ارزیابی عملکرد شبکۀ عصبی مصنوعی (ANN) و ماشین بردار پشتیبان (SVM) در تخمین مقادیر روزانۀ تبخیر (مطالعۀ موردی: ایستگاه‌های هواشناسی تبریز و مراغه)

Introduction
Evaporation is a fundamental component of the hydrology cycle and has an important role in water resources management. Daily evaporation is an important variable in reservoir capacity, rainfall-runoff modeling, crop management and water balance. Measurement of actual evaporation is almost impossible, but evaporation can be estimated using several methods. There are two general viewpoints for estimation of evaporation: direct and indirect methods. It is inoperative to measurement of the evaporation by direct methods in all locations. The direct methods are usually used for proximate reservoirs or irrigation projects. The indirect methods of evaporation estimation need various input data that are not easily available. Moreover, the evaporation have very complex and nonlinear process that simulation of its complex process using simple methods is impractical. In recent years, the artificial intelligent methods such as Artificial Neural Network (ANN) and Support Vector Machine (SVM) have been successfully utilized for modeling the hydrological nonlinear process such as rainfall, precipitation, rainfall-runoff, evaporation, temperature, water quality, stream flow, water level and suspended sediment, etc. Therefore, this research evaluates the performance of ANN and SVM models in daily evaporation estimation.
 
Materials and methods
The daily climatic data, air temperature, wind speed, air pressure, relative humidity, rainfall, dew point temperature and sun shine hours of Tabriz and Maragheh synoptic stations are used as inputs to the ANN and SVM models to estimate the daily evaporation. For this purpose, 75 percent of the daily evaporation data were selected to calibrate the models and 25 percent of the data were used to validate the models. Different combinations of seven input and then individual inputs have been applied for  evaporation estimation.
ANNs are parallel information processing systems consisting of a set of neurons arranged in layers. These neurons provide suitable conversion functions for weighted inputs. In this study, we used Multilayer feed-forward perceptron (MLP) network. The MLP is trained with the use of back propagation learning algorithm. The back-propagation training algorithm is a supervised training mechanism and is normally adopted in most of the engineering applications. The neurons in the input layer have no transfer function. The logarithmic sigmoid transfer function was used in the hidden layer and linear transfer function was employed as an activation function from the hidden layer to the output layer, because the linear function is known to be robust for a continuous output variable. The optimal number of neuron in the hidden layer was identified using a trial and error procedure by varying the number of hidden neurons from 1 to 20. In recent years, SVM as one of the most important data-driven models has been considered in this regards. This model is a useful learning system based on constrained optimization theory that uses induction of structural error minimization principle and results as a general optimized answer. The SVM is a computer algorithm that are learnt by example to find the best function of classifier/hyperplane to separate the two classes in the input space. The SVM analyzes two kinds of data, i.e., linearly and non-linearly separable data. For a given training data with N number of samples, represented by, where x is an input vector and y is a corresponding output value, SVM estimator (f) on regression can be represented by:
 
Where w is a weight vector, b is a bias, and “.” denotes the dot product and  is a non-linear mapping function. Typically, three kernel functions, radial basis, polynomial and linear are applied in SVM. Use of each function with various parameters for evaporation estimation may have different results. Therefore, it is necessary to evaluate the accuracy of each of these functions and select the appropriate kernel functions for evaporation estimation. Two performance criteria are used in this study to assess the goodness of fit in the models. These are Correlation Coefficient (CC) and Root Mean Square Error (RMSE).
 
Results and discussion
In this paper, ten different combinations of seven inputs and then individual inputs are applied to  estimate the evaporation. Results of evaporation estimation in Tabriz station indicate that the first and eighth combinations have minimum RMSE and maximum CC in test period of ANN and SVM models, respectively. Also results of evaporation estimation in Maragheh station indicate that the first and Seventh combinations have minimum RMSE and maximum CC in test period of ANN and SVM models, respectively. The ANN model using first combination including air temperature, wind speed, air pressure, relative humidity, rainfall, dew point temperature and sun shine hours of climate data can achieve the values of 2.12 (mm) and 0.78 for RMSE and R statistics in test period for Tabriz station. The SVM model using eighth combination including wind speed, air pressure, relative humidity, rainfall, dew point temperature and sun shine hours of climate data, also achieve the values of 2.17 (mm) and 0.78 for RMSE and R statistics in test period for Tabriz station. Evaporation estimation of Maragheh station using ANN and SVM models, respectively, returned 1.62 (mm) and 1.43 (mm) for RMSE statistic in the test period. In next step, individual input results show that ANN model has better estimation of evaporation values in Tabriz station and SVM model in Maragheh station. The results also indicate that the SVM and ANN models have better estimation of evaporation values using individual inputs including average temperature and sun shine hours  compaired with other inputs, respectively.
 
Conclusion
The results of these models indicate that both ANN and SVM models have acceptable performance in evaporation estimation. Evaluation results show that the average temperature is better input than other six parameters in estimation of evaporation. The investigations of this study indicate that although there is no significant difference in the results of three kernel functions of support vector machine, but the Radial Basis kernel function has high accuracy and better performance in estimation of daily evaporation in comparison to other kernel functions.