Application of support vector machine algorithm and wavelet transform for modeling rainfall-runoff process (case study: Aghchai-Iran)

The most important factor in improving the environmental planning and hydrological management decisions is introduced as the modeling and exact simulation of rainfall and runoff processes. The accurate and exact modeling of hydrological processes such as rainfall-runoff can give impressive information for urban planning, land use, flood and water resources management for a given watershed. Also, in order to mitigate drought impacts on water resource systems, the management attempts are based on hydrological process modeling. So, the need for accurate modeling of the rainfall-runoff process has grown rapidly in the past decades. Recently, new techniques in Artificial Intelligence (AI) like Support Vector Machine (SVM) have been used by hydrologists.
New techniques on AI, with a great variety of applications, have been recognized over the past decade. One of them is the SVM which is used in the classification and regression algorithms assortment. Support Vector Machines (SVMs) are kernel machines useful for classification and regression problems. The SVM model is based on the statistical learning theory. This model is a supervised learning technique that provides the input-output mapping functions with respect to a set of training data. The advantage of SVM modeling in comparison with the other methods is that this modeling works with less training data and variables. Compared to a traditional neural network, the SVM method replaces traditional empirical risk with structure risk minimization and solves a quadratic optimization problem which can get the optimal global solution in theory. In this paper, the wavelet analysis was linked to the SVM model concept for modeling Aghchai watershed rainfall–runoff process. To do this, the main time series of two variables, rainfall and runoff were decomposed to some multi-scale time series by wavelet theory. On the other hand, the annual or seasonal data were decomposed into large-scale approximation sub–signals and daily data in small periods were decomposed into the detailed sub-signals; then, these decomposed rainfall and runoff data act as the inputs of SVM to predict the daily runoff discharge. As a result, the runoff discharge was forecasted about 1 day ahead. To reach this aim, the classical SVM was first used for data modeling. The Kernel function was employed for data classification in the SVM. There were various kinds of Kernel functions. In this paper, the SVM modeling was done by three kinds of Kernel functions with respect to rainfall and runoff data concerning Aghchai watershed. Afterwards, some input combinations (combs. 1-5) were used as the inputs of SVM model; then, the performance of each combination was measured. The most significant part of the study occurred when the wavelet transform was combined with the SVM. So, the single SVM modeling gets promoted by the wavelet transform. In this step, the time series of each watershed were calibrated and verified by the Wavelet-Support Vector Machine (WSVM) model with the different kinds of mother wavelet types including Haar, db2, sym1 and coife1 and different decomposition levels (1-4).
The obtained results indicated that the RBF-Kernel function has the highest efficiency as compared to Poly and MLP Kernel functions for both watersheds. So, the RBF-Kernel function was employed in next steps. The comparison results of data combinations showed that the combination (2) has a better compatibility as the SVM input for both watersheds. Finally, in the WSVM model, the db2 mother wavelet and the decomposition level 3 were selected as high-efficiency ones for both watersheds and their calibration and verification results were illustrated in the given figures. So the maximum value of determination coefficient (R2) and the minimum value of root mean square error (RMSE) in verification for the SVM model was 0.69 and 0.79, respectively and for the WSVM model was 0.92 and 0.35, respectively. As a result, the proposed hybrid model was relatively more appropriate because the WSVM model uses some multi-scale processed time series with different resolution levels as inputs to model instead of using raw rainfall-runoff data time series. Also, the WSVM model had a high performance to predict the peak values of runoff discharges by considering seasonality and multi-scale time series. Finally, studying compatibility of the model with other river's data, the hybrid WSVM model caused accurate results for the watershed of Eel-River, located in California State. Also, WSVM model showed better performance in comparison with the other hybrid model such as Wavelet-Artificial Neural Network (WANN).