meta-modelling approach using the Dempster-Shafer theory of evidence for developing saltwater intrusion management strategies in coastal aquifers. Water Resour Manag 33:775–795. https://doi.org/10.1007/s11269-018-2142-y
Roy DK, Datta B (2020) Saltwater intrusion prediction in coastal aquifers utilizing a weighted-average heterogeneous ensemble of prediction models based on Dempster-Shafer theory of evidence. Hydrol Sci J 1–13. https://doi.org/10.1080/02626667.2020.1749764
Salam R, Islam ARMT (2020) Potential of RT, bagging and RS ensemble learning algorithms for reference evapotranspiration prediction using climatic data-limited humid region in Bangladesh. J Hydrol 590:125241. https://doi.org/10.1016/j.jhydrol.2020.125241
Sattari MT, Apaydin H, Shamshirband S, Mosavi A (2020a) Comparative analysis of kernel-based versus ANN and deep learning methods in monthly reference evapotranspiration estimation. Hydrol Earth Syst Sci 25:603–618. https://doi.org/10.5194/hess-25-603-2021
Sattari MT, Apaydin H, Shamshirband S (2020b) Performance evaluation of deep learning-based Gated Recurrent Units (GRUs) and tree-based models for estimating ETo by using limited meteorological variables. Mathematics 8(6):972. https://doi.org/10.3390/math8060972
Shannon CE (1948) A mathematical theory of communication. Bell Syst Tech J 27:379–423. https://doi.org/10.1002/j.1538-7305.1948.tb01338.x
Siddique N, Adeli H (2013) Computational intelligence: Synergies of fuzzy logic, neural networks and evolutionary computing. Wiley, Hoboken, NJ
Sikorska-Senoner AE, Seibert J (2020) Flood-type trend analysis for alpine catchments. Hydrol Sci J 65:1281–1299. https://doi.org/10.1080/02626667.2020.1749761
Sowmya MR, Kumar MBS, Ambat SK (2020) Comparison of deep neural networks for reference evapotranspiration prediction using minimal meteorological data. In: 2020 Advanced Computing and Communication Technologies for High Performance Applications (ACCTHPA), pp 27–33
Sugeno M (1985) Industrial applications of fuzzy control. Elsevier Science Inc.655 Avenue of the Americas New York, NY United States
Sugeno M, Yasukawa T (1993) A fuzzy-logic-based approach to qualitative modeling. IEEE Trans Fuzzy Syst 1:7. https://doi.org/10.1109/TFUZZ.1993.390281
Takagi T, Sugeno M (1985) Fuzzy identification of systems and its applications to modeling and control. IEEE Trans Syst Man Cybern SMC 15:116–132. https://doi.org/10.1109/TSMC.1985.6313399
Tao H, Diop L, Bodian A, Djaman K, Ndiaye PM, Yaseen ZM (2018) Reference evapotranspiration prediction using hybridized fuzzy model with firefly algorithm: regional case study in Burkina Faso. Agric Water Manag 208:140–151. https://doi.org/10.1016/j.agwat.2018.06.018
Tikhamarine Y, Malik A, Pandey K et al (2020a) Monthly evapotranspiration estimation using optimal climatic parameters: Efficacy of hybrid support vector regression integrated with whale optimization algorithm. Environ Monit Assess 192:696. https://doi.org/10.1007/s10661-020-08659-7
Tikhamarine Y, Malik A, Souag-Gamane D, Kisi O (2020b) Artificial intelligence models versus empirical equations for modeling monthly reference evapotranspiration. Environ Sci Pollut Res 27:30001–30019. https://doi.org/10.1007/s11356-020-08792-3
Walls S, Binns AD, Levison J, MacRitchie S (2020) Prediction of actual evapotranspiration by artificial neural network models using data from a Bowen ratio energy balance station. Neural Comput Appl 32:14001–14018. https://doi.org/10.1007/s00521-020-04800-2
Wang S, Lian J, Peng Y et al (2019) Generalized reference evapotranspiration models with limited climatic data based on random forest and gene expression programming in Guangxi, China. Agric Water Manag 221:220–230. https://doi.org/10.1016/j.agwat.2019.03.027
Wei C-C, Hsu N-S (2008) Derived operating rules for a reservoir operation system: Comparison of decision trees, neural decision trees and fuzzy decision trees. Water Resour Res 44:2428. https://doi.org/10.1029/2006WR005792
Wu L, Huang G, Fan J et al (2020) Hybrid extreme learning machine with meta-heuristic algorithms for monthly pan evaporation prediction. Comput Electron Agric 168:105115. https://doi.org/10.1016/j.compag.2019.105115
Zarei AR, Mahmoudi MR, Shabani A (2021) Using the fuzzy clustering and principle component analysis for assessing the impact of potential evapotranspiration calculation method on the modified RDI index. Water Resour Manag 35:3679–3702. https://doi.org/10.1007/s11269-021-02910-7
Zheng H, He J, Zhang Y et al (2019) A general model for fuzzy decision tree and fuzzy random forest. Comput Intell 35:310–335. https://doi.org/10.1111/coin.12195
Zhu B, Feng Y, Gong D et al (2020) Hybrid particle swarm optimization with extreme learning machine for daily reference evapotranspiration prediction from limited climatic data. Comput Electron Agric 173:105430. https://doi.org/10.1016/j.compag.2020.105430
Funding
This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of Interest
The authors declare that there is no conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Roy, D.K., Saha, K.K., Kamruzzaman, M. et al. Hierarchical Fuzzy Systems Integrated with Particle Swarm Optimization for Daily Reference Evapotranspiration Prediction: a Novel Approach. Water Resour Manage 35, 5383–5407 (2021). https://doi.org/10.1007/s11269-021-03009-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11269-021-03009-9