Theoretical and Applied Climatology

, Volume 133, Issue 3–4, pp 1119–1131 | Cite as

Pan evaporation prediction using a hybrid multilayer perceptron-firefly algorithm (MLP-FFA) model: case study in North Iran

  • M. A. Ghorbani
  • Ravinesh C. Deo
  • Zaher Mundher YaseenEmail author
  • Mahsa H. Kashani
  • Babak Mohammadi
Original Paper


An accurate computational approach for the prediction of pan evaporation over daily time horizons is a useful decisive tool in sustainable agriculture and hydrological applications, particularly in designing the rural water resource systems, water use allocations, utilization and demand assessments, and the management of irrigation systems. In this study, a hybrid predictive model (Multilayer Perceptron-Firefly Algorithm (MLP-FFA)) based on the FFA optimizer that is embedded within the MLP technique is developed and evaluated for its suitability for the prediction of daily pan evaporation. To develop the hybrid MLP-FFA model, the pan evaporation data measured between 2012 and 2014 for two major meteorological stations (Talesh and Manjil) located at Northern Iran are employed to train and test the predictive model. The ability of the hybrid MLP-FFA model is compared with the traditional MLP and support vector machine (SVM) models. The results are evaluated using five performance criteria metrics: root mean square error (RMSE), mean absolute error (MAE), Nash-Sutcliffe efficiency (NS), and the Willmott’s Index (WI). Taylor diagrams are also used to examine the similarity between the observed and predicted pan evaporation data in the test period. Results show that an optimal MLP-FFA model outperforms the MLP and SVM model for both tested stations. For Talesh, a value of WI = 0.926, NS = 0.791, and RMSE = 1.007 mm day−1 is obtained using MLP-FFA model, compared with 0.912, 0.713, and 1.181 mm day−1 (MLP) and 0.916, 0.726, and 1.153 mm day−1 (SVM), whereas for Manjil, a value of WI = 0.976, NS = 0.922, and 1.406 mm day−1 is attained that contrasts 0.972, 0.901, and 1.583 mm day−1 (MLP) and 0.971, 0.893, and 1.646 mm day−1 (SVM). The results demonstrate the importance of the Firefly Algorithm applied to improve the performance of the MLP-FFA model, as verified through its better predictive performance compared to the MLP and SVM model.


Firefly Algorithm Forecasting Hybrid model Multilayer perceptron Pan evaporation Support vector machine 



The authors wish to express their gratitude to the Gilan Meteorological Organization (GMO) for providing the data. Also, our appreciation extended to the anonymous reviewers and editor for their constructive and useful comments that helped us to improve the quality of the paper.

Compliance with ethical standards

Conflict of interest

Regarding the conflict of interest declaration, the authors prefer all the potential reviewers from the authors’ countries are excluded from reviewing the manuscript.


  1. Abudu S, Cui C, King JP et al (2011) Modeling of daily pan evaporation using partial least squares regression. Sci China Technol Sci 54:163–174. doi: 10.1007/s11431-010-4205-z CrossRefGoogle Scholar
  2. Al-Shammari ET, Mohammadi K, Keivani A et al (2016) Prediction of daily dewpoint temperature using a model combining the support vector machine with firefly algorithm. J Irrig Drain Eng. doi: 10.1061/(ASCE)IR.1943-4774.0001015
  3. Bruton JM, McClendon RW, Hoogenboom G (2000) Estimating daily pan evaporation with artificial neural networks. Trans ASAE 43:491–496. doi: 10.13031/2013.2730 CrossRefGoogle Scholar
  4. Cekaite A (2016) A comparative study for estimation of wave height using traditional and hybrid soft-computing methods. Int J Comput Collab Learn 4:319–341. doi: 10.1007/s11412-009-9067-7 Google Scholar
  5. Ch S, Sohani SK, Kumar D et al (2014) A Support Vector Machine-Firefly Algorithm based forecasting model to determine malaria transmission. Neurocomputing 129:279–288. doi: 10.1016/j.neucom.2013.09.030 CrossRefGoogle Scholar
  6. Chai T, Draxler RR (2014) Root mean square error (RMSE) or mean absolute error (MAE)?—arguments against avoiding RMSE in the literature. Geosci Model Dev 7:1247–1250. doi: 10.5194/gmd-7-1247-2014 CrossRefGoogle Scholar
  7. Deo RC, Şahin M (2015) Application of the artificial neural network model for prediction of monthly standardized precipitation and evapotranspiration index using hydrometeorological parameters and climate indices in eastern Australia. Atmos Res 161–162:65–81. doi: 10.1016/j.atmosres.2015.03.018 CrossRefGoogle Scholar
  8. Deo RC, Samui P (2017) Forecasting evaporative loss by least-square support-vector regression and evaluation with genetic programming, Gaussian process, and minimax probability machine regression: case study of Brisbane City. J Hydrol Eng 22:5017003. doi: 10.1061/(ASCE)HE.1943-5584.0001506 CrossRefGoogle Scholar
  9. Deo RC, Samui P, Kim D (2015) Estimation of monthly evaporative loss using relevance vector machine, extreme learning machine and multivariate adaptive regression spline models. Stoch Environ Res Risk Assess. doi: 10.1007/s00477-015-1153-y
  10. Dogan E, Gumrukcuoglu M, Sandalci M, Opan M (2010) Modelling of evaporation from the reservoir of Yuvacik dam using adaptive neuro-fuzzy inference systems. Eng Appl Artif Intell 23:961–967. doi: 10.1016/j.engappai.2010.03.007 CrossRefGoogle Scholar
  11. Drucker H, Burges CJ, Kaufman L, Smola AJ, Vapnik V (1997) Support vector regression machines. Adv Neural Inf Process Syst 155–161Google Scholar
  12. Fahimi F, Yaseen ZM, El-shafie A (2017) Application of soft computing based hybrid models in hydrological variables modeling: a comprehensive review. Theor Appl Climatol 128(3–4):875–903Google Scholar
  13. Ghorbani MA, Khatibi R, Hosseini B, Bilgili M (2013) Relative importance of parameters affecting wind speed prediction using artificial neural networks. Theor Appl Climatol 114:107–114. doi: 10.1007/s00704-012-0821-9 CrossRefGoogle Scholar
  14. Ghorbani MA, Zadeh HA, Isazadeh M, Terzi O (2016) A comparative study of artificial neural network (MLP, RBF) and support vector machine models for river flow prediction. Environ Earth Sci 75:1–14. doi: 10.1007/s12665-015-5096-x CrossRefGoogle Scholar
  15. Ghorbani MA, Shamshirband S, Zare Haghi D et al (2017) Application of firefly algorithm-based support vector machines for prediction of field capacity and permanent wilting point. Soil Tillage Res 172:32–38. doi: 10.1016/j.still.2017.04.009 CrossRefGoogle Scholar
  16. Gleckler PJ, Taylor KE, Doutriaux C (2008) Performance metrics for climate models. J Geophys Res Atmos. doi: 10.1029/2007JD008972
  17. Gocić M, Motamedi S, Shamshirband S et al (2015) Soft computing approaches for forecasting reference evapotranspiration. Comput Electron Agric 113:164–173. doi: 10.1016/j.compag.2015.02.010 CrossRefGoogle Scholar
  18. Goyal MK, Bharti B, Quilty J et al (2014) Modeling of daily pan evaporation in sub tropical climates using ANN, LS-SVR, Fuzzy Logic, and ANFIS. Expert Syst Appl 41:5267–5276. doi: 10.1016/j.eswa.2014.02.047 CrossRefGoogle Scholar
  19. Günay ME (2016) Forecasting annual gross electricity demand by artificial neural networks using predicted values of socio-economic indicators and climatic conditions: case of Turkey. Energy Policy 90:92–101. doi: 10.1016/j.enpol.2015.12.019 CrossRefGoogle Scholar
  20. Hassanzadeh T, Faez K, Seyfi G (2012) A speech recognition system based on structure equivalent fuzzy neural network trained by firefly algorithm. In Biomedical Engineering (ICoBE), 2012 International Conference on (pp. 63–67). IEEE, Penang. doi: 10.1109/ICoBE.2012.6178956
  21. Heo K-Y, Ha K-J, Yun K-S et al (2013) Methods for uncertainty assessment of climate models and model predictions over East Asia. Int J Climatol. doi: 10.1002/joc.3692
  22. Hong W-C (2009) Hybrid evolutionary algorithms in a SVR-based electric load forecasting model. Int J Electr Power Energy Syst 31:409–417. doi: 10.1016/j.ijepes.2009.03.020 CrossRefGoogle Scholar
  23. Hsu C-W, Chang C-C, Lin C-J (2008) A practical guide to support vector classification. BJU Int 101:1396–1400. doi: 10.1177/02632760022050997 CrossRefGoogle Scholar
  24. Inc TM (2015) MATLAB (R2015a). MathWorks Inc.Google Scholar
  25. IPCC (2007) Climate change 2007: the physical science basis. Intergov Panel Clim Chang 446:727–728. doi: 10.1038/446727a Google Scholar
  26. Kaushik A, Tayal DK, Yadav K, Kaur A (2016) Integrating firefly algorithm in artificial neural network models for accurate software cost predictions. J Softw Evol Process 28:665–688. doi: 10.1002/smr.1792 CrossRefGoogle Scholar
  27. Kavousi-Fard A, Samet H, Marzbani F (2014) A new hybrid modified firefly algorithm and support vector regression model for accurate short term load forecasting. Expert Syst Appl 41:6047–6056. doi: 10.1016/j.eswa.2014.03.053 CrossRefGoogle Scholar
  28. Kayarvizhy N, Kanmani S, Uthariaraj RV (2014) ANN models optimized using swarm intelligence algorithms. WSEAS Trans Comput 13:501–519Google Scholar
  29. Keshtegar B, Piri J, Kisi O (2016) A nonlinear mathematical modeling of daily pan evaporation based on conjugate gradient method. Comput Electron Agric 127:120–130. doi: 10.1016/j.compag.2016.05.018 CrossRefGoogle Scholar
  30. Keskin ME, Terzi Ö, Taylan D (2009) Estimating daily pan evaporation using adaptive neural-based fuzzy inference system. Theor Appl Climatol 98:79–87. doi: 10.1007/s00704-008-0092-7 CrossRefGoogle Scholar
  31. Kişi Ö (2006) Daily pan evaporation modelling using a neuro-fuzzy computing technique. J Hydrol 329:636–646. doi: 10.1016/j.jhydrol.2006.03.015 CrossRefGoogle Scholar
  32. Kisi O (2007) Evapotranspiration modelling from climatic data using a neural computing technique. Hydrol Process 21:1925–1934. doi: 10.1002/hyp.6403 CrossRefGoogle Scholar
  33. Kisi O, Genc O, Dinc S, Zounemat-Kermani M (2016) Daily pan evaporation modeling using chi-squared automatic interaction detector, neural networks, classification and regression tree. Comput Electron Agric 122:112–117. doi: 10.1016/j.compag.2016.01.026 CrossRefGoogle Scholar
  34. Lima AR, Cannon AJ, Hsieh WW (2016) Forecasting daily streamflow using online sequential extreme learning machines. J Hydrol 537:431–443. doi: 10.1016/j.jhydrol.2016.03.017 CrossRefGoogle Scholar
  35. Lin HT, Lin CJ (2003) A study on sigmoid kernels for SVM and the training of non-PSD kernels by SMO-type methods. Neural Comput 1–32Google Scholar
  36. Lukasik S, Zak S (2009) Firefly algorithm for continuous constrained optimization tasks. Firefly Algorithm Contin Constrained Optim Tasks 5796:97–106. doi: 10.1007/978-3-642-04441-0_8 Google Scholar
  37. Macfarlane C, Ogden GN (2012) An improved evaporation dome for forest environments. Comput Electron Agric 89:126–129. doi: 10.1016/j.compag.2012.09.004 CrossRefGoogle Scholar
  38. Mba L, Meukam P, Kemajou A (2016) Application of artificial neural network for predicting hourly indoor air temperature and relative humidity in modern building in humid region. Energy Build 121:32–42. doi: 10.1016/j.enbuild.2016.03.046 CrossRefGoogle Scholar
  39. McClelland JL, Rumelhart DE (1988) Explorations in parallel distributed processing: a handbook of models, programs, and exercises. Explor Parallel Distrib Process Handb Model Programs Exerc 344:ix, 344. doi: 10.2307/1423065 Google Scholar
  40. Misra D, Oommen T, Agarwal A et al (2009) Application and analysis of support vector machine based simulation for runoff and sediment yield. Biosyst Eng 103:527–535. doi: 10.1016/j.biosystemseng.2009.04.017 CrossRefGoogle Scholar
  41. Moghaddamnia A, Ghafari Gousheh M, Piri J et al (2009) Evaporation estimation using artificial neural networks and adaptive neuro-fuzzy inference system techniques. Adv Water Resour 32:88–97. doi: 10.1016/j.advwatres.2008.10.005 CrossRefGoogle Scholar
  42. Mohanty S, Jha MK, Raul SK et al (2015) Using artificial neural network approach for simultaneous forecasting of weekly groundwater levels at multiple sites. Water Resour Manag 29:5521–5532. doi: 10.1007/s11269-015-1132-6 CrossRefGoogle Scholar
  43. Nash JE, Sutcliffe JV (1970) River flow forecasting through conceptual models part I—a discussion of principles. J Hydrol 10:282–290. doi: 10.1016/0022-1694(70)90255-6 CrossRefGoogle Scholar
  44. Soleymani SA, Goudarzi S, Anisi MH et al (2016) A novel method to water level prediction using RBF and FFA. Water Resour Manag:1–19. doi: 10.1007/s11269-016-1347-1
  45. Taylor KE (2001) Summarizing multiple aspects of model performance in a single diagram. J Geophys Res Atmos 106:7183–7192. doi: 10.1029/2000JD900719 CrossRefGoogle Scholar
  46. Trajkovic S (2005) Temperature-based approaches for estimating reference evapotranspiration. J Irrig Drain Eng 131:316–323. doi: 10.1061/(ASCE)0733-9437(2005)131:4(316) CrossRefGoogle Scholar
  47. Vapnik V (1995) The nature of statistical learning theory. Springer-Verlag New York, Inc., New YorkCrossRefGoogle Scholar
  48. Willmott CJ, Matsuura K (2005) Advantages of the mean absolute error (MAE) over the root mean square error (RMSE) in assessing average model performance. Clim Res 30:79–82. doi: 10.3354/cr030079 CrossRefGoogle Scholar
  49. Willmott CJ, Robeson SM, Matsuura K (2012) A refined index of model performance. Int J Climatol 32:2088–2094. doi: 10.1002/joc.2419 CrossRefGoogle Scholar
  50. Yang X-S (2010) Firefly algorithm, stochastic test functions and design optimization. Int J Bio-inspired Comput 2(2):78–84. doi: 10.1504/IJBIC.2010.032124 CrossRefGoogle Scholar
  51. Yaseen ZM, El-shafie A, Jaafar O et al (2015) Artificial intelligence based models for stream-flow forecasting: 2000–2015. J Hydrol 530:829–844. doi: 10.1016/j.jhydrol.2015.10.038 CrossRefGoogle Scholar
  52. Yaseen ZM, Allawi MF, Yousif AA, Jaafar O, Hamzah FM, El-Shafie A (2016a) Non-tuned machine learning approach for hydrological time series forecasting. Neural Comput & Appl 1–13. doi:  10.1007/s00521-016-2763-0
  53. Yaseen ZM, Jaafar O, Deo RC et al (2016b) Stream-flow forecasting using extreme learning machines: a case study in a semi-arid region in Iraq. J Hydrol. doi: 10.1016/j.jhydrol.2016.09.035
  54. Yoon H, Jun SC, Hyun Y, Bae GO, & Lee KK (2011) A comparative study of artificial neural networks and support vector machines for predicting groundwater levels in a coastal aquifer. JHydrol 396(1):128–138Google Scholar

Copyright information

© Springer-Verlag GmbH Austria 2017

Authors and Affiliations

  • M. A. Ghorbani
    • 1
    • 2
  • Ravinesh C. Deo
    • 3
  • Zaher Mundher Yaseen
    • 4
    • 5
    Email author
  • Mahsa H. Kashani
    • 6
  • Babak Mohammadi
    • 1
  1. 1.Department of Water EngineeringUniversity of TabrizTabrizIran
  2. 2.Engineering FacultyNear East UniversityMersin 10Turkey
  3. 3.School of Agricultural, Computational and Environmental Sciences, Institute of Agriculture and Environment (IAg & E)University of Southern QueenslandSpringfieldAustralia
  4. 4.Civil and Structural Engineering Department, Faculty of Engineering and Built EnvironmentUniversiti Kebangsaan MalaysiaBangiMalaysia
  5. 5.Dams and Water Resources Department, College of EngineeringUniversity of AnbarRamadiIraq
  6. 6.Department of Water EngineeringUniversity of Mohaghegh ArdabiliArdabilIran

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