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GLUE analysis of meteorological-based crop coefficient predictions to derive the explicit equation

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Abstract

The crop coefficient (Kc) is a scaling factor to calculate crop evapotranspiration (ETc). Accurate prediction of Kc affects planning to allocate water resources, especially in arid and semi-arid areas with limited water sources availability. The conventional FAO approach has some limited applications due to using plant characteristics. However, existing artificial intelligence approaches have high performances, but encounter some instability in prediction. In the present study, the generalized likelihood uncertainty estimation (GLUE) approach was applied to assess uncertainties arising from both model structure and input parameters. In addition, this study aims to derive the explicit predictive and usable equation for calculating the monthly Kc of maize. The equations were developed from the best hybrid MLP model using minimal meteorological data in four regions of Egypt. For this, the predictive utility of MLP-based models that hybridized with meta-heuristic optimization algorithms was examined. The rat swarm optimization (RSO), firefly algorithm (FFA), bat algorithm (BA), and genetic algorithm (GA) hybridized with MLP (MLP-RSO, MLP-FFA, MLP-BA, and MLP-GA) are used as equation derivation tools. The results showed that a unique hybrid Gamma Test-RSO is a powerful approach for determining the optimal combination (Tmax, Tmin, Rs) as the best input vector. The results showed that the hybrid MLP-RSO model decreased the average RMSE by 13.87, 39.95, 45.68, and 53.09% than MLP-BA, MLP-FFA, MLP-GA, and MLP models, respectively. In addition, the uncertainty results showed that the Kc predictions were more stable and confident in MLP-RSO, while the average of 95PPU covered 94.5 and 91.5% of actual Kc for input parameters and model structure uncertainties, respectively. In conclusion, the developed hybrid model and the techniques illustrated in the current study suggest substantial benefits for other researchers to derive mathematical equations from easily available meteorological variables in different regions and climates. Also, the findings provide a fundamental guideline for the local water users and agricultural development planners to achieve accurate and fast irrigation scheduling.

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Data availability statements

The datasets generated during the current study are available for other researchers.

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Authors and Affiliations

  1. Agricultural Engineering Department, Faculty of Agriculture, Mansoura University, Mansoura, 35516, Egypt

    Ahmed Elbeltagi

  2. Department of Water Science & Engineering, Faculty of Agriculture, Vali-e-Asr University of Rafsanjan, P.O. Box 518, Rafsanjan, Iran

    Akram Seifi

  3. Department of Water Engineering and Hydraulic Structures, Faculty of Civil Engineering, Semnan University, Semnan, Iran

    Mohammad Ehteram

  4. Vegetable Chemistry-Water-Energy Research Laboratory, Faculty of Civil Engineering and Architecture, University of Chlef, Hassiba Benbouali, B.P. 78C, Ouled Fares, 02180, Chlef, Algeria

    Bilel Zerouali

  5. Department of Irrigation and Drainage Engineering, G.B. Pant, University of Agriculture and Technology, Pantnagar, Uttarakhand, 263145, India

    Dinesh Kumar Vishwakarma

  6. Punjab Agricultural University, Ludhiana, Punjab, 141004, India

    Kusum Pandey

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Elbeltagi, A., Seifi, A., Ehteram, M. et al. GLUE analysis of meteorological-based crop coefficient predictions to derive the explicit equation. Neural Comput & Applic 35, 14799–14824 (2023). https://doi.org/10.1007/s00521-023-08466-4

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