Mapping and evaluation of reference evapotranspiration methods under arid conditions

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Introduction.
Reference evapotranspiration (ETo) is the synchronized transpiration and evaporation processes in a soil-plant system (Tabari et al., 2011).ETo has a great importance in irrigation scheduling,  (Sentelhas et al., 2010).Several methods have been developed to estimate ETo and they vary in required climatic-data.For many regions and climatic conditions, the Penman-Monteith method (P-M) has proved to be the best method and gives consistent ETo values (Allen et al. 2005(Allen et al. , 2006)).Thus, it is widely applied in various fields, among which are agronomy and irrigation management (Alexandris et al. 2006;Landeras et al, 2008;Du, et al., 2010;Hassanli, et al., 2010;Sentelhas et al. 2010).
In case of limited data required for P-M method, especially in the developing countries, significant attention has been paid to the evaluation of simple ETo methods and their application.The FAO-Penman-Monteith method (P-M) has proved of superior performance (Jensen et al. 1990 , 2006).Therefore, simpler equations must be evaluated against the P-M method or lysimetric measurements in order to find out the most suitable ETo method for each region where weather data are inadequate to apply the P-M method (Trajkovic and Kolakovic, 2009).
The present work was carried out to assess the performance of six simple ETo methods that require less readily available data against the P-M method in order to select the most suitable method to estimate ETo values in Libya.Maps representing the distribution of the ETo values and their relation to elevation above sea level is performed.
Materials and methods.The present investigation was carried out in the country of Libya (area of 1,760,000 km 2 ) with a Mediterranean Coastline of nearly 1,800 kilometers.Seventeen meteorological stations were selected to represent the different regions of the country.Figure 1 shows the distribution of chosen stations (as a point map); the geographic characteristics of these stations are presented in Table 1.The combination methods for ETo estimation depends upon recorded temperature, relative humidity, wind speed and solar radiation or sunshine.If such data are available, the P-M method ranked the first to estimate (ETo) between all other combination methods.As mentioned above, FAO 56-PM method was selected in this study to be the reference method.The equations of each method are presented in   Percentage error of estimates (PE) calculated by the following equation: To evaluate The RMSD criterion was used to compare the estimated ETo values by different methods and P-M ETo method.The RMSD was selected as an appropriate ranking criterion because of the fact that this statistical parameter indicates the ability of equations and adjusted equations to accurately estimate reference evapotranspiration during all months (Trajkovic and Kolakovic, 2009: where n -total number of observations. Mean bias error (MBE): According to these statistical parameters, the criteria used to select the best method is to have the smallest absolute deviation value.The criteria applied to select the more suitable method was associated with the smallest absolute deviation value obtained.
GIS application.Elevation Data.The digital elevation model (DEM) used in this study is the SRTM (NGA SRTM «finished» 3arcsec) data, which was retrieved freely from https://lpdaac.usgs.gov.Then, it was clipped to the boundary of the study area.Geostatistical analysis.Kriging analysis was applied to generate the ETo maps of the study area.Where the point map of the stations was utilized in geostatistical analysis to generate spatial distribution maps of ETo.Where one map was generated to represent the ETo values of the P-M method.On the other hand, the estimated ETo values for each station based on the relevant best-method were used to generate ETo map for the study area.
Results and discussion.Evaluation of estimation methods.For the studied stations, the monthly ETo values were estimated using the tested seven equations.Then, the obtained values from the six simple ETo method were compared with that values of P-M method.The calculated statistical parameters i.e., PE, MBE and RMSD for all methods in each station as compared to the P-M method are given in Table 3.As shown in Table 3, most of the best methods exceeded ETo values estimated by the P-M method.The overview of all results revealed that the Turc and B-C methods perform better among the stations.The selection of the best method was done according to the values of PE, MBE and RMSD statistical parameters.Thus, for each station, the method having best values in two or three statistical parameters were assigned as the best method.Furthermore, generally, the study area could be divided into two zones; Northern and Southern ones (Figure 3).ETo Mapping.Values of evapotranspiration estimated by the P-M method and by the best method for each station were interpolated using ordinary kriging to generate ETo maps of the study area, Figure 4.As shown in Figure 4a, the ETo value ranges from 3.4 to 7.1 (mm day-1), while in case of the best methods (Figure 4b) ETo ranges between 3.4 and 7.4 (mm day-1), and generally, ETo value increases from north to south.This could be resulted as the distribution of mean airtemperature that also increases towards south.a b Figure4.Spatial distribution of ETo (mm day-1) in the study area: a -using P-M method; b -most reliable estimation method for each station Conclusion Seven methods were applied to estimate reference evapotranspiration using weather data from seventeen stations separated at whole Libya.The FAO P-M method was used as the standard of comparison for evaluating the other six methods for all stations.It was concluded that there are two regions

Figure 1 .
Figure 1.Study area and location of the weather stations.

Figure 2 .
Figure 2. Average mean temperature and relative humidity in Libya.
In order to evaluate ETo values using the different methods in comparison with FAO P-M method.Data of all methods were tested on basis of the following statistical parameters (El-Mageed, T.A.A. and El-Wahed, M.A., 2014).

Figure 3 .
Figure 3. ETo zones and the best ETo methods overlaid on DEM of the study area (A) Northern zone: which extended from the coastal line towards south including the following locations: Nalut, Zuara, Mosrata, Sirt, Shahat, Derna, Tubruk, Hon, Galo and Gagbub where the best method was Turc, while for Tripoli the best method was HG. (B) Southern zone: as for Opari and Tazirbu, the best method was HG; BC for Kufra and Ghadames; FAO-Rad for Sebha; and JH for Ghat.The poor performance of the J-H method obtained in this study is in a good agreement with the results found in Serbia (Trajkovic and Kolakovic 2009), Florida (Irmak et al. 2003a, b) and Iran (Tabari et al. 2011).ETo Mapping.Values of evapotranspiration estimated by the P-M method and by the best method for each station were interpolated using ordinary kriging to generate ETo maps of the study area, Figure4.As shown in Figure4a, the ETo