Evaluation of relationships between meteorological parameters and actual evapotranspiration using regression and hierarchical clustering (Case Study: Castelvetrano, Italy)

Introduction
Actual evapotranspiration, one of the most important components of the hydrological cycle, causes 60% of precipitation to return to the atmosphere. This value increases up to 90% in dry and semi-arid areas. In recent years, with population growth, increasing water demand, and climate change, the importance of this phenomenon has doubled. Despite its importance, actual evapotranspiration remains largely unknown and its estimation by direct measurement methods is costly and time-consuming. In this regard, the Penman-Monteith method, the most accepted method for estimating reference evaporation and transpiration, also requires a lot of meteorological data. Despite the weakness of the conceptual model, using experimental methods to estimate evaporation and transpiration is still common due to its simplicity. In addition, examining the conceptual model and statistical methods without prejudice makes it possible to identify the influential variables and create experimental relationships compatible with the conceptual model.
 
Materials and Methods
The case study, with an area of 13 ha, is located in the southwest of Sicily (Italy), about five km from Castelvetrano. The landscape is flat and the soil type is relatively homogeneous. The main crops are olives (70% coverage), vineyards (24%), fruit trees (2.6%), and other garden products (3.4%). The plants are about 3.5 m tall and are arranged in a regular grid of five m by eight m (density of 250 plants per ha). The climate of the region is Mediterranean and the soil texture class, according to the USDA classification, is silty clay loam. In this research, one-hour meteorological data from 23 meteorological variables from the Sicily meteorological-agricultural station and actual evapotranspiration data extracted from the Eddy covariance method for the statistical period of 2009-2016 were used. Linear regression methods were used to investigate the relationships between the 24 variables and actual evapotranspiration. Integrated hierarchical clustering was used also to classify the 24 variables.
 
Results and Discussion
Evaluating the relationships between the 24 variables (23 meteorological variables and actual evapotranspiration) using the linear regression method led to the extraction of relationships between parameters in the form of a 24x24 matrix. In other words, to predict each variable (as a dependent variable), 23 relationships with other parameters (as independent parameters) were extracted. Then, the priority of the independent variables to predict each dependent variable was determined based on the correlation coefficient (R). The average of the 23 numerical ranks of an independent variable to predict other dependent variables indicates the degree of competence of that variable to predict other variables. The result of integrated hierarchical clustering with a 70% correlation is seven clusters. The members of cluster number one are different temperature variables (instantaneous, minimum, maximum, and average), cluster number two, rainfall variable (the only single member cluster), cluster number three, humidity variables (instantaneous, minimum, maximum, and average), cluster number four, pressure variables (station pressure and sea level pressure), cluster number five, variables of total solar radiation and evaporation and transpiration (the only cluster with non-identical members), cluster number six, different wind speed variables (instantaneous, minimum, maximum and average at the height of two and 10 m) and cluster number seven showed the wind direction variables. The summary of the classification results generally shows that the meteorological variables are independent except for the variables of the same name (such as temperature variables) all Variables with the same name were placed in a cluster, and the only variables with different names that were located in a cluster were total solar radiation and evaporation and transpiration. The representative of each cluster is the best predictor (based on rank) among the members of that cluster to predict other variables. Based on this, average temperature variables, rainfall, average relative humidity, sea level pressure, total solar radiation, maximum wind speed at a height of two m, and wind direction at a height of 10 m were determined as representatives of seven clusters. Also, the best predictor of these representatives was determined from inside and outside the cluster members. Based on the regression analysis, the best predictor of actual evapotranspiration with a correlation coefficient of more than 70% in total solar radiation. Instantaneous and minimum relative humidity variables with a correlation coefficient of about 50% (inverse relationship) took second and third place respectively to estimate actual evapotranspiration. The fourth and fifth ranks also belong to the average and maximum humidity with a correlation coefficient of about 49%. The independent variable of the duration of wetness of the leaves with a correlation coefficient of 40% has taken the sixth place. The characteristics of wind speed, temperature, wind direction, total annual rainfall, and pressure have the next ranks to estimate the actual evapotranspiration, respectively, with correlation coefficients of less than 30%.
 
Conclusion
In general, the high correlation between total solar radiation and actual evapotranspiration in a cluster indicates the key role of this meteorological variable in estimating evaporation and transpiration and is a justification for using methods based on energy balance to estimate this parameter. The high correlation between the estimation of actual evapotranspiration with the total solar radiation, considering the dependence of this variable on other climatic and hydrological variables, can be a useful point for use in watersheds lacking data and information. Also, the state of relative humidity ranks first and second respectively to predict other variables and actual evapotranspiration, indicating the key role of this variable in the case study. Contrary to some research about the key role of precipitation in the estimation of evaporation and transpiration in the Mediterranean climate, in this research no acceptable correlation was observed between the independent variable of precipitation and the dependent variable of actual evapotranspiration, although this issue may be related to the form of the equation. In this regard, instantaneous, minimum, average, and maximum relative humidity were ranked after total solar radiation. On the other hand, the total solar radiation in the estimation of the actual evapotranspiration with a correlation coefficient (71%) compared to the independent variable of relative humidity is in the first rank of the predictors, although it is ranked after the average and minimum relative humidity in the estimation of 23 meteorological variables. However, total solar radiation and relative humidity (average and minimum) were identified as two independent variables that are effective in estimating meteorological variables, especially actual evapotranspiration, and it is suggested that more research be done in watersheds with different climatic variations to discover the internal relationships of actual evapotranspiration and other climatic variables.