kernel function

In recent years by growing technology, new methods have been substantially developed to solve nonlinear problems such as river flow forecasting. Among the available various methods, Support Vector Machine (SVM) and Adaptive Neuro-Fuzzy Inference System (ANFIS) models have been recently used by many researchers. In this study, these methods were used to predict the monthly flow of NazluChai and Sezar Rivers during 1956-2016 period. Firstly, the data were prepared in two modes: (a) using flow data and considering the role of memory; (b) influencing the periodic term. Modeling was done by 80% of the data (576 months) for training and the remaining 20% (144 months) for testing. The root mean square error (RMSE), Nash-Sutcliffe (NS) and mean absolute relative error (MARE) metrics were used to evaluate the performance of the proposed models. The results showed that the SVM method with the RBF kernel function had the best performance in predicting monthly flow of the studied rivers. In addition, the periodic term significantly increased the prediction accuracy of the SVM-RBF model. Also, the performance of the ANFIS method was improved by using the periodic term and this model had the least error in estimating the monthly flow of the Saesar and Nazlu chi Rivers in M6 and M7 patterns, respectively. In general, the results of this study showed that the SVM method performs better than the ANFIS model in monthly flow prediction and the selection of appropriate kernel function has a direct effect on its efficiency.

Traditional method in flood frequency analysis is parametric approach. This method lacks the ability to describe multimodal and Asymmetric densities. In order to overcome this problem¡ the nonparametric models can be used. Two methods of nonparametric approach are: fixed and variable kernel density. In fixed kernel density method¡ the probability density function can be estimated by selecting a kernel function and optimal bandwidth and in variable kernel density method the probability density function can be estimated by selecting a kernel function and bandwidth at each observation point. Cross validation and Rule of thumb are common methods for estimating the optimum bandwidth. In this paper¡ besides mentioned methods Plug in bandwidth method is used and nonparametric flood frequency analysis is performed using annual maximum flood data of the Dez river. Finally results were compared with parametric method. According to RMSE¡ it is concluded that plug in bandwidth is the most accurate method for estimating optimum bandwidth. As well as Nonparametric method based on variable kernel density is more accurate than fixed kernel density and both types of these models are more accurate than LP3 distribution.

In this research, a first order Markov chain model was applied to simulate soil salinity in nine standard depths and 10 classes in the cultivated pistachio areas of Ardakan city. Transition probability matrix, kernel and uniform distribution were used to simulate 500000 soil profiles. Results indicate kernel function could reproduce soil salinity values with statistical criteria (i.e. mean, standard deviation, skewness and kurtosis) more closely to the observed data when compared to data simulated by uniform function. Moreover, simulation processes from down-up is more accurate than that of up-down method. Overall, Makov simulation technique is able to consider the relationship between different classes.