Implementation of evolutionary computing models for reference evapotranspiration modeling: short review, assessment and possible future research directions

Figures & data

Figure 1. Schematic diagram of hydrological cycle showing the importance of evapotranspiration (ET).

Table 1. Short review of the implementation of evolutionary computing models for the estimation of reference evapotranspiration (2007–2019).

Authors (year)	Predictive models	Input/output variables	Timescale	Region	Best predictive model	Performance metrics
Parasuraman et al. (2007)	GP, ANN	NR, ST, T, WS, RH/EC-LE	Hourly	Canada	GP	RMSE, MARE, R
Guven et al. (2008)	GEP	SR, T, ST, RH, VP, WS, WD, RF/ETo	Daily	California	GA	MSE, R^2
Kim and Kim (2008)	COMBINE-GRNNM-GA, EXTREME-GRNNM-GA and Average-GRNNM-GA based on GRNN and GA	Tmax, Tmean, Tmin, RHmin, RHmean, SD, WSmean, WSmax, SD, DPmean	Daily	Republic of Korea	COMBINE-GRNNM-GA	RMSE, MAE, E, CC
Kisi and Guven (2010)	LGP, SVR, ANN	Tmax, RH, SR, WS/ETo	Daily	Windsor, Oakville, Santa Rosa	LGP	RMSE, R^2, MAE
El-Baroudy et al. (2010)	GEP, EPR, ANN	NR, T, ST, WS, RH/ETo	Hourly	Canada	EPR	RMSE, MARE, R
Izadifar and Elshorbagy (2010)	GP, ANN, statistical models, Penman	NR, ST, T, RH, WS/EC-AET	Hourly	Canada	GP	RMSE, MARE, R
Kisi (2010)	FG1, FG2, ANN, Hargreaves, Ritchie, Turc	Tmax, RH, SR, WS/ETo	Daily	California	FG2	RMSE, MAE, R
Shiri et al. (2012)	GEP, ANFIS, empirical formulations	Tmax, Tmean, Tmin, RH, SR, WS/ETo	Daily	Spain	GEP	RMSE, R^2, SI
Traore and Guven (2012)	GEP	NR, Tmean, RH, WS/ETo	Daily	Burkina Faso	GEP	RMSE, R^2
Jean et al. (2012)	GEP, PM	Tmean, SR, soil HF, NR, WS, evaporation seepage loss	Monthly	Datong Basin	GEP	–
Eslamian et al. (2012)	ANN-GA, ANN	Tmax, Tmean, Tmin, RH, SR, WS/ETo	Monthly	Iran	ANN-GA	MSE, NMSE, MAE, min/max absolute error, R^2
Shiri et al. (2013)	GEP, ANFIS, empirical formations	Tmax, Tmean, Tmin, RH, SR, WS/ETo	Daily	Iran	GEP	MAE, SI, NS, R^2
Traore and Guven (2013)	GEP	Tmax, Tmin, RF, RH, Sh, WS/ETo	Daily	Burkina Faso	GEP	RMSE, R^2
Shiri, Nazemi, et al. (2014)	ANN, ANFIS, SVR, GEP, empirical formulations	Tmax, Tmean, Tmin, RH, SR, WS/ETo	Daily	Iran	GEP	RMSE, R^2, SI, MAE
Shiri, Sadraddini, et al. (2014)	GEP1–3	Tmax, Tmean, Tmin, RH, SR, WS/ETo	Daily	Iran	GEP	RMSE, R^2, AARE, MAE
Kisi et al. (2015)	ANN, ANFIS-GP, ANFIS-SC, GEP	Data periodic, station latitude, longitude and altitude/ETo	Monthly	Iran	ANFIS-GP, ANFIS-SC	RMSE, R^2
Martí et al. (2015)	GEP, empirical formulations	ETo/ETo	Daily	Spain	GEP	RMSE, R^2, MAE
Gocić et al. (2015)	GP, SVR-FFA, ANN, WA-SVR, Penman	Tmax, Tmin, VP, Sh, WS/ETo	Monthly	Serbia	SVM-wavelet	RMSE, R^2, r, MAE, MAPE
Yassin, Alazba, and Mattar (2016a)	ANN, GEP, Penman	Tmax, Tmean, Tmin, RHmax, RHmean, RHmin, SR, WS/ETo	Daily	Saudi Arabia	ANN	RMSE, R^2, OI, MAE
Alazba et al. (2016)	GEP	Tmax, Tmean, Tmin, RHmax, RHmean, RHmin, SR, WS/ETo	Daily	Saudi Arabia	GEP	RMSE, R^2, MAE
Yassin et al. (2016b)	GEP	Tmax, Tmean, Tmin, RHmax, RHmean, RHmin, SR, WS/ETo	Daily	Saudi Arabia	GEPMOD8	RMSE, R^2, OI, MAE
Kumar et al. (2016)	ELM, ANN, SVM, GP	Tmax, Tmin, RHmax, RHmin, SR, IS, rainfall, WS/ETo	Daily	India	ELM	RMSE, R^2, Time
Karimi et al. (2017)	SVM, GEP	Tmax, Tmin, RH, SR, WS/ETo	Daily	Republic of Korea	GEP	MAE, CRM
Kiafar et al. (2017)	GEP, mass transfer, temperature- and radiation-based models	Tmax, Tmean, Tmin, RH, SR, WS/ETo	Daily	Iran, Spain	GEP	RMSE, R^2, CRM
Mehdizadeh et al. (2017)	MARS, SVR, GEP	Tmax, Tmean, Tmin, RH, SR, WS/ETo	Monthly	Iran	MARS	RMSE, R^2, MAE
Traore et al. (2017)	GEP, Penman	Tmax, Tmean, Tmin, RH, Sh, WS/ETo	Daily	China	GEPMLP	RMSE, R, MAE, RRSE
Shiri (2017)	KP temperature-based radiation-based and GEP1–8	Tmax, Tmin, Tmean, RHmean, SR, WS/ETo	Daily	Iran	GEP	SI, MAE, NS
Feng et al. (2017)	RF, GRNN	Tmax, Tmin, RH, SR, SD, WS/ETo	Daily	China	RF	RRMSE, MAE, NS
Landeras et al. (2018)	ANN, GEP	Tmax, Tmin, Tmean, RHmax, RHmin, RHmean, SD, WS/ETo	Daily	Ghana	GEP	RMSE, MAE, SI
Mattar and Alazba (2018)	GEP, MLR, Penman	Tmax, Tmin, RHmean, SR, WS/ETo	Monthly	Egypt	GEP	RMSE, R, MAE
Mattar (2018)	GEP, empirical formulations	Tmax, Tmin, RHmean, SR, WS/ETo	Monthly	Egypt	GEP	RMSE, OI, IAs
Mehdizadeh (2018)	MARS, GEP	T, RH, SR, WS/ETo	Daily	Iran	GEP1-ARCH	RMSE, R^2, MAE, MAPE
Jovic et al. (2018)	GP	Tmax, Tmean, Tmin, RH, Sh, WS/ETo	Monthly	–	GP6	RMSE, R^2
Mohammad et al. (2018)	SVM, ANFIS, GEP	Tmax, Tmean, Tmin, RH, Sh, WS/ETo	Daily	Zabol, Zahedan, Iranshahr, Chabahar	SVM	RMSE, R^2, MAE
Shiri (2019)	GEP	Tmax, Tmean, Tmin, RH, Sh, WS/ETo	Monthly	Island	E1-GEP4, E2-GEP4	IOA, RMSE, NS
Sanikhani et al. (2019)	MLP, GRNN, RBFNN, ANFIS-GP, ANFIS-SC, GEP	Tmax, Tmean, Tmin, RH, Sh, WS/ETo	Monthly	Antalya, Isparta	RBNN, GEP	RMSE, R^2, MAE, CRM, NS
Shiri et al. (2019)	GEP, temperature- and radiation-based models	Tmax, Tmean, Tmin, Ra, SR/ETo	Daily	North-western Iran	GEP	SI, NS

Notes: AARE = average absolute relative error; ANFIS = adaptive neuro-fuzzy inference system; ANFIS-GP = adaptive neuro-fuzzy inference system integrated with grid partition; ANFIS-SC = adaptive neuro-fuzzy inference system integrated with subtractive clustering; ANN = artificial neural network; ARCH = autoregressive conditional heteroscedasticity; CC = correlation coefficient; CRM = coefficient of residual mass; DP = dew point; E = efficiency; EC-AET = eddy covariance-measured actual evapotranspiration; EC-LE = eddy-covariance-measured latent heat; ELM = extreme learning machine; EPR = evolutionary polynomial regression; ET_o = reference evapotranspiration; FFA = firefly algorithm; FG = fuzzy genetic; GA = genetic algorithm; GEP = gene expression programming; GP = genetic programming; GRNN = generalized regression neural network; GRNNM = generalized regression neural networks model; HF = heat flux; IAs = index of agreements; IOA = index of agreement; SI = scatter index; KP = Kimberly–Penman; LGP = linear genetic programming; MAE = mean absolute error; MAPE = mean absolute percentage error; MARE = mean absolute relative error; MARS = multivariate adaptive regression spline; MLP = multilayer perceptron; MLR = multiple linear regression; MSE = mean square error; NMSE = normalized mean square error; NR = net radiation; NS = Nash–Sutcliffe efficiency coefficient; OI = overall index; PM = Penman–Monteith; Ra = extraterrestrial radiation; R² = coefficient of determination; RBFNN = radial basis function neural network; RBNN = radial basis neural network; RF = rainfall; RH = relative humidity; RMSE = root mean square error; RRMSE = relative root mean square error; RRSE = root relative squared error; SD = sunshine duration; Sh = sunshine; SI = scatter index; SR = solar radiation; ST = soil temperature; SVM = support vector machine; SVR = support vector regression; T = temperature; T_max, T_mean and T_min = maximum, mean and minimum air temperature; VP = vapor pressure; WA = wavelet; WD = wind direction; WS = wind speed.

Parasuraman, K., Elshorbagy, A., & Carey, S. K. (2007). Modelling the dynamics of the evapotranspiration process using genetic programming. Hydrological Sciences Journal, 52(3), 563–578. doi: 10.1623/hysj.52.3.563

 Web of Science ®Google Scholar

Guven, A., Aytek, A., Yuce, M. I., & Aksoy, H. (2008). Genetic programming-based empirical model for daily reference evapotranspiration estimation. Clean - Soil, Air, Water, 36(10–11), 905–912. doi: 10.1002/clen.200800009

 Web of Science ®Google Scholar

Kim, S., & Kim, H. S. (2008). Neural networks and genetic algorithm approach for nonlinear evaporation and evapotranspiration modeling. Journal of Hydrology, 351(3–4), 299–317. doi: 10.1016/j.jhydrol.2007.12.014

 Web of Science ®Google Scholar

Kisi, O., & Guven, A. (2010). Evapotranspiration modeling using linear genetic programming technique. Journal of Irrigation and Drainage Engineering, 136(October), 715–723.

 Web of Science ®Google Scholar

El-Baroudy, I., Elshorbagy, A., Carey, S. K., Giustolisi, O., & Savic, D. (2010). Comparison of three data-driven techniques in modelling the evapotranspiration process. Journal of Hydroinformatics, 12(4), 365–379. doi: 10.2166/hydro.2010.029

 Web of Science ®Google Scholar

Izadifar, Z., & Elshorbagy, A. (2010). Prediction of hourly actual evapotranspiration using neural networks, genetic programming, and statistical models. Hydrological Processes, 24(23), 3413–3425. doi: 10.1002/hyp.7771

 Web of Science ®Google Scholar

Kisi, O. (2010). Fuzzy genetic approach for modeling reference evapotranspiration. Journal of Irrigation and Drainage Engineering, 136(March), 175–183.

 Web of Science ®Google Scholar

Shiri, J., Kişi, Ö, Landeras, G., López, J. J., Nazemi, A. H., & Stuyt, L. C. P. M. (2012). Daily reference evapotranspiration modeling by using genetic programming approach in the Basque Country (Northern Spain). Journal of Hydrology, 414–415, 302–316. doi: 10.1016/j.jhydrol.2011.11.004

 Web of Science ®Google Scholar

Traore, S., & Guven, A. (2012). Regional-specific numerical models of evapotranspiration using gene-expression programming interface in sahel. Water Resources Management, 26(15), 4367–4380. doi: 10.1007/s11269-012-0149-3

 Web of Science ®Google Scholar

Jean, M., Paix, D., Lanhai, L. I., Jiwen, G. E., Jean, N., & Verenyam, A. (2012). Water losses in arid and semi-arid zone: Evaporation, evapotranspiration and seepage. Journal of Mountain Science, 9, 256–261. doi: 10.1007/s11629-012-2186-z

 Web of Science ®Google Scholar

Eslamian, S. S., Gohari, S. A., Zareian, M. J., & Firoozfar, A. (2012). Estimating Penman–Monteith reference evapotranspiration using artificial neural networks and genetic algorithm: A case study. Arabian Journal for Science and Engineering, 37(4), 935–944.

 Web of Science ®Google Scholar

Shiri, J., Marti, P., Kisi, O., Landeras, G., Fard, A. F., Nazemi, A. H., & Sadraddini, A. A. (2013). Evaluation of different data management scenarios for estimating daily reference evapotranspiration. Hydrology Research, 44(6), 1058–1070. doi: 10.2166/nh.2013.154

 Web of Science ®Google Scholar

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), 1–10. doi: 10.1007/s00271-011-0288-y

 Web of Science ®Google Scholar

Shiri, J., Nazemi, A. H., Sadraddini, A. A., Landeras, G., Kisi, O., Fakheri Fard, A., & Marti, P. (2014). Comparison of heuristic and empirical approaches for estimating reference evapotranspiration from limited inputs in Iran. Computers and Electronics in Agriculture, 108, 230–241. doi: 10.1016/j.compag.2014.08.007

 Web of Science ®Google Scholar

Shiri, J., Sadraddini, A. A., Nazemi, A. H., Kisi, O., Landeras, G., Fakheri Fard, A., & Marti, P. (2014). Generalizability of gene expression programming-based approaches for estimating daily reference evapotranspiration in coastal stations of Iran. Journal of Hydrology, 508, 1–11. doi: 10.1016/j.jhydrol.2013.10.034

 Web of Science ®Google Scholar

Kisi, O., Sanikhani, H., Zounemat-Kermani, M., & Niazi, F. (2015). Long-term monthly evapotranspiration modeling by several data-driven methods without climatic data. Computers and Electronics in Agriculture, 115, 66–77. doi: 10.1016/j.compag.2015.04.015

 Web of Science ®Google Scholar

Martí, P., González-Altozano, P., López-Urrea, R., Mancha, L. A., & Shiri, J. (2015). Modeling reference evapotranspiration with calculated targets. Assessment and implications. Agricultural Water Management, 149, 81–90. doi: 10.1016/j.agwat.2014.10.028

 Web of Science ®Google Scholar

Gocić, M., Motamedi, S., Shamshirband, S., Petković, D., Ch, S., Hashim, R., & Arif, M. (2015). Soft computing approaches for forecasting reference evapotranspiration. Computers and Electronics in Agriculture, 113, 164–173. doi: 10.1016/j.compag.2015.02.010

 Web of Science ®Google Scholar

Yassin, M. A., Alazba, A. A., & Mattar, M. A. (2016a). Artificial neural networks versus gene expression programming for estimating reference evapotranspiration in arid climate. Agricultural Water Management, 163, 110–124. doi: 10.1016/j.agwat.2015.09.009

 Web of Science ®Google Scholar

Alazba, A. A., Yassin, M. A., & Mattar, M. A. (2016). Modeling daily evapotranspiration in hyper-arid environment using gene expression programming. Arabian Journal of Geosciences, 9(3), 202. doi: 10.1007/s12517-015-2273-x

 Web of Science ®Google Scholar

Yassin, M. A., Alazba, A. A., & Mattar, M. A. (2016b). Comparison between gene expression programming and traditional models for estimating evapotranspiration under hyper arid conditions. Water Resources, 43(2), 412–427. doi: 10.1134/S0097807816020172

 Web of Science ®Google Scholar

Kumar, D., Adamowski, J., Suresh, R., & Ozga-zielinski, B. (2016). Estimating evapotranspiration using an extreme learning machine model: Case study in North Bihar, India. Journal of Irrigation and Drainage Engineering, 142(9), 1–9. doi: 10.1061/(ASCE)IR

 Web of Science ®Google Scholar

Karimi, S., Kisi, O., & Kim, S. (2017). Modelling daily reference evapotranspiration in humid locations of South Korea using local and cross-station data management scenarios. International Journal of Climatology, 37(November 2016), 3238–3246. doi: 10.1002/joc.4911

 Web of Science ®Google Scholar

Kiafar, H., Babazadeh, H., Marti, P., Kisi, O., Landeras, G., Karimi, S., & Shiri, J. (2017). Evaluating the generalizability of GEP models for estimating reference evapotranspiration in distant humid and arid locations. Theoretical and Applied Climatology, 130(1–2), 377–389. doi: 10.1007/s00704-016-1888-5

 Web of Science ®Google Scholar

Mehdizadeh, S., Behmanesh, 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. doi: 10.1016/j.compag.2017.05.002

 Web of Science ®Google Scholar

Traore, S., Luo, Y., & Fipps, G. (2017). Gene-expression programming for short-term forecasting of daily reference evapotranspiration using public weather forecast information. Water Resources Management, 31(15), 4891–4908. doi: 10.1007/s11269-017-1784-5

 Web of Science ®Google Scholar

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. doi: 10.1016/j.agwat.2017.04.009

 Web of Science ®Google Scholar

Feng, Y., Cui, N., Gong, D., Zhang, Q., & Zhao, L. (2017). Evaluation of random forests and generalized regression neural networks for daily reference evapotranspiration modelling. Agricultural Water Management, 193, 163–173. doi: 10.1016/j.agwat.2017.08.003

 Web of Science ®Google Scholar

Landeras, G., Bekoe, E., Ampofo, J., Logah, F., Diop, M., Cisse, M., & Shiri, J. (2018). New alternatives for reference evapotranspiration estimation in West Africa using limited weather data and ancillary data supply strategies. Theoretical and Applied Climatology, 132, 701–716. doi: 10.1007/s00704-017-2120-y

 Web of Science ®Google Scholar

Mattar, M. A., & Alazba, A. A. (2018). GEP and MLR approaches for the prediction of reference evapotranspiration. Neural Computing and Applications, 1–13. doi: 10.1007/s00521-018-3410-8

 Web of Science ®Google Scholar

Mattar, M. A. (2018). Using gene expression programming in monthly reference evapotranspiration modeling: A case study in Egypt. Agricultural Water Management, 198, 28–38. doi: 10.1016/j.agwat.2017.12.017

 Web of Science ®Google Scholar

Mehdizadeh, S. (2018). Estimation of daily reference evapotranspiration (ETo) using artificial intelligence methods: Offering a new approach for lagged ETo data-based modeling. Journal of Hydrology, 559, 794–812. doi: 10.1016/j.jhydrol.2018.02.060

 Web of Science ®Google Scholar

Jovic, S., Nedeljkovic, B., Golubovic, Z., & Kostic, N. (2018). Evolutionary algorithm for reference evapotranspiration analysis. Computers and Electronics in Agriculture, 150(April), 1–4. doi: 10.1016/j.compag.2018.04.003

 Web of Science ®Google Scholar

Mohammad, O., Pour, R., Piri, J., & Kisi, O. (2018). Comparison of SVM, ANFIS and GEP in modeling monthly potential evapotranspiration in arid region (case study: Sistan and baluchestan province –Iran). Water Science & Technology, 19(2), 392–403. doi:10.2166/ws.2018.084

 Web of Science ®Google Scholar

Shiri, J. (2019). Modeling reference evapotranspiration in island environments: Assessing the practical implications. Journal of Hydrology, 570(January), 265–280. doi: 10.1016/j.jhydrol.2018.12.068

 Web of Science ®Google Scholar

Sanikhani, H., Kisi, O., Maroufpoor, E., & Yaseen, Z. M. (2019). Temperature-based modeling of reference evapotranspiration using several artificial intelligence models: Application of different modeling scenarios. Theoretical and Applied Climatology, 135(1-2), 449–462. doi: 10.1007/s00704-018-2390-z

 Web of Science ®Google Scholar

Shiri, J., Marti, P., Karimi, S., & Landeras, G. (2019). Data splitting strategies for improving data driven models for reference evapotranspiration estimation among similar stations. Computers and Electronics in Agriculture, 162(March), 70–81. doi: 10.1016/j.compag.2019.03.030

 Web of Science ®Google Scholar