Using Path Analysis in identification of dominant effective meteorological parameters on ET0 in Eest Azarbaijan

Introduction Reference potential evapotranspiration (ET0) is one of the main elements of hydrologic cycle which can be estimated from weather data. This element can be used in calculating crop water requirements, scheduling irrigation systems, preparing input data to hydrological water-balance models, regional water resources assessment, and planning and management of water in a region and/or basin. The use of ET0 permits a physically realistic characterization of the effect of the microclimate of a field on the evaporative transfer of water from the soil-plant system to the atmosphere. It provides a measure of the integrated effect of radiation, wind speed, temperature and humidity on evapotranspiration. The long-term mean ET0 value in a certain time scale (month, season or year) can be changed during the recent decades in a given station. By decreasing ET0, crop water demand decreases, too. Conversely, by increasing ET0 the crop water requirements increases accordingly. Therefore, it can be suggest that change in the rates of ET0 due to climate change would have great importance to agriculturalists and water decision makers. On the other hand, accurate estimation of ET0 is crucial in improving the irrigation efficiency in a region. Many climatic parameters impacted the ET0 value in a single site. On the other hand these parameters are correlated to each other. Materials & Methods The climatic data from the synoptic stations with at least 20 years of continues records in East Azarbaijan province gathered from the Islamic Republic of Iran Meteorological Organization (IRIMO). The obtained data include maximum air temperature (Tmax), minimum air temperature (Tmin), wind speed in 10 m height (U), maximum relative humidity (RHmax), minimum relative humidity (RHmin), and duration of sunshine hours (n). The well-known FAO-PM56 method was used to calculate the ET0. There are many methods for ET0 estimation. The Penman–Monteith (PM) method is recommended as the standard by the United Nations Food and Agriculture Organization (UNFAO) and has gained worldwide acceptance and received much research interests. The PM equation has been widely used in ET0 estimation. However, this method needs more meteorological data which is not available in many regions. This led scientists to use other methods which do not need more parameters. Among the empirical methods which estimate ET0 using less climatic parameters are Hargreaves, Tornth-Wait, Belaney-Criddle and Priestley–Taylor. Unfortunately, output of these models are not accurate in all the sites. Therefore for using these simple empirical models the calibration process should be done as well. Therefore, the following issues need urgent study: (1) selection of as few dominant meteorological variables as possible meteorological parameters affecting ET0, and (2) universal application of an established model in more regions. The alternative method namely multiple linear regression (MLR) can be used to estimate the ET0. In order to evaluate the performance of the MLR method some measures calculated by comparing the results of MLR with FAO56-PM method. These measures are the root mean square error (RMSE), mean absolute error (MAE), Nash–Sutcliffe efficiency (NSE), and the coefficient of determination (R2). Then, the correlation coefficients (ryxi) calculated between the ET0 time series (y) and each of the meteorological parameters (xi). Then, the partial correlation coefficients (rij) calculated between the explanatory variables (xi and xj) as well. Both of the direct and indirect effects of each climatic parameter on ET0 evaluated by path analysis. These effects are denoted by P and Rdc, respectively. By solving the Eq. 6 the elements of P (direct effect of xi on y or ET0 ) are obtained. By multiplying the obtained P vector (direct effects) on r_(x_i x_j ) the indirect effect of xi through the xj on ET0) were calculated. This process repeated for all the selected sites. Path analysis was first proposed in 1921 as a mathematical and statistical method by the geneticist Sewell Wright. Nowadays, the method is broadly used in agriculture and energy demands, revealing direct or indirect relationships between some morphological characters. However, little information is available on the use of this technique to evaluate the affecting factors of ET0. Given the fact that all the meteorological variables are strongly correlated and ultimately lead to multi-collinearity, traditional trend and correlation analyses cannot quantify the interactions among the meteorological factors when filtering the suitable parameters. Path analysis is a type of multivariate statistical analysis for studying relationships among variables, and it can reveal the strength of effect of independent variables on a dependent variable. Path analysis can determine direct and indirect effects of independent variables on the dependent variable, multi-collinear independent variables resulting from their own strong correlations, and optimal regression equations without unnecessary independent variables. The path coefficient is a type of standard partial regression coefficient (without units) that expresses causalities among related variables, and is also a directional correlation coefficient between independent and dependent variables. This analysis conducted for each of the selected stations in East Azarbaijan province, Iran. To do this firstly correlation coefficients between each of the climatic parameters and ET0 time series calculated. Similarly, correlation coefficients matrix between the climatic parameters which affect ET0 obtained for each of the stations. Results and discussion Results showed that the values of MAPE obtained for the stations were between 0.433 and 0.874. However, the R2 values were between 0.972 and 0.9953. Similarly, the RMSE were between 0.042 (mm/day) and 0.982 (mm/day), and the obtained MAE values were between 0.033 and 0.057, respectively. Also, it was found that the wind speed at the stations namely Tabriz, Jolfa, Sarab, Sahand, Maragheh and Mianeh had significant correlation (at the 0.01% level) with ET0. The strongest correlation detected in the station Ahar, which was between ET0 and the wind speed (at the 0.01% level). The results of path analysis showed that the maximum value of P (direct effect of meteorological parameters on ET0 belonged to the wind speed. The P values of wind speed in the stations Tabriz, Julfa, Sahand, Sarab, Maragheh, and Mianeh were equal to 0.637, 0.787, 0.877, 0.578, 0.850, and 0.780, respectively. In the station Ahar, the highest value of the P observed, which belonged to the Tmax (equal to 0.398).

Accurate estimation of ET0 is very important from the view of optimal water management in any region. Wind speed was found to be the dominant direct climatic parameter due to having the largest value of the P. In general, it can be concluded that the causal analysis method can be considered as an effective way to investigate the direct and indirect effects of meteorological parameters on ET0. Overall, it is more reasonable and scientific to apply path analysis method to evaluating dominant meteorological parameters which affect the ET0 in direct and indirect manners. The further research can be oriented in analysis on why dominant factors vary with meteorological stations. Development of other soft computing techniques which calculate ET0 using the climatic methods (such as firefly algorithm, artificial neural networks, support vector regression, and genetic expression programming) and comparing their accuracy with that of the MLR recommended for further studies.