3. Study area and data collected

For the purpose of this study, 15 meteorological stations in India were chosen. Figure 1 shows the geographical locations of these selected stations and their related agro-ecological regions (AERs). These stations are having daily meteorological data of from 2001 to 2005 of following variables: minimum air temperature (Tmin), maximum air temperature (Tmax), minimum relative humidity (RHmin), maximum relative humidity (RHmax), mean wind speed (ws), and solar radiation (Sra). Table 1 shows the details of 15 climatic stations of India along with altitude and duration of available data. The study area is bounded between the longitudes of 68° 7<sup>0</sup> and 97° 25<sup>0</sup> E and the latitudes of 8° 4<sup>0</sup> and 37° 6' N. The annual potential evapotranspiration of India is 1771 mm. It varies from a minimum of 1239 mm in Jammu and Kashmir to a maximum of 2100 mm in Gujarat [30].

Estimation of ETo is complex due to influence of various climatic variables (maximum and minimum air temperature, wind speed, solar radiation and maximum and minimum relative humidity) and existence of nonlinearity in between climatic data and ETo. Though users have number of methods for measuring or estimating ETo directly or indirectly, most of them have some limitations regarding

The above limitations lead to the need of developing some techniques that can accurately estimate ETo values with a minimum input data and are also easy to apply without knowing physical process inside the system. Artificial neural network (ANN) techniques, which can provide a model to predict and

This section follows the discussion of some of the significant contributions made by various researchers in the application of different ANN techniques for modeling ETo or pan evaporation (Ep). A radial basis function (RBF) neural network was developed in C language to estimate daily soil water evaporation [26]. The input layer of network consists of average relative air humidity, air temperature, wind speed (Ws) and soil water content. They compared the results of RBF networks with the multiple linear regression (MLR) techniques. A feed-forward back propagation (FFBP)-based ANN model was developed to estimate daily Ep based on measured weather variables [27]. They used different input combinations to model Ep. They compared the developed ANN models with the Priestly-Taylor & MLR models. RBF neural network model was developed to estimate the FAO Blaney-Criddle b factor [28]. The input layer to RBF model consists of minimum daily relative humidity (RHmin), day time Ws and mean ratio of actual to possible sunshine hours (n/N). The b values estimated by the RBF models were compared to the appropriate b values produced using regression equations. FFBP ANN models were implemented for the estimation of daily ETo using six basic climatic parameters as inputs [16]. They trained ANNs using three learning methods (with different learning rates and momentum coefficients), different number of processing elements in the hidden layers, and the number of hidden layers. The compared the results of developed ANN models with the Penman Monteith (PM) method and with a lysimeter measured ETo. ANN-based back propagation models for estimating Class A Ep with minimum climate data (four input combinations) were developed

and compared with the existing conventional methods [22].

investigate the process without having a complete understanding of it, can be a useful tool for the above purpose. These techniques are also interesting because of its knowledge discovering property. In contrast to conventional methods, ANNs can estimate ETo accurately with minimum climate data, which may have the advantages of being inexpensive, independent of specific climatic condition, ignored physical relations, and precise modeling of nonlinear complex system. In the last decade, many researchers have used ANN techniques for modeling of the ETo

data availability or regional applicability. In addition, in order to use these methods, users are required to make reasonable estimates for some of the parameters in the employed ETo models, which involve some uncertainties and might not result in reliable ETo estimates [5]. Further, it is difficult to develop accurately representative physically based models for the complex non-linear hydrological processes, such as ETo. This is because the physical relationships involving in a system can be too complicated to be accurately represented in a

Advanced Evapotranspiration Methods and Applications

physically based manner.

process [6–25].

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2. Review of literature
