REPLY to Discussion of An explicit neural network formulation for evapotranspiration

OpenAlex İngilizce

Aytek et al. (2008) explored the black-box modelling tool of artificial neural network (ANN) technology for use in modelling evapotranspiration by providing an explicit equation with four independent variables (solar radiation, R s , air temperature, T a , relative humidity, RH, and wind speed at 2 m above the ground, u 2 ) and one dependent variable (evapotranspiration, ET 0 ).Equation (5) in Aytek et al. (2008) is the general representation of the proposed model.Equation ( 9) together with equation ( 10) is the explicit way showing the link between the dependent and independent variables.The up-to-date application of the NN technology allows modelling by black-box NN tools, whilst Aytek et al. (2008) provided an explicit neural network formulation (ENNF).The ENNF uses daily climatic data from the California Irrigation Management Information System (CIMIS) database.One of the most important conclusions achieved is the simplicity of the developed ENNF.It is so simple that it can be used by anyone, even if not familiar with neural networks (NNs), in a spreadsheet on a PC, or even on a hand-held calculator, if the input variables are available to the user.Validated on the CIMIS model, the ENNF gives a fast and practical formulation to obtain accurate results for ET 0 and seems to be beneficial in other aspects of water engineering studies, such as rainfall-runoff-sediment transport modelling (although as an alternative ET 0 formulation it offers only a marginal gain in skill compared with simpler linear techniques).The fact that the ENNF is a major step in the development of artificial neural networks technology is recognized by Abrahart et al. (2009) who state "The ENNF is an interesting alternative construct for relating four hydrometeorological variables to CIMIS ET 0 " and "the translation of hidden neural network internal mechanisms into a transparent equation represents a major step forward."Finally, Abrahart et al. (2009) recognize that the ENNF runs on a simple computer or a hand held calculator, does not require the use of complex software, and offers a portable neural network model that could be applied, or tested out, under different environmental conditions.However, several points have been argued in the discussion by Abrahart et al. (2009).Here, we have extracted the points needing discussion, as follows: 1.In the second paragraph, the discussers emphasize that ET 0 in the CIMIS database is not measured but estimated.It is true that the CIMIS ET 0 data available are not measured but estimated by using the CIMIS ET 0 equation (Eching & Moellenberndt, 1998;Temesgen et al., 2005).It is based on the Penman equation and modified by CIMIS (Eching & Moellenberndt, 1998).Many (Alexandris & Kerkides, 2003;Temesgen et al., 2005;Allen et al., 2005;Hidalgo et al., 2005;Alexandris et al., 2006;Kisi, 2006) have used this equation in their ET 0 -related studies and employed the CIMIS data set.We believe that the CIMIS database has already been proved reliable and useful.Therefore, we had no hesitation to use the data, although we understand the sensitivity of the discussers request to us to stress that the data set is estimated by employing the CIMIS equation and not measured in the field.The logic of fitting ANNs to such estimated (instead of measured) data has also been criticized by Koutsoyiannis (2007).We believe that the discussers are aware of the web site from which detailed information can be found on the CIMIS ET 0 data: http://www.cimis.water.ca.gov/ cimis/data.jsp.