Evapotranspiration Estimation Using Support Vector Machines and Hargreaves-Samani Equation for St. Johns, FL, USA

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1 Evirometal Egieerig 0th Iteratioal Coferece eissn / eisbn Vilius Gedimias Techical Uiversity Lithuaia, April 207 Article ID: eviro DOI: Evapotraspiratio Estimatio Usig Support Vector Machies ad Hargreaves-Samai Equatio for St. Johs, FL, USA Fatih Üeş, Yuus Ziya Kaya 2, Mustafa Mamak 3, Mustafa Demirci 4, 4 Civil Egieerig Departmet, Iskederu Techical Uiversity, Iskederu, Turkey 2, 3 Civil Egieerig Departmet, Osmaiye Korkut Ata Uiversity, Osmaiye Turkey s: fatihues66@gmail.com; 2 yuuszkaya@osmaiye.edu.tr; 3 mmamak@osmaiye.edu.tr (correspodig author); 4 mustafa.demirci@iste.edu.tr Abstract. Iformatio about Evapotraspiratio (ET) calculatios are ot clear eough eve it is a importat part of hydrological cycle. There are may parameters which effect ET directly or idirectly such as Solar Radiatio (SR) ad Air Temperature (AT). I this study authors focused o the modellig ET usig Support Vector Machies (SVM) method because this method has abilities to solve oliear problems. For the traiig SVM 58 daily AT, SR, Wid Speed (U) ad Relative Humidity (RH) meteorological parameters are used ad model is tested usig 385 daily parameters. Data set is take from St. Johs, Florida, USA weather statio. To uderstad the abilities of SVM for ET predictio agaist Hargreaves-Samai formula, the test set is applied to this empirical equatio. Determiatio coefficiet of SVM with observed daily ET values is calculated as 0.93 ad determiatio coefficiet of Hargreaves- Samai formula with observed daily ET is foud as Compariso betwee both methods is doe usig Mea Square Error (MSE), Mea Absolute Error (MEA) ad determiatio coefficiet statistics. As a result it is see that SVM method is trustier tha Hargreaves-Samai formula for daily ET predictio. Keywords: evapotraspiratio, hargreaves-samai, estimatio, modellig. Coferece Topic: Water egieerig. Itroductio Evapotraspiratio estimatio takes a major role for irrigatio maagemet ad hydraulic desigs. Despite this major role, ET is ot uderstood well eough (Brutsaert 982). Evapotraspiratio is a combiatio of evaporatio ad traspiratio. Whe the crop is small i a stated area, evaporatio is the mai factor of ET but whe the crop is well developed the the mai factor is goig to be traspiratio ( FAO. d.). Therefore, to uderstad the ET mechaism, it is eeded to uderstad evaporatio ad traspiratio. Basically, evaporatio takes place at the topsoil whe the water is available ad traspiratio is the removal of vapour to the atmosphere from the crop tissues (Kişi 2007). Difficulties of ET predictio come from oliear direct or idirect effects o ET such as SR, AT, RH meteorological variables. Hece, i the past decade some artificial itelligece ad data miig methods are used to estimate daily ET, evaporatio ad pa evaporatio. For istace M5T method is used to estimate Referece ET (Pal, Deswal 2009), artificial eural etworks for ET predictio (Kumar et al. 20) ad geeralized eural etworks for ET predictio (Kişi 2006). I this study, ET is estimated usig Support Vector Machies (SVM) as a data miig method. SR, AT, RH, U daily meteorological parameters are used to trai SVM model ad test set results are obtaied. SVM model results are compared with Hargreaves-Samai empirical formula test set results usig determiatio coefficiet, Mea Square Error (MSE) ad Mea Absolute Error (MAE). Data set is dowloaded from USGS website (USGS.gov. d.) for the St. Johs FL, USA regio. Methodology Support Vector Machies (SVM) SVM is a data miig method which is i use for regressio ad classificatio. This method is described by Vapik (Vapik et al. 996). It is possible to classify variables o a plae by drawig a borderlie betwee them. The borderlie which is draw betwee variables must be as far as possible to each variable. Here it is SVM defies how to draw this borderlie betwee variables group. SVM workig priciple is give by Figure. 207 Fatih Üeş, Yuus Ziya Kaya, Mustafa Mamak, Mustafa Demirci. Published by VGTU Press. This is a ope-access article distributed uder the terms of the Creative Commos Attributio (CC BY-NC 4.0) Licese, which permits urestricted use, distributio, ad reproductio i ay medium, provided the origial author ad source are credited.

2 Üeş, F.; Kaya, Y. Z.; Mamak, M.; Demirci, M Evapotraspiratio estimatio usig support vector machies ad Fig.. SVM workig priciples (Kişi 205) Forecastig vector, support vector, oliear fuctio, Kerel fuctio ad forecastig results are the stages of SVM workig priciple as give by Figure. For further iformatio about Support Vector Machies (SVM) readers are referred to (Vapik et al. 996). Hargreaves-Samai Formula Necessary parameters for calculatio of daily ET with Hargreaves-Samai equatio are daily maximum temperature (T max), daily miimum temperature (T mi) ad extraterrestrial solar radiatio (R s) (Hargreaves, Samai 985). The equatio which is used for calculatio is give below; ET= Rs ( T+ 7.8 ), () where: T represets daily mea temperature ad Rs extraterrestrial solar radiatio i Hargreaves-Samai equatio. Evaluatio Criteria Mea Square Error (MSE), Mea Absolute Error (MAE) ad determiatio coefficiet statistics are calculated usig equatios (2, 3 & 4). R= MSE= * fi yi ; ( ) 2 (2) N i = MAE= * fi yi ; (3) N i = i= i i ( y ) ( x ). 2 2 ( x ). ( ) i y i= i= i where: f i represets predicted values ad y i represets daily observed values for equatio (2&3) x i shows ith actual value, y i shows ith predicted value, x represets x mea ad y represets y mea at equatio (4)., (4) Results This study is focused o SVM method abilities o ET estimatio. Hece, a SVM model is created by usig SR, AT, RH, U daily meteorological parameters as iput. Model test results are compared with Hargreaves-Samai empirical equatio. Compariso is doe with Mea Square Error (MSE), Mea Absolute Error (MAE) ad determiatio coefficiet statistics. Distributio graph ad scatter chart of SVM model ad Hargreaves-Samai formula results are give separately. 2

3 Üeş, F.; Kaya, Y. Z.; Mamak, M.; Demirci, M Evapotraspiratio estimatio usig support vector machies ad Fig. 2. SVM test results distributio graph It is show i Figure 2 that distributio of SVM model results is i same directio with observed daily values for test set. R 2 =0.93 Fig. 3. SVM test results scatter chart Determiatio coefficiet of SVM method is calculated as 0.93 which is also give i Figure 3. Fig. 4. Distributio graph of Hargreaves-Samai equatio test results 3

4 Üeş, F.; Kaya, Y. Z.; Mamak, M.; Demirci, M Evapotraspiratio estimatio usig support vector machies ad Daily distributio graph of Hargreaves-Samai which is give by Figure 4 shows that there is high correlatio betwee empirical formula ad observed daily values. R 2 =0.90 Fig. 5. Scatter chart of Hargreaves-Samai equatio test set results Scatter chart of Hargreaves-Samai empirical formula is give by Figure 5. Determiatio coefficiet is calculated as 0.90 which that meas determiatio coefficiet is almost same as SVM model determiatio coefficiet. The determiatio coefficiet, MSE ad MAE values of SVM model ad Hargreaves-Samai equatio are give i Table. Although the determiatio coefficiets of both methods seem to be equal, MSE ad MAE values of SVM model are less tha Hargreaves-Samai method. Method Table. Compariso statistics Parameters Used Determiatio Coefficiet MSE MAE SVM SR, AT, RH, U Hargreaves-Samai AT, SR Coclusio Authors study o ET estimatio usig SVM model for St. Johs, FL, USA regio. It is uderstood that SVM method gives quite close results to Hargreaves-Samai empirical equatio results. MSE, MAE error calculatios preset that both method could be employed ET predictio successfully, but accordig to the error calculatios it is clear that SVM method results are better tha empirical equatio results. This study is carried out for a particular regio St. Johs, FL, USA. That is why authors proposed that SVM method should be applied to differet regios to verify SVM method ability o ET estimatio. Refereces Brutsaert, W Evaporatio ito the atmosphere: theory, history ad applicatios. Spriger Netherlads. FAO.. d. Chapter Itroductio to evapotraspiratio [olie], [cited 0 December 207]. Available from Iteret: Hargreaves, G. H.; Samai, Z. A Referece crop evapotraspiratio from temperature, Applied Egieerig i Agriculture : Kişi, O Pa evaporatio modelig usig least square support vector machie, multivariate adaptive regressio splies ad M5 model tree, Joural of Hydrology 528: Kişi, O Evapotraspiratio modellig from climatic data usig a eural computig techique, Hydrological Processes 2:

5 Üeş, F.; Kaya, Y. Z.; Mamak, M.; Demirci, M Evapotraspiratio estimatio usig support vector machies ad Kişi, Ö Geeralized regressio eural etworks for evapotraspiratio modellig, Hydrological Scieces Joural 5: Kumar, M.; Raghuwashi, N. S.; Sigh, R. 20. Artificial eural etworks approach i evapotraspiratio modelig: a review, Irrigatio Sciece 29: Pal, M.; Deswal, S M5 model tree based modellig of referece evapotraspiratio, Hydrological Processes 23: USGS.gov..d. Sciece for a chagig world [olie], [cited 2 Jauary 207]. Available from Iteret: Vapik, V.; Vapik, V.; Golowich, S. E.; Smola, A Support vector method for fuctio approximatio, regressio estimatio, ad sigal processig, Advaces i Neural Iformatio Processig Systems 9: