Skip to main content

Hybrid signal processing/machine learning and PSO optimization model for conjunctive management of surface–groundwater resources


Conjunctive management of surface–groundwater resources systems by means of mathematical optimization–simulation techniques becomes an important issue for sustainable water resources development, namely in water-scarce regions. In this study, the particle swarm optimization (PSO) method has been coupled with a hybrid wavelet/ANFIS–fuzzy C-means (FCM) simulation model to determine the optimal agricultural irrigation water allocation in the Miandarband plain, western Iran. Firstly, the optimal amount of conveyed water (CW) from the Gavoshan Dam into the plain is determined by constrained PSO. The constraints are the long-term minimum monthly exceedance streamflows that are estimated for different exceedance probabilities—with a 70% value found to best reflect the average annual river inflow of 3.4 m3/s into the dam—using the two-parameter Weibull distribution as well as the classical Weibull nonparametric plotting position method. Then, based on the politically prioritized proportions of the dam’s allocated water for domestic, environmental and agricultural uses, as well as the share of the plain devoted to  agriculture, the optimal monthly CW available for the plain (= 112 MCM/a) is obtained. However, the subsequent estimation of the irrigation water request (IWR) (= 265.8 MCM/a), calculated by the FAO-56 method and using empirical crop coefficients of the present agricultural pattern in the plain, indicates that there is an irrigation water deficit of 153.1 MCM/a that must be made up by groundwater withdrawal (GW), in a way that neither waterlogging nor severe drop conditions in groundwater levels (GL) will occur. The latter are then calculated by the hybrid wavelet/ANFIS (FCM) model, wherefore good performance indicators R2 and RMSE, equal to 0.98 and 0.21 m and 0.94 and 0.31 m in the training and testing phases, respectively, are obtained. Finally, PSO and the hybrid model are coupled to simulate the GL fluctuations—with the above GL constraints—under conjunctive use of the optimal surface (CW) and groundwater resources (GW) in the Miandarband plain. In conclusion, the innovative coupled simulation/optimization model turns out to be a very useful tool for optimal and sustainable conjunctive management of surface–groundwater resources in an irrigation area.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig.  16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22



Artificial intelligence


Adaptive neuro-fuzzy inference


Artificial neural network


Conveyed water


Crop water requirement


Continuous wavelet transform


Daubechies wavelet


Discrete wavelet transform


Crop evapotranspiration


Food and Agriculture Organization


Fuzzy C-means clustering method


Feedforward neural network


Genetic algorithm


Groundwater level


Groundwater withdrawal


Irrigation water requirement


Million cubic meter


Machine learning


Maximum likelihood estimation


Multiresolution analysis


Penalty function


Particle swarm optimization


Recommended volume of irrigation water


Symlet wavelet


  1. 1.

    Koch M (2008) Challenges for future sustainable water resources management in the face of climate change. In: Paper presented at the 1st NPRU Academic Conference, Nakhon Pathom University, Thailand, October 23–24

  2. 2.

    Fink G, Koch M (2010) Climate change effects on the water balance in the fulda catchment, Germany, during the 21st Century. In: Symposium on Sustainable Water Resources Management and Climate Change Adaptation, Nakhon Pathom University, Thailand, 16–17 June 2010

  3. 3.

    Zare M, Koch M (2016) Integrating spatial multi criteria decision making (SMCDM) with geographic information systems (GIS) for determining the most suitable areas for artificial groundwater recharge. In: Erpicum S, Dewals B, Archambeau P, Pirotton M (eds) Sustainable hydraulics in the era of global change: proceedings of the 4th IAHR Europe congress (Liege, Belgium, 27–29 July 2016). CRC Press, London, pp 108–117

  4. 4.

    Das B, Singh A, Panda SN, Yasuda H (2015) Optimal land and water resources allocation policies for sustainable irrigated agriculture. Land Use Policy 42:527–537.

    Article  Google Scholar 

  5. 5.

    Mani A, Tsai FTC, Kao S-C, Naz BS, Ashfaq M, Rastogi D (2016) Conjunctive management of surface and groundwater resources under projected future climate change scenarios. J Hydrol 540:397–411.

    Article  Google Scholar 

  6. 6.

    Peralta RC, Forghani A, Fayad H (2014) Multiobjective genetic algorithm conjunctive use optimization for production, cost, and energy with dynamic return flow. J Hydrol 511:776–785.

    Article  Google Scholar 

  7. 7.

    Yousefi M, Banihabib ME, Soltani J, Roozbahani A (2018) Multi-objective particle swarm optimization model for conjunctive use of treated wastewater and groundwater. Agric Water Manag 208:224–231.

    Article  Google Scholar 

  8. 8.

    Gaur S, Ch S, Graillot D, Chahar BR, Kumar DN (2013) Application of artificial neural networks and particle swarm optimization for the management of groundwater resources. Water Resour Manage 27(3):927–941.

    Article  Google Scholar 

  9. 9.

    Mitchell TM (1997) Machine Learning. McGraw-Hill, New York

    MATH  Google Scholar 

  10. 10.

    Witten IH, Frank E (2005) Data mining: practical machine learning tools and techniques, 2nd edn. Elsevier, Amsterdam

    MATH  Google Scholar 

  11. 11.

    Hegde J, Børge R (2020) Applications of machine learning methods for engineering risk assessment—A review. Saf Sci 122:104492.

    Article  Google Scholar 

  12. 12.

    Le LT, Nguyen H, Dou J, Zhou J (2019) A comparative study of PSO-ANN, GA-ANN, ICA-ANN, and ABC-ANN in estimating the heating load of buildings’ energy efficiency for smart city planning. Appl Sci 9(13):2630

    Article  Google Scholar 

  13. 13.

    Jahandideh-Tehrani M, Bozorg-Haddad O, Loáiciga HA (2020) Application of particle swarm optimization to water management: an introduction and overview. Environ Monit Assess 192(5):281.

    Article  Google Scholar 

  14. 14.

    Jahandideh-Tehrani M, Bozorg-Haddad O, Loáiciga HA (2019) Application of non-animal–inspired evolutionary algorithms to reservoir operation: an overview. Environ Monit Assess 191(7):439.

    Article  Google Scholar 

  15. 15.

    He X, Guan H, Qin J (2015) A hybrid wavelet neural network model with mutual information and particle swarm optimization for forecasting monthly rainfall. J Hydrol 527:88–100.

    Article  Google Scholar 

  16. 16.

    Raman H, Chandramouli V (1996) Deriving a general operating policy for reservoirs using neural network.

    Article  Google Scholar 

  17. 17.

    Singh A (2014) Conjunctive use of water resources for sustainable irrigated agriculture. J Hydrol 519:1688–1697.

    Article  Google Scholar 

  18. 18.

    Safavi HR, Enteshari S (2016) Conjunctive use of surface and ground water resources using the ant system optimization. Agric Water Manag 173:23–34.

    Article  Google Scholar 

  19. 19.

    Rezaei F, Safavi HR, Mirchi A, Madani K (2017) f-MOPSO: an alternative multi-objective PSO algorithm for conjunctive water use management. J Hydro-environ Res 14:1–18.

    Article  Google Scholar 

  20. 20.

    Adeyemo J, Stretch D (2018) Review of hybrid evolutionary algorithms for optimizing a reservoir. S Afr J Chem Eng 25:22–31.

    Article  Google Scholar 

  21. 21.

    Zarei A, Mousavi S-F, Eshaghi Gordji M, Karami H (2019) Optimal reservoir operation using bat and particle swarm algorithm and game theory based on optimal water allocation among consumers. Water Resour Manag 33(9):3071–3093.

    Article  Google Scholar 

  22. 22.

    Zare M, Koch M (2016) Using ANN and ANFIS Models for simulating and predicting Groundwater Level Fluctuations in the Miandarband Plain, Iran. In: Sustainable Hydraulics in the Era of Global Change: Proceedings of the 4th IAHR Europe Congress (Liege, Belgium, 27–29 July 2016). CRC Press, London

  23. 23.

    Zare M, Koch M (2018) Groundwater level fluctuations simulation and prediction by ANFIS- and hybrid Wavelet-ANFIS/Fuzzy C-Means (FCM) clustering models: application to the Miandarband plain. J Hydro-environ Res 18:63–76.

    Article  Google Scholar 

  24. 24.

    Zare M, Koch M (2016) Computation of the Irrigation Water Demand in the Miandarband Plain, Iran, using FAO-56- and Satellite- estimated. Crop Coeff Thai Interdiscipl Res 12(3):10.

    Article  Google Scholar 

  25. 25.

    Zare M, Koch M (2014) 3D- groundwater flow modeling of the possible effects of the construction of an irrigation/drainage network on water-logging in the Miandarband plain, Iran. Bas Res J Soil Environ Sci 2(3):29–39

    Google Scholar 

  26. 26.

    Anonymous (2010) Miandarband plain irrigation and drainage network, final report. Mahab Ghods Co, (in Farsi)

  27. 27.

    Mahboubi AR, Aminpour M, Kazempour S Finite element modeling and back analysis of Gavoshan dam during construction and pondage intervals. In: 5th International Conference on Dam Engineering, 14–16 Feb, Lisbon, Portugal, 2007

  28. 28.

    Anonymous (2016) Hydrogeological, hydrological and meteorological data of Kermanshah. Regional Water Organization of Kermanshah, Ministry of Power, Iran (in Farsi)

    Google Scholar 

  29. 29.

    IRIMO (2018) Iran meteorological Organization. Accessed 01.02.2018

  30. 30.

    Zare M (2009) Study effects of constructing Gavoshan dam’s irrigation and drainage network on ground water of Miandarband plain, using conceptual, mathematical model GMS 6.5. Razi university of Kermanshah, Kermanshah, Iran

  31. 31.

    Chow VT, Maidment DR, Mays LW (1988) Applied hydrology. McGraw-Hill, New York

    Google Scholar 

  32. 32.

    Cunnane C (1978) Unbiased plotting positions—a review. J Hydrol 37(3):205–222.

    Article  Google Scholar 

  33. 33.

    Hirsch RM (1987) Probability plotting position formulas for flood records with historical information. J Hydrol 96(1):185–199.

    Article  Google Scholar 

  34. 34.

    Pook LP, Laboratory NE (1984) Approximation of two parameter Weibull distribution by rayleigh distributions for fatigue testing. National Engineering Laboratory

  35. 35.

    Agbede AO, Abiona O (2012) Plotting position probability fittings to lagos metropolitan precipitation: hydrological tools for hydraulic structures design in flood control. Int J Pure Appl Sci Technol 10(1):6

    Google Scholar 

  36. 36.

    Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Proceedings of the IEEE International Conference on Neural Networks, 1995, vol 1944. pp 1942–1948.

  37. 37.

    Rao RV, Savsani VJ (2012) Mechanical design optimization using advanced optimization techniques. Springer, Incorporated

    Book  Google Scholar 

  38. 38.

    Gill MK, Kaheil YH, Khalil A, McKee M, Bastidas L (2006) Multiobjective particle swarm optimization for parameter estimation in hydrology. Water Resour Res 42(7):1.

    Article  Google Scholar 

  39. 39.

    Robinson J, Rahmat-Samii Y (2004) Particle swarm optimization in electromagnetics. IEEE Trans Antennas Propag 52(2):397–407.

    MathSciNet  Article  MATH  Google Scholar 

  40. 40.

    Ab Wahab MN, Nefti-Meziani S, Atyabi A (2015) A comprehensive review of swarm optimization algorithms. PLoS One 10(5):e0122827.

    Article  Google Scholar 

  41. 41.

    Clerc M, Kennedy J (2002) The particle swarm—explosion, stability, and convergence in a multidimensional complex space. IEEE Trans Evol Comput 6(1):58–73.

    Article  Google Scholar 

  42. 42.

    Percival DB, Walden AT (2006) Wavelet methods for time series analysis. Cambridge University Press, London

    MATH  Google Scholar 

  43. 43.

    Mallat SG (1989) A theory for multiresolution signal decomposition: the wavelet representation. IEEE Trans Pattern Anal Mach Intell 11(7):674–693.

    Article  MATH  Google Scholar 

  44. 44.

    Vetterli M, Herley C (1992) Wavelets and filter banks: theory and design. IEEE Trans Signal Process 40(9):2207–2232.

    Article  MATH  Google Scholar 

  45. 45.

    Salazar L, Nicolis O, Ruggeri F, Kisel’ák J, Stehlík M (2019) Predicting hourly ozone concentrations using wavelets and ARIMA models. Neural Comput Appl 31(8):4331–4340.

    Article  Google Scholar 

  46. 46.

    Moosavi V, Vafakhah M, Shirmohammadi B, Behnia N (2013) A wavelet-ANFIS hybrid model for groundwater level forecasting for different prediction periods. Water Resour Manage 27(5):1301–1321.

    Article  Google Scholar 

  47. 47.

    Bezdek JC (1981) Pattern recognition with fuzzy objective function algorithms. Plenum Press, New York

    Book  Google Scholar 

  48. 48.

    Ayvaz MT, Karahan H, Aral MM (2007) Aquifer parameter and zone structure estimation using kernel-based fuzzy c-means clustering and genetic algorithm. J Hydrol 343(3–4):240–253.

    Article  Google Scholar 

  49. 49.

    Sadri S, Burn DH (2011) A fuzzy C-means approach for regionalization using a bivariate homogeneity and discordancy approach. J Hydrol 401(3–4):231–239.

    Article  Google Scholar 

  50. 50.

    Jang JSR (1993) ANFIS: adaptive-network-based fuzzy inference systems. IEEE Trans Syst Man Cybern 23(3):665–685

    Article  Google Scholar 

  51. 51.

    Tahmasebi P, Hezarkhani A (2012) A hybrid neural networks-fuzzy logic-genetic algorithm for grade estimation. Comput Geosci 42:18–27

    Article  Google Scholar 

  52. 52.

    Allen RG, Pereira LS, Raes D, Smith M (1998) Crop evapotranspiration-Guidelines for computing crop water requirements-FAO Irrigation and drainage paper 56. FAO, Rome 300(9):D05109

    Google Scholar 

  53. 53.

    Shoorehdeli MA, Teshnehlab M, Sedigh AK, Khanesar MA (2009) Identification using ANFIS with intelligent hybrid stable learning algorithm approaches and stability analysis of training methods. Appl Soft Comput 9(2):833–850.

    Article  Google Scholar 

Download references

Author information



Corresponding author

Correspondence to Mohammad Zare.

Ethics declarations

Conflict of interest

The authors declare that they have 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

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Zare, M., Koch, M. Hybrid signal processing/machine learning and PSO optimization model for conjunctive management of surface–groundwater resources. Neural Comput & Applic 33, 8067–8088 (2021).

Download citation


  • Conjunctive surface–groundwater management
  • Hybrid wavelet/ANFIS–FCM model
  • Particle swarm optimization
  • Irrigation water requirement Miandarband plain
  • Iran