Application of Set Pair Analysis-Based Similarity Forecast Model and Wavelet Denoising for Runoff Forecasting

This study presents the application of a set pair analysis-based similarity forecast (SPA-SF) model and wavelet denoising to forecast annual runoff. The SPA-SF model was built from identical, discrepant and contrary viewpoints. The similarity between estimated and historical data can be obtained. The weighted average of the annual runoff values characterized by the highest connection coefficients was regarded as the predicted value of the estimated annual runoff. In addition, runoff time series were decomposed using wavelet transforms to acquire approximate and detailed runoff signals at various resolution levels. At each resolution level, threshold quantifications were performed by setting the values of a detailed signal below a fixed threshold to zero. The denoised runoff time series data were obtained from the approximation at the final resolution level and processed detailed signals using threshold quantification at all resolution levels of runoff by wavelet reconstruction. Instead of using the original annual runoff, the denoised annual runoff was applied to compute the similarity between estimated and historical data for model calibration. The original data were used for model calibration and validation; the denoised runoff data were used as input data to calibrate the model (obtaining different connection coefficients) that is then applied for validation purposes by using as benchmark the same original data. To verify the accuracy of the proposed method, the annual runoff data of six stations in Eastern Taiwan were analyzed. Based on a root mean square error (RMSE) criterion, the analytical results demonstrated that, for all six stations, the proposed method using denoised annual runoff outperformed the traditional SPA-SF model, using original annual runoff, because noise was effectively removed from the detailed data, using a constant threshold, thus enhancing the accuracy of the annual runoff forecasting for the SPA-SF model.