Evaluation of Experimental and intelligent Models in Estimation of Reference Evapotranspiration: Case Study Aligodarz

Abstract One of the most important components of the water requirement is the reference evapotranspiration (ET0), which is one of the most important components of the hydrological cycle that dependent to climate variables such as: wind speed near ground, air temperature, radiation Solar and relative humidity. Consequently, ET0 values can be estimated and simulated using meteorological models based on physical equations or the empirical relationship of meteorological variables. There are various methods for calculating reference evapotranspiration, each of which has different results depending on the different meteorological assumptions and data they consider. Worldwide, the FAO model is used as a reference method for estimating evapotranspiration. But this model requires a lot of input information such as: max air temperature, min air temperature, max relative humidity, min relative humidity, solar radiation and wind speedy, which sometimes is not possible to access all the information especially in arid and semi-arid regions like Iran and this necessitates the selection of models with less input data and appropriate accuracy. In this study, seven reference evapotranspiration estimation models that require less data including: Kimberley penman, FAO radiation model, Hargreaves Samani, Makkink, belany Kridle FAO 24, Turc and Peristly Teylor, were evaluated than the FAO model. The reference evapotranspiration was then modeled using Gene Expression Programming Model (GEP) and the results were compared with experimental methods. Multivariate regression was used to determine the model input patterns and to investigate the effect of climatic parameters on ET0. Multivariate regression in fact expresses the relationship between several predictor variables with the response variable in question. Such models have assumptions. The assumption that distinguishes multivariate regression from simple regression is that: 1) The number of predictor (independent) variables in the regression should be less than the number of observations. 2) There is a complete linear correlation between predictor and response variables. If the two assumptions are violated, the regression equation cannot be estimated. Gene expression planning is a combination of the GA and GP methods developed by Ferreira in 1999. In this method, linear and simple chromosomes of constant length, similar to the genetic algorithm and branch structures of different sizes and shapes, are combined, similar to the decomposition trees in genetic programming. In short, it can be stated that in this way the genotype and phenotype are separated and the system will be able to enjoy all the evolutionary benefits. Although the phenotype in GEP is similar to the branched structure of GP, the branched structure in GEP, also called tree expression, represents all independent genomes. In summary, it can be briefly stated that in GEP refinement takes place in a linear structure and then expressed as a tree structure, which will result in only the modified genome being transferred to the next generation. It does not need heavy structures to reproduce and mutate. For this purpose, daily maximum and minimum temperature, maximum and minimum relative humidity, Wind Speed and sunlight hours of the 35-year period (1983–2017) were used for the Aligodarz Synoptic Station. 70% of the data were used for training and 30% of the data were used for testing the model. Also, two types of mathematical operators including four-element operations and default model operators were used in the GEP method. The results showed that the Kimberley penman and FAO radiation models are more accurate than the other experimental models. Multivariate regression results showed acceptable modeling accuracy with R2 = 0.95. The analysis of model coefficients showed the highest effect of maximum Temperature with a coefficient of 0.58 on reference evapotranspiration. After that, respectively, wind speed, sunshine hours, minimum temperature, maximum and minimum relative humidity have the most influence on prediction and estimation of evapotranspiration. Therefore, six models for model inputs were determined. In Gene Expression Programming, model 2 with model default operators with RMSE = 0.843 and R2 = 0.932 at training stage and RMSE = 0.76 and R2 = 0.941 Performed better in the test phase. Comparison of the reference evapotranspiration estimation models indicated that the Gene Expression Programming model outperformed the other models. The results of this study showed that the GEP model has acceptable ability to estimate reference evapotranspiration under Aligodarz climatic conditions and introduced it as a usable model in this field.