1. Introduction

Evapotranspiration (ET) is the combining process of evaporation and transpiration losses. Almost 62% of precipitation falls on continents are returned back to the atmosphere through the ET process [1]. ET plays a significant role in the hydrological cycle and its estimation is very important in various fields of water resources. A common procedure for estimating actual crop evapotranspiration (ETcrop) is to first estimate reference evapotranspiration (ETo) and to then apply an appropriate crop coefficient (kc). ETo is an important and one of the most difficult components of the hydrologic cycle to quantify accurately. ETo is measured from a hypothetic crop of uniform height (12 cm), active growing (crop resistance of 70 s m<sup>1</sup> ), completely shading the ground (albedo of 0.23) and unlimited supply of water [2]. The Food and Agricultural Organization (FAO) consider the above definition as standard and sole method for estimating ETo if sufficient climatic data are available [3, 4].

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 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 physically based manner.

The potential of RBF neural network for estimating the rice daily crop ET using limited climatic data was demonstrated [23]. Six RBF networks, each using varied input combinations of climatic variables were trained and tested. The model estimates were compared with measured lysimeter ET. A sequentially adaptive RBF network was applied for forecasting of monthly ETo [29]. Sequential adaptation of parameters and structure was achieved using extended Kalman filter. Criterion for network growing was obtained from the Kalman filter's consistency test. Criteria for neuron/connections pruning were based on the statistical parameter significance test. The results showed that the developed network was learned

to forecast ETo,t+1 (current or next month) based on ETo,t-11 (at a lag of 12 months) and ETo,t-23 (at a lag of 24 months) with high reliability. The study examined that whether it is possible to attain the reliable estimation of ETo only on the basis of the temperature data [24]. He developed RBF neural network for estimating ETo and compared the developed model with temperature-based

Nonlinear Evapotranspiration Modeling Using Artificial Neural Networks

DOI: http://dx.doi.org/10.5772/intechopen.81369

ered for this comparison. Generalized ANN (GANN)-based ETo models

tested with different stations which were not used in training. Multilayer

corresponding to FAO-56 PM, FAO-24 Radiation, Turc and FAO-24 Blaney-Criddle methods were developed [15]. These models were trained using the pooled data from four California Irrigation Management Information System (CIMIS) stations with FAO-56 PM computed values as targets. The developed GANN models were

perceptron (MLP) neural networks for estimating the daily Ep using input data of maximum and minimum air temperature and the extraterrestrial radiation was developed [20]. The potential for the use of ANNs to estimate the ETo based on air temperature data was examined [21]. He also conducted comparison of estimates provided by the ANNs and by Hargreaves equation by using the FAO-56 PM model

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

ANN-based daily ETo models were trained based on different categories of conventional ETo estimation methods such as temperature based (FAO-24 Blaney-Criddle), radiation based (FAO-24 Radiation method for arid and Turc method for humid regions) and combinations of these (FAO-56 PM) [14]. A comparison of the Hargreaves and ANN methods for estimating monthly ETo only on the basis of temperature data was done [19]. They developed ANN models with the data from six stations and tested these developed models with the data from remaining six stations, which were not used in model development. The capability of ANN for converting Ep to ETo was studied using temperature data [18]. The conventional method that uses pan coefficient (Kp) as a factor to convert Ep to ETo was consid-

empirical models.

as reference model.

25

3. Study area and data collected

maximum of 2100 mm in Gujarat [30].

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 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 process [6–25].
