Original papersComparative analysis of reference evapotranspiration equations modelling by extreme learning machine
Introduction
Reference evapotranspiration (ET0), introduced by the United Nations Food and Agriculture Organization (FAO) as a methodology for computing crop evapotranspiration (Doorenbos and Pruitt, 1977), can be measured using lysimeter, eddy covariance systems, bowen ratio-energy balance, scintillometer (Benli et al., 2006, Miranda et al., 2006, Williams and Ayars, 2005, Liu et al., 2013, Liu et al., 2012, Savage, 2009, Savage et al., 2009) or calculated using equations based on temperature, radiation or pan evapouration or combination-type equations. ET0 is needed for the management of water resources, irrigation scheduling and agricultural production. Potential improvement of crop yields requires knowledge of supplementary irrigation and water balance model, in which one of the important components is evapotranspiration (Djaman and Irmak, 2013).
The FAO-56 Penman–Monteith (FAO-56 PM) equation (Allen et al., 1998) has been applied to be more superior in comparison with other ET0 empirical models, and has been recommended as the reference equation (Gavilan et al., 2007, Lopez-Urrea et al., 2006, Pereira et al., 2015, Sentelhas et al., 2010). It can be validated using lysimeters under various climatic conditions. The FAO-56 PM requires a full-set of weather data i.e. such as minimum and maximum air temperatures, relative humidity, wind speed and radiation which are not available in the most of the stations. This is a major disadvantage of the FAO-56 PM equation (Gocic and Trajkovic, 2010, Todorovic et al., 2013, Valiantzas, 2015). Thus, the adjusted Hargreaves (Trajkovic, 2007), Priestley and Taylor, 1972, Turc, 1961 equations were applied in this study because they do not require the full-set of weather data.
Computational intelligence (soft computing) methods can be used as alternative techniques in estimating and forecasting ET0. For instance, the artificial neural network (ANN) has been applied in creating a model of evapotranspiration process (Sudheer et al., 2003, Kisi, 2007, Khoob, 2008, Kumar et al., 2011, Landeras et al., 2008, Cobaner, 2011). The adaptive neuro-fuzzy inference system (ANFIS) has been developed and applied to estimate ET0 (Shiri et al., 2011, Kisi and Zounemat-Kermani, 2014, Citakoglu et al., 2014, Petkovic et al., 2015). Genetic programming (GP) is used for mathematical formulation of the ET0 (Kisi and Cengiz, 2013, Traore and Guven, 2012, Shiri et al., 2014a). Support vector machine (SVM) and wavelet neural networks are one of the novel soft learning algorithms that has been applied in ET0 modelling (Kisi and Cimen, 2009, Kisi, 2011, Cobaner, 2013, Shiri et al., 2014b, Gocic et al., 2015).
Recently, the Extreme Learning Machine (ELM) has been introduced as an algorithm for single layer feed forward neural network (Huang et al., 2004, Wang and Han, 2014, Tavares et al., 2015). It is capable to solve problems caused by gradient descent based algorithms like back propagation which applied in ANNs, and to decrease required time for training neural network. Several researchers applied ELM to solve the problems in different scientific fields. Nian et al. (2014) applied ELM towards dynamic model hypothesis in fish ethology research. The ELM can be used for prediction of non-stationary time series (Wang and Han, 2014), dynamic voltage stability status (Velayati et al., 2015), short-term load (Li et al., 2015) and bankruptcy (Yu et al., 2014) or in solving classification problems (Yin et al., 2015). The review of ELM trends can be found in Huang et al. (2015). Abdullah et al. (2015) applied ELM to predict Penman–Monteith ET0 for three meteorological stations in Iraq, and concluded that ELM can be used on both complete and incomplete sets of weather data. Feng et al. (2016) used ELM, backpropagation neural networks optimized by genetic algorithm (GANN) and wavelet neural networks (WNN) models to estimate ET0 and concluded ELM and GANN models were much better than WNN model.
The main aim of this study is to apply ELM approach in modelling of monthly ET0 using the following models: adjusted Hargreaves, Priestley–Taylor and Turc methods. These methods are selected because they require the minimum weather data in their calculation. The performance of ELM models is compared with the FAO-56 PM equation. The value of the ET0 calculated with mean monthly weather data is very similar to the average of the daily ET0 values calculated with daily average weather data for that month (Allen et al., 1998).
Section snippets
Studied region and used data
The monthly set of meteorological data of two meteorological stations in Serbia, Belgrade (latitude 44°48′N, longitude 20°28′E, elevation 132 m) and Nis (latitude 43°20′N, longitude 21°54′E, elevation 204 m), were used in this study.
The data sample covers 31 years (1980–2010) of monthly records of maximum (Tmax) and minimum (Tmin) air temperatures, actual vapour pressure (ea), wind speed (U2) and sunshine hours (n). Mean annual values of the meteorological variables for the selected stations used
FAO-56 Penman–Monteith equation
The FAO-56 Penman–Monteith (PM) equation (Allen et al., 1998) is used to estimate reference evapotranspiration:where ET0,PM is reference evapotranspiration (mm day−1), Δ is slope of the saturation vapour pressure function (kPa °C−1), Rn is net radiation (MJ m−2 day−1), G is soil heat flux density (MJ m−2 day−1), γ is psychrometric constant (kPa °C−1), T is mean air temperature (°C), U2 is average 24-h wind speed at 2 m height (m s−1), es is saturation
Experimental data
The estimated ET0 values using the three selected equations during the period 1980–2010, were used to train the ELM models. In other words, the three equations are incorporated in ELM. Data sets used for the model were divided into training and testing data sets since the ELM model was trained at the beginning, and afterwards the model was tested to verify the prediction accuracy of the ELM model. Each of them consists of 186 records (50% for training and 50% for testing procedures). Table 1,
Conclusion
The comparative analysis of ET0 equations modelling by the ELM approach is investigated in this study. For this purpose, the monthly weather data consist of minimum and maximum air temperatures, wind speed, actual vapour pressure and sunshine hours from Belgrade and Nis stations in Serbia were used as inputs to the ELM models for estimating ET0 obtained using the adjusted Hargreaves, Priestley–Taylor and Turc equations. The obtained test results were compared with standard FAO-56
Acknowledgements
The work is supported by the Ministry of Education, Science and Technological Development, Republic of Serbia (Grant No. TR37003) and the ICT COST Action IC1408 Computationally-intensive methods for the robust analysis of non-standard data (CRoNoS). This research is supported by University of Malaya under UMRG grant (Project No: RP006A-14HNE).
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