kernel functions

Identifying, predicting and managing crisis in a climate structure is of great importance. Models are used as practical tools for understanding complex systems and simulating and predicting their behavior. Support vector machines are one of the supervised learning methods used for classification and regression. Support vector machines are able to detect hidden patterns and respond to complex changes in climate data. In this article, the structure of the support vector machine method and its application in climate data classification are presented. The characteristics of the structure of support vector machines are related to the selection of the kernel function type, so sufficient care must be taken in the selection of the kernel function type And on the other hand, PCI in climate forecasting is an important step in climate forecasting in order to make the best fit between forecasting and predicted data with the optimal number of parameters.

Evaporation is the one of main processes in the hydrological cycle, and one of the most important factors in the related studies, namely agriculture, hydrology, aerology, exploitation of reservoirs, designing of irrigation and drainage systems, irrigation scheduling, and water resources management. Therefore, accurate simulation of evaporation rates has of the high importance in hydrology researches. In this regard, intelligent methods of Genetic Programming, Support Vector Regression, and Artificial Neural Networks have been used for evaluation and simulation of the pan evaporation rates over Tabriz and Golfa synoptic stations, in the present research. For this purpose, meteorological data including evaporation, temperature, relative humidity, wind speed, and solar radiation during the period of 1993-2013 were used and the accuracy of studied methods were investigated by using statistical parameters of root mean square error, mean absolute error, correlation coefficient and Taylor diagram. The results showed that in the optimum case of Tabriz and Golfa stations, genetic programming with error of 2.18 and 2.68, support vector regression with error of 2.19 and 2.22, and artificial neural network with error of 2.14 and 2.21, respectively, had reasonable performance in evaporation simulation. Conclusively, the second scenario of artificial neural network method through the input parameters of temperature and wind speed and the seventh scenario of artificial neural network method through the input parameters of temperature, humidity, wind speed, and solar radiation by having the best performance, were suggested as the accurate models with reasonable precision for simulating pan evaporation at Tabriz and Golfa stations, respectively.

Accurate prediction of river flow has an important role in the optimum management of available water resources. In recent years, support vector machine (SVM) that is 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 a general optimized answer. Such as other data mining models, the SVM model can also be used for runoff simulation when the only available data is runoff (autoregressive simulation). Typically, three kernel functions, namely, radial basis, polynomial of degree d and linear are applied in SVM that use of each function with various parameters for river flow estimation may have different results. Therefore, it is necessary to evaluate the accuracy of each of these functions and select the appropriate kernel function for runoff simulation. Since time series models, namely, AR, ARMA and ARIMA are the main models for autoregressive simulation of runoff, relative accuracy of kernel functions can be investigated by comparing their performance with these models. Therefore, assessment of the accuracy of kernel functions for monthly river flow simulation and comparison of their performance with time series models is main aim of this study.
In this study Kherkherehchiy river basin was selected as the study area and observed monthly river flow of this basin in the Santeh gauging station were applied for calibration and validation of models. For this purpose, first 75 percent of monthly river flow data (1367-1384) were selected to calibrate models and 25 percent of data (1385-1390) were used to validate models. Next, probability distribution of monthly river flow data in Santeh station were studies based on Kolmogorov-Smirnov and Shapiro- Wilk test and then normalization of data distribution were done. After optimization of parameters for each kernel functions the monthly flow values were predicted in Santeh station and the performance of these functions were evaluated using root mean square errors (RMSE) and the correlation coefficient (CC).
The investigations of this study indicated that although there is no significant difference in the results of three kernel functions, but the polynomial kernel function of degree 4 with CC and RMSE values of 0.86 and 5.88 (m3/sec) respectively in the testing period, has high accuracy and better performance in prediction of monthly flow in comparison to other kernel functions. Also the results showed that ARMA(6,2) with CC and RMSE values of 0.82 and 6.47 (m3/sec) respectively in the testing period, has good performance in prediction of Kherkherehchiy monthly flow compared to the other time series models.
Finally, the predicted monthly river flow using polynomial kernel function of degree 4 (as a representative of SVM model) was compared with the results of ARMA(6,2) (as a representative of time series model) and this conclusion was obtained that the SVM model has a better performance than time series models in the monthly river flow prediction of the Kherkherehchiy basin