Ali Aytek

New Approach for Stage–Discharge Relationship: Gene-Expression Programming

This study presents gene-expression programming (GEP), which is an extension to genetic programming, as an alternative approach to modeling stage–discharge relationship. The results obtained are compared to more conventional methods, stage rating curve and multiple linear regression techniques. Statistical measures such as average, standard deviation, minimum and maximum values, as well as criteria such as mean square error and determination coefficient, the coefficient of efficiency, and the adjusted coefficient of efficiency are used to measure the performance of the models developed by employing GEP. Also, the explicit formulations of the developed GEP models are presented. Statistics and scatter plots indicate that the proposed equations produce quite satisfactory results and perform superior to conventional models.

Sea water level forecasting using genetic programming and comparing the performance with Artificial Neural Networks

Water level forecasting at various time intervals using records of past time series is of importance in water resources engineering and management. In the last 20 years, emerging approaches over the conventional harmonic analysis techniques are based on using Genetic Programming (GP) and Artificial Neural Networks (ANNs). In the present study, the GP is used to forecast sea level variations, three time steps ahead, for a set of time intervals comprising 12h, 24h, 5 day and 10 day time intervals using observed sea levels. The measurements from a single tide gauge at Hillarys Boat Harbor, Western Australia, were used to train and validate the employed GP for the period from December 1991 to December 2002. Statistical parameters, namely, the root mean square error, correlation coefficient and scatter index, are used to measure their performances. These were compared with a corresponding set of published results using an Artificial Neural Network model. The results show that both these artificial intelligence methodologies perform satisfactorily and may be considered as alternatives to the harmonic analysis.

An explicit neural network formulation for evapotranspiration

Abstract An explicit neural network formulation (ENNF) is developed for estimating reference evapotranspiration (ET0) using daily meteorological variables obtained from the California Irrigation Management Information System (CIMIS) database. First, the ENNF is trained and tested using the CIMIS database, and then compared with five conventional ET0 models, as well as the multiple linear regression method. Statistics such as average, standard deviation, minimum and maximum values, and criteria such as mean square error and determination coefficient are used to measure the performance of the ENNF. Daily atmospheric data of four climatic stations in central California are taken into consideration in the model development and those of three other stations are used for comparison purposes. The meteorological variables employed in the formulation are solar radiation, air temperature, relative humidity and wind speed. It is concluded from the results that ENNF offers an alternative ET0 formulation, but that the gain in skill is marginal compared with simpler linear techniques. However, this finding needs to be tested using sites drawn from a wider range of climate regimes.

Discussion of “Generalized regression neural networks for evapotranspiration modelling”

Kisi (2006) used generalized regression neural networks (GRNNs) for modelling reference evapotranspiration (ET0). Results presented in the study show the potential of GRNNs as an alternative to the existing methods. Working on ET0 modelling by means of similar, soft computational methods, we think that the study contains some points, which, from our experience, require further discussion and clarification.

A practical approach to formulate stage–discharge relationship in natural rivers

This study proposes a new formulation technique for modeling stage–discharge relationship, as an alternative approach to standard regression techniques. An explicit neural network formulation (ENNF) is derived by using data obtained from United States Geological Survey data base. The neural network model is trained and tested using time series of daily stage and discharge data from two stations in Pennsylvania, USA. The model is compared with the standard rating curve (SRC) technique. Statistical parameters such as average, standard deviation, minimum, and maximum values, as well as criteria such as root mean square error, the efficiency coefficient (E), and determination coefficient (R2) are used to measure the performance of the ENNF. Considerably, well performance is achieved in modeling streamflow by using ENNF. The comparison results reveal that the suggested formulations perform better than the conventional SRC.

REPLY to Discussion of “An explicit neural network formulation for evapotranspiration”

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, Rs, air temperature, Ta, relative humidity, RH, and wind speed at 2 m above the ground, u2) and one dependent variable (evapotranspiration, ET0). 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 ET0 and seems to be beneficial in other aspects of water engineering studies, such as rainfall–runoff–sediment transport modelling (although as an alternative ET0 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 ET0” 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 ET0 in the CIMIS database is not measured but estimated. It is true that the CIMIS ET0 data available are not measured but estimated by using the CIMIS ET0 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 ET0-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 ET0 data: http://www.cimis.water.ca.gov/ cimis/data.jsp.

EXPLICIT NEURAL NETWORK IN SUSPENDED SEDIMENT LOAD ESTIMATION

Correct estimation of sediment volume carried by a river is very im- portant for many water resources projects. Traditionally, artificial neural networks (ANNs) are used as black-box models without understanding what happens inside the box. The question is that, how anyone who may be unfamiliar with ANNs can apply this kind of models in any other study, while the model has not been formu- lated. This paper proposes an explicit neural network (ENN) formulation which is simple and can be used, by anyone who is even not familiar with ANNs, for mod- eling daily suspended sediment-discharge relationship. The daily streamflow and suspended sediment data from two stations on Tongue River in Montana are used as case studies. Two different sediment rating curves (SRC), multi-linear regres- sion (MLR) and nonlinear regression (NLR) are also applied to the same data. The ENN estimates are compared with those of the SRC, MLR and NLR models. The root mean square errors (RMSE), mean absolute errors (MAE), correlation coeffi- cient (R) and model efficiency (E) statistics are used to evaluate the performance of the models. The comparison results reveal that the suggested model performs better than the conventional SRC, MLR and NLR.