Application of ANFIS and SVM Systems in Order to Estimate Monthly Reference Crop Evapotranspiration in the Northwest of Iran

Crop evapotranspiration modeling process mainly performs with empirical methods, aerodynamic and energy balance. In these methods, the evapotranspiration is calculated based on the average values of meteorological parameters at different time steps. The linear models didn’t have a good performance in this field due to high variability of evapotranspiration and the researchers have turned to the use of nonlinear and intelligent models. For accurate estimation of this hydrologic variable, it should be spending much time and money to measure many data (19).
Recently the new hybrid methods have been developed by combining some of methods such as artificial neural networks, fuzzy logic and evolutionary computation, that called Soft Computing and Intelligent Systems. These soft techniques are used in various fields of engineering.
A fuzzy neurosis is a hybrid system that incorporates the decision ability of fuzzy logic with the computational ability of neural network, which provides a high capability for modeling and estimating. Basically, the Fuzzy part is used to classify the input data set and determines the degree of membership (that each number can be laying between 0 and 1) and decisions for the next activity made based on a set of rules and move to the next stage. Adaptive Neuro-Fuzzy Inference Systems (ANFIS) includes some parts of a typical fuzzy expert system which the calculations at each step is performed by the hidden layer neurons and the learning ability of the neural network has been created to increase the system information (9).
SVM is a one of supervised learning methods which used for classification and regression affairs. This method was developed by Vapink (15) based on statistical learning theory. The SVM is a method for binary classification in an arbitrary characteristic space, so it is suitable for prediction problems (12).
The SVM is originally a two-class Classifier that separates the classes by a linear boundary. In this method, the nearest samples to the decision boundary called support vectors. These vectors define the equation of the decision boundary. The classic intelligent simulation algorithms such as artificial neural network usually minimize the absolute error or sum of square errors of the training data, but the SVM models, used the structural error minimization principle (5).
Results Based on the results of performance evaluations, and RMSE and R criteria, both of the SVM and ANFIS models had a high accuracy in predicting the reference evapotranspiration of North West of Iran. From the results of Tables 6 and 8, it can be concluded that both of the models had similar performance and they can present high accuracy in modeling with different inputs. As the ANFIS model for achieving the maximum accuracy used the maximum, minimum and average temperature, sunshine (M8) and wind speed. But the SVM model in Urmia and Sanandaj stations with M8 pattern and in other stations with M9 pattern achieves the maximum performance. In all of the stations (apart from Sanandaj station) the SVM model had a high accuracy and less error than the ANFIS model but, this difference is not remarkable and the SVM model used more input parameters (than the ANFIS model) for predicting the evapotranspiration.
In this research, in order to predict monthly reference evapotranspiration two ANFIS and SVM models employed using collected data at the six synoptic stations in the period of 38 years (1973-2010) located in the north-west of Iran. At first monthly evapotranspiration of a reference crop estimated by FAO-Penman- Monteith method for selected stations as the output of SVM and ANFIS models. Then a regression equation between effective meteorological parameters on evapotranspiration fitted and different input patterns for model determined. Results showed Relative humidity as the less effective parameter deleted from an input of the model. Also in this paper to investigate the effect of memory on predict of evapotranspiration, one, two, three and four months lag used as the input of model. Results showed both models estimated monthly evapotranspiration with the high accuracy but SVM model was better than ANFIS model. Also using the memory of evapotranspiration time series as the input of model instead of meteorological parameters showed less accuracy.