Monthly pan evaporation modeling using linear genetic programming
Introduction
Evaporation is a major component of the hydrologic cycle and its estimation is very important for agricultural irrigation, water supply, water balance studies and water resources management. Accurate estimation of evaporation loss is necessary in irrigation planning and management in many areas where water resources are scarce. (Brutsaert, 1982, Jackson, 1985). Engineers and/or researchers commonly use evaporation pans (Class A pan of the U.S. Weather Bureau Class A pan that is 4 ft in diameter and 10 in. deep) throughout the world for estimating evaporation loss from reservoirs and for estimating reference evapotranspiration (Frevert et al., 1983, Irmak et al., 2002).
Estimating pan evaporation (Ep) is a complex and nonlinear phenomenon because it has complex interactions between the components of the land–plant–atmosphere system (Singh and Xu, 1997). Maintaining Class A pan evaporimeters is difficult for longer duration. As an alternative, therefore, pan evaporation is estimated from meteorological parameters measured in automatic weather stations. Climate based models (Stephens and Stewart, 1963), artificial neural network (ANN) models (Sudheer et al., 2002, Keskin and Terzi, 2006, Tan et al., 2007, Kisi, 2009a, Kisi, 2009b, Kisi, 2009c, Kisi, 2013, Tabari et al., 2010, Kim et al., 2012), support vector machines (Eslamian et al., 2008) and adaptive neuro-fuzzy inference system (ANFIS) (Terzi et al., 2006, Kisi, 2006, Moghaddamnia et al., 2009, Dogan et al., 2010, Kisi et al., 2012) were successfully used by researchers for modeling pan evaporation. Among these, the most frequently used method is ANN with different network structures and weather variables (Shirsath and Singh, 2010). Recently, Kisi and Tombul (2013) used fuzzy genetic (FG) approach for modeling monthly pan evaporations in Mediterranean Region of Turkey. They compared FG models with those of the ANN and ANFIS models and found that the proposed models performed better than the others.
Genetic programming (GP) is a relatively new technique compared to ANN and ANFIS. The most powerful feature of GP is that the user can easily obtain an explicit formulation of the relation between the input and output. This makes GP more practical and useful for decision makers and designers. GP has been successfully applied in eater resources engineering, but the general literature of GP application in water resources engineering is out of the scope of this study. The interested reader can refer Guven and Azamathulla (2012), and Traore and Guven (2013) for detailed review on GP. This study specifically focuses on linear genetic programming (LGP) which is a version of GP. LGP has been limitedly used in estimation hydrological parameters since the last decade (Guven, 2009, Guven et al., 2009, Kisi and Guven, 2010a, Kisi and Guven, 2010b, Guven and Kisi, 2011a). More relevantly, Guven and Kisi (2011b) estimated the daily pan evaporation of the Mediterranean Region of Turkey by using LGP. To the knowledge of the author, no study was carried out to show the input–output mapping ability of LGP in modeling monthly pan evaporations. This provides an impetus for the present investigation.
The aim of this study is investigate and compare the accuracy of LGP models with those of the fuzzy genetic, neuro-fuzzy, ANN and Stephens–Stewart (SS) models employed in Kisi and Tombul (2013) for estimating pan evaporation.
Section snippets
Linear genetic programming
There are several variants of GP, and most pronounced ones are: linear genetic programming, and gene-expression programming (Oltean and Groşan, 2003). LGP utilizes a specific linear representation of computer programs, however, a LGP model is composed of nonlinear programs which is not restricted to a linear list of nodes only (Brameier, 2004). In comparison to tree-based GEP, LGP directly uses C or C++ as programming. Hence, sometimes LGP is also called as machine-coded genetic programming (
Case study
In the present study, the monthly air temperature (T), solar radiation (SR), wind speed (W), humidity (H) and pan evaporation (PE) data from two automated stations, Antalya (lat 36°42′N, long 30°44′E) and Mersin (lat 36°48′N, long 34°38′E) operated by the Turkish Meteorological Organization (TMO) in Turkey were used. The same data were also used by Kisi and Tombul (2013). The altitudes of the Antalya and Mersin are 64 and 3 m, respectively. The Mediterranean Region has Mediterranean climate and
Application and results
Kisi and Tombul (2013) examined the ability of the FG method in estimating monthly pan evaporations. In the first part of the study, they estimated pan evaporations data of the Antalya and Mersin stations, separately. In the second part of the study, they estimated the pan evaporations of the Mersin Station by using the data of both stations. They examined and compared the accuracy of two different FG models with those of the ANFIS, ANN and SS models. The SS model (Stephens and Stewart, 1963)
Conclusions
This study investigated the accuracy of LGP, FG, ANFIS, ANN and SS methods in modeling pan evaporations. Monthly climatic data from two stations, Antalya and Mersin, in Mediterranean Region of Turkey were used in the study. In the first part of the study, the comparison of LGP models with those of the FG, ANFIS, ANN and SS models in estimating pan evaporations of Antalya and Mersin stations is focused. Comparison results indicated that the accuracy of the both two- and four-parameter LGP models
Acknowledgements
The data used in this study were obtained from Turkish Meteorological Organization (TMO). The authors wish to thank the staff of the TMO who is associated with data observation and processing.
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