Daily reference evapotranspiration prediction using empirical and data-driven approaches: A case study of Adana plain

Abstract

Precise determination of the reference evapotranspiration (ET0) is vital to studying the hydrological cycle. In addition, it plays a significant role in properly managing and allocating water resources in agriculture. The objective of this research was to examine the effectiveness of five different data-driven techniques, including artificial neural networks "multilayer perceptron" (ANN), gene expression programming (GEP), random forest (RF), support vector machine "radial basis function" (SVM), and multiple linear regression (MLR) to model the daily ET0. These methods were also compared with Hargreaves-Samani (HS), Oudin, Ritchie, Makkink (MAK), and Jensen Haise (JH) empirical models and their calibrated versions. The empirical models JH and MAK performed better than the models HS and Oudin after being calibrated by linear regression. All data-driven methods with four inputs were superior to the original and calibrated empirical models. Generally, data-driven models provided increased accuracy and enhanced generalization in predicting daily reference evapotranspiration compared to empirical models. The RF and ANN methods generally demonstrated better estimation accuracy than other data-driven methods. The performance of the RF and ANN models that utilized Tmax, Tmin, and Rs inputs, as well as those that incorporated Tmax, Tmin, Rs, and U2 inputs, proved to be superior to their corresponding MLR-based and GEP-based models for predicting ET0 in the Adana plain, which is characterized by a Mediterranean climate. Nevertheless, the GEP and MLR methods have the advantage of utilizing explicit algebraic equations, making them more convenient to apply, especially in the context of agricultural irrigation practices.

Keywords

• Reference evapotranspiration
• Data-driven approaches
• Empirical models
• Calibration
• Adana plain

References

1. Abrishami N, Sepaskhah A R & Shahrokhnia M H (2019). Estimating wheat and maize daily evapotranspiration using artificial neural network. Theoretical and Applied Climatology 135: 945-958. https://doi.org/10.1007/s00704-018-2418-4
2. Achite M, Jehanzaib M, Sattari M T, Toubal A K, Elshaboury N, Wałęga A, Krakauer N Y, Yoo J & Kim T (2022). Modern techniques to modeling reference evapotranspiration in a semiarid area based on ANN and GEP models. Water 14(8): 1210. https://doi.org/10.3390/w14081210
3. Allen R G, Pereira L S, Raes D & Smith M (1998). Crop evapotranspiration. Guidelines for computing crop water requirements. FAO Irrigation and Drainage Paper (56) Rome: FAO
4. Almorox J & Grieser J (2016). Calibration of the Hargreaves–Samani method for the calculation of reference evapotranspiration in different Köppen climate classes. Hydrology Research 47(2): 521-531. https://doi.org/10.2166/nh.2015.091
5. Antonopoulos V Z & Antonopoulos A V (2017). Daily reference evapotranspiration estimates by artificial neural networks technique and empirical equations using limited input climate variables. Computers and Electronics in Agriculture 132: 86-96. https://doi.org/10.1016/j.compag.2016.11.011
6. Banda P, Cemek B & Küçüktopcu E (2018). Estimation of daily reference evapotranspiration by neuro computing techniques using limited data in a semiarid environment. Archives of Agronomy and Soil Science 64(7): 916-929. https://doi.org/10.1080/03650340.2017.1414196
7. Bayram S & Çıtakoğlu H (2023). Modeling monthly reference evapotranspiration process in Turkey: application of machine learning methods. Environmental Monitoring and Assessment 195(1): 67. https://doi.org/10.1007/s10661-022-10662-z
8. Benzaghta M A, Mohammed T A, Ghazali A H, Amin M S M & Soom M A B M (2012). Prediction of evaporation in tropical climate using artificial neural network and climate based models. Scientific Research and Essays 7(36): 3133-3148. https://doi.org/10.5897/SRE11.1311

9. Breiman L (2001). Random forests. Machine Learning 45: 5-32
10. Chen Z, Zhu Z, Jiang H and Sun S (2020). Estimating daily reference evapotranspiration based on limited meteorological data using deep learning and classical machine learning methods. Journal of Hydrology 591(2020): 125286. https://doi.org/10.1016/j.jhydrol.2020.125286
11. Choi Y, Kim M, O'Shaughnessy S, Jean J, Kim Y & Song W J (2018). Comparison of artificial neural network and empirical models to determine daily reference evapotranspiration. Journal of Korean Society of Agricultural Engineers 60(6): 43-54. https://doi.org/10.5389/KSAE.2018.60.6.043
12. Citakoglu H, Cobaner M, Haktanir T & Kisi O (2014). Estimation of monthly mean reference evapotranspiration in Turkey. Water Resources Management 28: 99-113. https://doi.org/10.1007/s11269-013-0474-1
13. Cobaner M, Citakoglu H, Haktanir T & Kisi O (2017). Modifying Hargreaves–Samani equation with meteorological variables for estimation of reference evapotranspiration in Turkey. Hydrology Research 48: 480-497. https://doi.org/10.2166/nh.2016.217
14. Corzo G & Solomatine D (2007). Baseflow separation techniques for modular artificial neural network modelling in flow forecasting. Hydrological Sciences Journal 52(3): 91-507. https://doi.org/10.1623/hysj.52.3.491
15. CSB (2023). Urbanization and climate change. The governor of Adana, Ministry of Environment. https://adana.csb.gov.tr/ilim izi-taniyalim-i-1222, Accessed 16 February 2023.
16. Cutler A, Cutler D R & Stevens J R (2012). Random forests. Ensemble machine learning: Methods and applications, pp. 157-175. https://doi.org/10.1007/978-1-4419-9326-7_5.
17. Dimitriadou S & Nikolakopoulos K G (2022). Multiple linear regression models with limited data for the prediction of reference evapotranspiration of the Peloponnese, Greece. Hydrology 9(7): 124. https://doi.org/10.3390/hydrology9070124
18. Djaman K, Tabari H, Balde A B, Diop L, Futakuchi K & Irmak S (2016). Analyses, calibration and validation of evapotranspiration models to predict grass-reference evapotranspiration in the Senegal river delta. Journal of Hydrology: Regional Studies 8: 82-94. https://doi.org/10.1016/j.ejrh.2016.06.003
19. Dong J, Xing L, Cui N, Guo L, Liang C, Zhao L, Wang Z & Gong D (2024) Estimating reference crop evapotranspiration using optimized empirical methods with a novel improved Grey Wolf Algorithm in four climatic regions of China. Agricultural Water Management 291: 2024. https://doi.org/10.1016/j.agwat.2023.108620
20. Dou X & Yang Y (2018). Evapotranspiration estimation using four different machine learning approaches in different terrestrial ecosystems. Computers and Electronics in Agriculture 148: 95-106. https://doi.org/10.1016/j.compag.2018.03.010
21. Farias V D, Costa D L, Pinto J V, Souza P J, Souza E B & Ortega-Farias S (2020). Calibration of reference evapotranspiration models in Pará. Acta Scientiarum Agronomy 42. https://doi.org/10.4025/actasciagron.v42i1.42475
22. Farzanpour H, Shiri J, Sadraddini A A & Trajkovic S (2019). Global comparison of 20 reference evapotranspiration equations in a semiarid region of Iran. Hydrology Research 50(1): 282-300. https://doi.org/10.2166/nh.2018.174
23. Fauset L V (2006). Fundamentals of neural networks: architectures, algorithms and applications. Pearson Education India.
24. Feng Y, Cui N, Zhao L, Hu X & Gong D (2016). Comparison of ELM, GANN, WNN and empirical models for estimating reference evapotranspiration in humid region of Southwest China. Journal of Hydrology 536: 376-383. https://doi.org/10.1016/j.jhydrol.2016.02.053
25. Feng Y, Peng Y, Cui, N, Gong D & Zhang K (2017). Modeling reference evapotranspiration using extreme learning machine and generalized regression neural network only with temperature data. Computers and Electronics in Agriculture 136: 71-78. https://doi.org/10.1016/j.compag.2017.01.027
26. Ferreira C (2001). Gene expression programming: A new adaptive algorithm for solving problems. Complex Systems 13(2): 87-129
27. Ferreira L B, Cunha F F, Duarte A B, Sediyama G C & Cecon P R (2018). Calibration methods for the Hargreaves-Samani equation. Ciencia E Agrotecnologia 42: 104-114. http://dx.doi.org/10.1590/1413-70542018421017517
28. Ferreira L B, Cunha F F, de Oliveira R A & Filho E I (2019). Estimation of reference evapotranspiration in Brazil with limited meteorological data using ANN and SVM - A new approach. Journal of Hydrology 572: 556-570. https://doi.org/10.1016/j.jhydrol.2019.03.028
29. Gao X, Peng S, Xu J, Yang S & Wang W (2015). Proper methods and its calibration for estimating reference evapotranspiration using limited climatic data in Southwestern China. Archives of Agronomy and Soil Science 61(3): 415-426. https://doi.org/10.1080/03650340.2014.933810
30. Gavili S, Sanikhani H, Kisi O & Mahmoudi M H (2018). Evaluation of several soft computing methods in monthly evapotranspiration modelling. Meteorological Applications 25(1): 128-138. https://doi.org/10.1002/met.1676
31. Gharehbaghi A & Kaya B (2022). Calibration and evaluation of six popular evapotranspiration formula based on the Penman-Monteith model for continental climate in Turkey. Physics and Chemistry of the Earth, Parts A/B/C, 127, 103190. https://doi.org/10.1016/j.pce.2022.103190
32. Gocić M, Motamedi S, Shamshirband S, Petković D, Sudheer C, Roslan H & Muhammad A (2015). Soft computing approaches for forecasting reference evapotranspiration. Computers and Electronics in Agriculture 113: 164-173. https://doi.org/10.1016/j.compag.2015.02.010
33. Goldblum M, Finzi M, Rowan K & Wilson A G (2023). The no free lunch theorem, Kolmogorov complexity, and the role of inductive biases in machine learning. arXiv preprint arXiv:2304.05366. https://doi.org/10.48550/arXiv.2304.05366
34. Gomariz-Castillo F, Alonso-Sarria F & Cabezas-Calvo-Rubio F (2018). Calibration and spatial modelling of daily ET0 in semiarid areas using Hargreaves equation. Earth Science Informatics 11(3): 325-340. https://doi.org/10.1007/s12145-017-0327-1
35. Hargreaves G H & Samani Z A (1985). Reference crop evapotranspiration from temperature. Applied Engineering in Agriculture 1: 96-99.
36. Huo Z, Feng S, Kang S & Dai X (2012). Artificial neural network models for reference evapotranspiration in an arid area of northwest China. Journal of Arid Environments 82: 81-90. https://doi.org/10.1016/j.jaridenv.2012.01.016
37. Irmak S, Irmak A, Allen R G & Jones J W (2003). Solar and net radiation-based equations to estimate reference evapotranspiration in humid climates. Journal of Irrigation and Drainage Engineering 129(5): 336-347. https://doi.org/10.1061/(ASCE)0733-9437(2003)129:5(336)
38. Izadifar Z (2010). Modeling and analysis of actual evapotranspiration using data driven and wavelet techniques. Undergraduate Dissertation, University of Saskatchewan.
39. Jacovides C P & Kontoyiannis H (1995). Statistical procedures for the evaluation of evapotranspiration computing models. Agricultural Water Management 27: 365-371. https://doi.org/10.1016/0378-3774(95)01152-9
40. Jain S K, Nayak P C & Sudheer K P (2008). Models for estimating evapotranspiration using artificial neural networks, and their physical interpretation. Hydrological Processes 22(13): 2225-2234. https://doi.org/10.1002/hyp.6819
41. Jang J C, Sohn E H, Park K H & Lee S (2021). Estimation of daily potential evapotranspiration in real-time from GK2A/AMI data using artificial neural network for the Korean Peninsula. Hydrology 8(3): 129 https://doi.org/10.3390/hydrology8030129
42. Jensen M E & Haise H R (1963). Estimating evapotranspiration from solar radiation. Journal of the Irrigation and Drainage Division 89(4): 15-41. https://doi.org/10.1061/JRCEA4.000028
43. Jones J W & Ritchie J T (1990). Crop growth models. In: G. J. Hoffman, T. A. Howel, & K. H. Solomon (eds.) Management of farm irrigation systems. ASAE Monograph 9: 63–69
44. Kades C (2019). Economy of Adana in 2019 [in Turkish] https://www.adanato.org.tr/ WebDosyalar/V2/Dosyalar/2020/8/13/adana-ekonomisi-2019-16-53-18.pdf, Accessed 14 January 2023
45. Karimaldini F, Shui L T, Mohamed T A, Abdollahi M & Khalili N (2012). Daily evapotranspiration modeling from limited weather data by using neuro-fuzzy computing technique Journal of Irrigation and Drainage Engineering 138(1): 21-34. https://doi.org/10.1061/(ASCE)IR.1943-4774.000034
46. Karunanithi N, Grenney W J, Whitley L D & Bovee K (1994). Neural networks for river flow prediction. Journal of Computing in Civil Engineering 8(2): 201-220. https://doi.org/10.1061/(ASCE)0887-3801(1994)8:2(201)
47. Katipoğlu O M (2023). Evaporation prediction with wavelet-based hyperparameter optimized K-Nearest Neighbors and Extreme Gradient Boosting Algorithms in a semi-arid environment. Environmental Processes 10(4): 50-51. https://doi.org/10.1007/s40710-023-00669-0
48. Katipoğlu O M, Pekı̇n M A & Akil S (2023). The Impact of preprocessing approaches on neural network performance: A case sudy on evaporation in Adana, a Mediterranean climate.” Indonesian Journal of Earth Sciences 3(2): A821-A821 https://doi.org/10.52562/injoes.2023.821
49. Kaya Y Z, Zeleňáková M, Üneş F, Demirci M, Hlavatá H & Mésároš P (2021). Estimation of daily evapotranspiration in Košice City (Slovakia) using several soft computing techniques. Theoretical and Applied Climatology 144(2021): 287-298. https://doi.org/10.1007/s00704-021-03525-z
50. Khodayvandie B, Nazemi A H, Shiri J & Trajkovic S (2022). Adopting regional calibration scenarios for ensuring reliable ETo estimates in semiarid regions: assessing the ancillary data supply method. ISH Journal of Hydraulic Engineering 28(sup1): 299-309. https://doi.org/10.1080/09715010.2020.1784803
51. Kisi O (2016). Modeling reference evapotranspiration using three different heuristic regression approaches. Agricultural Water Management 169: 162-172. https://doi.org/10.1016/j.agwat.2016.02.026
52. Kumar M, Raghuwanshi N S & Singh R (2011). Artificial neural networks approach in evapotranspiration modeling: A review. Irrigation Science 29: 11-25. https://doi.org/10.1007/s00271-010-0230-8
53. Landeras G, Ortiz-Barredo A & López J J (2008). Comparison of artificial neural network models and empirical and semi-empirical equations for daily reference evapotranspiration estimation in the Basque Country (Northern Spain). Agricultural Water Management 95(5): 553-565. https://doi.org/10.1016/j.agwat.2007.12.011
54. Liu S & Xu Z (2018). Micrometeorological methods to determine evapotranspiration. In: Li, X., Vereecken, H. (eds) Observation and measurement. Ecohydrol. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-47871-4_7-2
55. Makkink G F (1957). Ekzameno de la formulo de Penman. Netherlands Journal of Agricultural Science 5: 290-305.
56. Mattar M A & Alazba A A (2019). GEP and MLR approaches for the prediction of reference evapotranspiration. Neural Computing and Applications 31: 5843-5855. https://doi.org/10.1007/s00521-018-3410-8
57. Mcgill R, Tukey J W & Larsen W A (1978). Variations of box plots. The American Statistician 32(1): 12–16. https://doi.org/10.1080/00031305.1978.10479236
58. Mehdizadeh S, Behmanes J & Khalili K (2017). Using MARS, SVM, GEP and empirical equations for estimation of monthly mean reference evapotranspiration. Computers and Electronics in Agriculture 139: 103-114. https://doi.org/10.1016/j.compag.2017.05.002
59. Mohsin S & Lone M A (2021). Modeling of reference evapotranspiration for temperate Kashmir Valley using linear regression. Modeling Earth Systems and Environment 7: 495-502. https://doi.org/10.1007/s40808-020-00921-8
60. Negm A, Minacapilli M & Provenzano G (2018). Downscaling of American National Aeronautics and Space Administration (NASA) daily air temperature in Sicily, Italy, and effects on crop reference evapotranspiration. Agricultural Water Management 209: 151-162. https://doi.org/10.1016/j.agwat.2018.07.016
61. Noi P T, Degener J & Kappas M (2017). Comparison of multiple linear regression, cubist regression, and random forest algorithms to estimate daily air surface temperature from dynamic combinations of MODIS LST Data. Remote Sensing 9(5): 398. https://doi.org/10.3390/rs9050398
62. Orange Data Mining (2024). Orange (Version 3.34) [Software]. https://orangedatamining.com/ Accessed 15 January 2024
63. Oudin L, Hervieu F, Michel C, Perrin C, Andréassian V, Anctil F & Loumagne C (2005). Which potential evapotranspiration input for a lumped rainfall–runoff model? Part 2—Towards a simple and efficient potential evapotranspiration model for rainfall–runoff modelling. Journal of Hydrology 303(1-4): 290-306. https://doi.org/10.1016/j.jhydrol.2004.08.026
64. Pereira L S, Allen R G, Smith M & Raes D (2015). Crop evapotranspiration estimation with FAO56: past and future. Agricultural Water Management 147: 4-20. https://doi.org/10.1016/j.agwat.2014.07.031
65. Prasad R, Deo R C, Li Y & Maraseni T (2017). Input selection and performance optimization of ANN-based streamflow forecasts in the drought-prone Murray Darling Basin region using IIS and MODWT algorithm. Atmospheric Research 197 (2017): 42-63. https://doi.org/10.1016/j.atmosres.2017.06.014, 2017
66. Rahimikhoob A (2010). Estimation of evapotranspiration based on only air temperature data using artificial neural networks for a subtropical climate in Iran. Theoretical and Applied Climatology 101: 83-91. https://doi.org/10.1007/s00704-009-0204-z
67. Niaghi A R, Hassanijalilian O & Shiri J (2021). Estimation of reference evapotranspiration using spatial and temporal machine learning approaches. Hydrology 8(1): 25. https://doi.org/10.3390/hydrology8010025
68. Reis M M, Silva A J, Junior J Z, Santos L D, Azevedo A M & Lopes E M (2019). Empirical and learning machine approaches to estimating reference evapotranspiration based on temperature data. Computers and Electronics in Agriculture 165: 104937. https://doi.org/10.1016/j.compag.2019.104937
69. Sabziparvar A A & Tabari H (2010). Regional estimation of reference evapotranspiration in arid and semiarid regions. Journal of Irrigation and Drainage Engineering 136: 724-731. https://doi.org/10.1061/(ASCE)IR.1943-4774.0000242
70. Samadianfard S, Kargar K, Shadkani S, Hashemi S, Abbaspour A & Safari M J (2022). Hybrid models for suspended sediment prediction: Optimized random forest and multilayer perceptron through genetic algorithm and stochastic gradient descent methods. Neural Computing and Applications 34: 3033–3051. https://doi.org/10.1007/s00521-021-06550-1
71. Sarıgöl M & Katipoğlu O M (2024). Estimation of monthly evaporation values using gradient boosting machines and mode decomposition techniques in the Southeast Anatolia Project (GAP) area in Turkey. Acta Geophysica 2023: 1–18. https://doi.org/10.1007/s11600-023-01067-8
72. Sayyadi H, Oladghaffari A, Faalian A & Sadraddini AA (2009). Comparison of RBF and MLP neural networks performance for estimation of reference crop evapotranspiration. Water and Soil Science 19(1): 1-12
73. Seifi A & Riahi H (2020). Estimating daily reference evapotranspiration using hybrid gamma test-least square support vector machine, gamma test-ANN, and gamma test-ANFIS models in an arid area of Iran. Journal of Water and Climate Change 11(1): 217-240. https://doi.org/10.2166/wcc.2018.003
74. Shiri J, Kisi O, Landeras G, Lopez J J, Nazemi A H & Stuyt L (2012). Daily reference evapotranspiration modeling by using genetic programming approach in the Basque Country (Northern Spain). Journal of Hydrology 414: 302-316. https://doi.org/10.1016/j.jhydrol.2011.11.004
75. Shiri J (2017). Evaluation of FAO56-PM, empirical, semi-empirical and gene expression programming approaches for estimating daily reference evapotranspiration in hyper-arid regions of Iran. Agricultural Water Management 188: 101-114. https://doi.org/10.1016/j.agwat.2017.04.009
76. Shiri J (2018). Improving the performance of the mass transfer-based reference evapotranspiration estimation approaches through a coupled wavelet-random forest methodology. Journal of Hydrology 561: 737-750. https://doi.org/10.1016/j.jhydrol.2018.04.042
77. Shirzad A & Safari M J S (2019). Pipe failure rate prediction in water distribution networks using multivariate adaptive regression splines and random forest techniques. Urban Water Journal 16(9): 653-661. https://doi.org/10.1080/1573062X.2020.1713384
78. Srivastava A, Sahoo B, Raghuwanshi N S & Chatterjee C (2018). Modelling the dynamics of evapotranspiration using Variable Infiltration Capacity model and regionally calibrated Hargreaves approach. Irrigation Science 36(4-5): 289-300. https://doi.org/10.1007/s00271-018-0583-y
79. Sterkenburg T F & Grünwald P D (2021). The no-free-lunch theorems of supervised learning. Synthese 199: 9979-10015. https://doi.org/10.1007/s11229-021-03233-1
80. Tabari H, Kisi O, Ezani A & Talaee P H (2012). SVM, ANFIS, regression and climate based models for reference evapotranspiration modeling using limited climatic data in a semiarid highland environment. Journal of Hydrology 444: 78-89. https://doi.org/10.1016/j.jhydrol.2012.04.007
81. Tabari H, Grismer M E & Trajkovic S (2013a). Comparative analysis of 31 reference evapotranspiration methods under humid conditions. Irrigation Science 31: 107–117. https://doi.org/10.1007/s00271-011-0295-z
82. Tabari H, Martinez C, Ezani A & Talaee P H (2013b). Applicability of support vector machines and adaptive neurofuzzy inference system for modeling potato crop evapotranspiration. Irrigation Science 31(4): 575-588. https://doi.org/10.1007/s00271-012-0332-6
83. Taylor K E (2001), Summarizing multiple aspects of model performance in a single diagram, Journal of Geophysical Research 106(D7): 7183–7192, https://doi:10.1029/2000JD900719
84. Traore S, Wang Y M & Kerh T (2010). Artificial neural network for modeling reference evapotranspiration complex process in Sudano-Sahelian zone. Agricultural Water Management 97(5): 707-714. https://doi.org/10.1016/j.agwat.2010.01.002
85. Traore S & Guven A (2012). Regional-specific numerical models of evapotranspiration using gene-expression programming interface in Sahel. Water Resource. Management 26: 4367-4380. https://doi.org/10.1007/s11269-012-0149-3
86. Traore S & Guven A (2013). New algebraic formulations of evapotranspiration extracted from gene-expression programming in the tropical seasonally dry regions of West Africa. Irrigation Science 31: 1-10. https://doi.org/10.1007/s00271-011-0288-y
87. TSMS (2022). General directorate of state meteorology affairs. https://mevbis.mgm.gov.tr/ mevbis/ui/index.html#Workspace, accessed 15 March 2022
88. TSMS (2023). General directorate of state meteorology affairs. https://www.mgm.gov.tr/ veridegerlendirme/il-ve-ilceler-istatistik. aspx?k=unde- fined&m=ADANA, accessed 15 January 2024 TSMS (2024). General directorate of state meteorology affairs. https://www.mgm.gov.tr/FILES/iklim/iklim_siniflandirmalari/koppen.pdf, Accessed 12 January 2024.
89. Üneş F, Kaya Y Z & Mamak M (2020. Daily reference evapotranspiration prediction based on climatic conditions applying different data mining techniques and empirical equations. Theoretical and Applied Climatology 141(2020): 763-773. https://doi.org/10.1007/s00704-020-03225-0
90. Valipour M (2015). Investigation of valiantzas' evapotranspiration equation in Iran. Theoretical and Applied Climatology 121: 267-278. https://doi.org/10.1007/s00704-014-1240-x
91. Vapnik V (1995). Support-vector networks. Machine Learning 20: 273-297. https://doi.org/10.1007/BF00994018
92. Wang S, Lian J, Peng Y, Hu B & Chen H (2019). Generalized reference evapotranspiration models with limited climatic data based on random forest and gene expression programming in Guangxi, China. Agricultural Water Management 221: 220-230. https://doi.org/10.1016/j.agwat.2019.03.027
93. Wang J, Raza A, Hu Y, Buttar N A, Shoaib M, Saber K… & Ray R L (2022). Development of monthly reference evapotranspiration machine learning models and mapping of Pakistan-A comparative study. Water 14(10): 1666. https://doi.org/10.3390/w14101666
94. Willmott C J (1981). On the validation of models. Physical Geography 2: 184-194. https://doi.org/10.1080/02723646.1981.10642213
95. Yamaç S S (2021). Reference evapotranspiration estimation with kNN and ANN models using different climate input combinations in the semiarid environment. Journal of Agricultural Sciences 27 (2): 129-137. https://doi.org/10.15832/ankutbd.630303
96. Yassin M A, Alazba A A & Mattar M A (2016). Artificial neural networks versus gene expression programming for estimating reference evapotranspiration in arid climate. Agricultural Water Management 163: 110-124. https://doi.org/10.1016/j.agwat.2015.09.009
97. Yildirim D, Küçüktopcu E, Cemek B & Simsek H (2023). Comparison of machine learning techniques and spatial distribution of daily reference evapotranspiration in Türkiye. Applied Water Science 13(4): 107. https://doi.org/10.1007/s13201-023-01912-7
98. Yirga S A (2019). Modelling reference evapotranspiration for Megecha catchment by multiple linear regression. Modeling Earth Systems and Environment 5: 471-477. https://doi.org/10.1007/s40808-019-00574-2
99. Yurtseven I & Serengil Y (2021). Comparison of different empirical methods and data-driven models for estimating reference evapotranspiration in semi-arid Central Anatolian Region of Turkey. Arabian Journal of Geosciences 14: 1-28. https://doi.org/10.1007/s12517-021-08150-8