Extreme Learning Machines: A new approach for prediction of reference evapotranspiration

Abstract

Recognizing the importance of precise determination of reference evapotranspiration (ET<inf>0</inf>) is a principal step in the attempts to reserve huge quantities of squandered water. This paper investigates the efficiency of Extreme Learning Machines (ELM) algorithm at predicting Penman-Monteith (P-M) ET<inf>0</inf> for Mosul, Baghdad, and Basrah meteorological stations, located at the north, mid, and southern part of Iraq. Data of weather parameters containing maximum air temperature (T<inf>max</inf>), minimum air temperature (T<inf>min</inf>), sunshine hours (R<inf>n</inf>), relative humidity (R<inf>h</inf>), and wind speed (U<inf>2</inf>) for the period (2000-2013) are used as inputs to the ELM model by using four different input cases including complete and incomplete sets of meteorological data. The performance of ELM model is compared with the empirical P-M equation and with feedforward backpropagation (FFBP) model. The evaluation criteria used for comparison are the root of mean squared error (RMSE), mean absolute error (MAE), and coefficient of determination (R2). The statistical results of both models are found to be encouraging; particularly results of running the ELM model with incomplete sets of data, noticing that the sensitivity of the proposed model to missing data changes from one location to another, as well as along the year for certain study location. The R<inf>n</inf> is found to be the most effective parameter in Mosul Station, while U<inf>2</inf> and R<inf>h</inf> are found to act almost in parallel with R<inf>n</inf> in Baghdad Station, and for conditions of Basrah Station; U<inf>2</inf> and R<inf>h</inf> prove to be the dominant parameters. The minimum and maximum time intervals required for running ELM model for all stations, and in all applied conditions, are (4.64-6.19) seconds respectively, while the same order of timing required for running the FFBP model is (6.30-27.80) seconds. The maximum R2 recorded for the ELM model is 0.991, while for the FFBP it is 0.985. The ELM proved to be efficient, simple in application, of high speed, and has very good generalization performance; therefore, this algorithm is highly recommended for locations similar to the geographical and meteorological conditions of Iraq that consists of both arid and semiarid regions. © 2015 Elsevier B.V.