Modeling of potential reference evapotranspiration using the limited weather parameters (Case study: Urmia Lake basin)

Introduction
One of the standard models for estimation of ET₀ that accepted by all hydrologists and climatologists is the FAO Penman-Monteith (FAO56PM) method. Although this model is accurate in ET₀ estimation, however, it has some limitations. The main limitation of this method in in its need for various meteorological data, including the solar radiation, air temperature, relative humidity, dew point temperature, wind speed and actual vapor pressure. Unfortunately, all of these parameters are not readily available in all the conditions. In this regard, many researchers interested to find a simple method for accurate ET0 estimation (Sentelhas et al., 2010; Dinpashoh, 2016; and many others). Based on our best knowledge there is no comprehensive study conducted in Urmia Basin for finding a simple and accurate method that needs less weather parameters for ET₀ estimation. Therefore, the main aim of this study is estimation of ET₀ that needs less weather parameters in Urmia Lake basin.
Materials and Methods
The area under study is the Urmia Lake Basin, located in North-West of Iran. This basin is approximately lied between the 35^⸰ 40´ E to 38^⸰ 29´ E latitudes and 44^⸰ 07´ to 47^⸰ 53 longitudes. The area of this basin is about 51700 km² which is equal to about 3.2 percent of Iran's area. Data used in this research are the daily recorded values of maximum air temperature, minimum air temperature, wind speed at 10 m height, relative humidity, sunshine duration, and some geographic information such as altitudes, latitudes and longitudes. The nine stations were selected from different points of the basin in this study. The FAO56PM method (Allen, 1998) was selected as the bench mark for ET₀ estimation in all the stations. In this method the following equation was used for ET₀ in the chosen sites.
                                                                  (1)
where ET₀ is the reference crop evapotranspiration (mm/day), R_n is the net solar radiation at crop surface (MJ m^-2 day^-1), G is the soil heat flux (MJ m^-2 day^-1), T is the mean air temperature at 2 m height (°C), u₂ is the wind speed at a 2 m height (m/s), the term (e_s-e_a) is the saturation vapor deficit (kPa), Δ is the slope of the vapor pressure curve at the point of air temperature (kPa/°C) and g is the psychometric constant (kPa/°C). In order to convert U from 10 m height to u₂ the following equation was used (Nandagiri and Kovoor, 2005; Sentelhas et al., 2010; Dinpashoh et al., 2011):
                                                                                                                       (2)
where U_z is the wind speed (m/s) at z m height, and z_w is the height (m) at which wind speed measured.
In this study, in order to find an alternative model, which uses less weather data in estimation of ET₀ the three empirical models namely Hargreaves (HG), Kimberly Penman (KPM), Priestly Taylor (PT), and Multivariate Linear and non-linear regression were used. Evaluation of the models performed using the three metrics, coefficient of determination (R²), Root Mean Square Error (RMSE), and Mean Absolute Error (MAE).
Results and Discussion
Results showed that, the median of the R² values for KP was more than 0.986. The median of the R² values for PT and HG models were found to be equal to 0.902 and 0.40, respectively. The median of RMSE for HG model was about 0.9 (mm day ^-1). This value for KPM and PT models were about 1.3 and 2.1 (mm day ^-1). The median of MAE for the selected stations for KPM was less than 1 (mm day ^-1). This value for HG was equal to 0.7 (mm day^-1) and in the case of PT was more than 1.5 (mm day ^-1). Therefore, considering the MAE values and RMSE, the HG model was detected to be the suitable method foe ET₀ estimation in Urmia Lake basin.