# Investigation of the EWT-PSO-SVM Model for Runoff Forecasting in the Karst Area
EEMD is an improved EMD method that essentially suppresses the issue of mode mixing by introducing zero-mean and well-characterized white noise. However, EEMD still has some problems, because the auxiliary white noise added in the decomposition process eventually needs to increase the number of ensemble averages to offset, and the mode components are uncontrollable, resulting in large errors in the model results. To solve these problems, [PERSON] [20] proposed the empirical wavelet transform (EWT) in 2013. EWT combinesEMD and wavelet transform, which has the adaptability of EMD and the completeness of wavelet transform theory, a simple and fast calculation. Because of its relatively reliable performance in separating nonlinear and nonstationary signals, EWT is widely used in mechanical fault diagnosis, medical disease diagnosis, intelligent wind speed forecasting, and financial time series forecasting [21; 22]. [PERSON] et al. [23] used EWT to decompose the bearing vibration signal to denoise the vibration signal and identify the bearing fault. Experiments showed that the denoising technology after EWT decomposition can detect early faults. [PERSON] et al. [24] decomposed the wind speed series by EWT, and effectively obtained the real information in the series so that the forecasting model obtained more accurate prediction ability. [PERSON] et al. [25] used EWT to decompose the financial time data into series more suitable for forecasting, which effectively reduced the influence of noise in financial time series on forecasting results. Many studies have shown that EWT can be well adopted to the decomposition of time series data, and makes the model achieve good forecasting results. Therefore, this study adopted EWT to assist the SVM model to capture the periodicity and regularity embedded in runoff series. Global karst areas cover about 12% of the earth's land surface and provide drinking water for almost 25% of the global population, so the study of karst area is significant in economic development [26]. Nevertheless, the geographical structural characteristics of the karst area have serious heterogeneity, which makes the hydrological process of the karst area more complex than that of the non-karst area, and constructing an accurate runoff forecasting model is a challenging task [27]. Therefore, the accuracy of simulation results of single models in karst areas is usually poor, and hybrid models must be explored more urgently. In summary, although many previous studies have been done on hybrid models for runoff forecasting, there are still some problems. The motivations and contributions of this study are summarized as follows. Firstly, EWT has been widely used in series decomposition studies in other fields, but still less in decomposition of runoff forecasting. Therefore, applying EWT to runoff forecasting studies in different basins can further demonstrate its generalizability. Secondly, previous studies of hybrid models have focused on non-karst basins, so it is necessary to discuss their feasibility in karst basins. Finally, previous studies on the performance of hybrid models have mainly used sequential structured data inputs, while few have discussed their performance when inputting monthly structured data. Therefore, it is meaningful to discuss the stability of the hybrid models under different data structure inputs. To achieve these objectives, the following studies are done: (1) A hybrid EWT-PSO-SVM model based on \"decomposition-forecasting-reconstruction\" is constructed. (2) Using the runoff data collected from karst area as the input data of the models, the forecasting results of SVM, GA-SVM, PSO-SVM, EMD-PSO-SVM, and EWT-PSO-SVM models with different performance metrics are compared to validate the superiority and feasibility of the developed model. (3) To further identify the stability of the developed model, the forecasting results under different input data structures are compared.