438 WEATHER AND FORECASTING VOLUME 27 Wavelet Support Vector Machines for Forecasting Precipitation in Tropical Cyclones: Comparisons with GSVM, Regression, and MM5 CHIH-CHIANG WEI Department of Information Management, Toko University, Pu-Tzu City, Taiwan (Manuscript received 5 January 2011, in final form 23 October 2011) ABSTRACT This study presents two support vector machine (SVM) based models for forecasting hourly precipitation during tropical cyclone (typhoon) events. The two SVM-based models are the traditional Gaussian kernel SVMs (GSVMs) and the advanced wavelet kernel SVMs (WSVMs). A comparison between the fifth- generation Pennsylvania State University–National Center for Atmospheric Research (PSU–NCAR) Mesoscale Model (MM5) and statistical models, including SVM-based models and linear regressions (re- gression), was made in terms of performance of rainfall prediction at the Shihmen Reservoir watershed in Taiwan. Data from 73 typhoons affecting the Shihmen Reservoir watershed were included in the analysis. This study designed six attribute combinations with different lag times for the forecast target. The modified RMSE, bias, and estimated threat score (ETS) results were employed to assess the predicted outcomes. Results show that better attribute combinations for typhoon climatologic characteristics and typhoon pre- cipitation predictions occurred at 0-h lag time with modified RMSE values of 0.288, 0.257, and 0.296 in GSVM, WSVM, and the regression, respectively. Moreover, WSVM having average bias and ETS values close to 1.0 gave better predictions than did the GSVM and regression models. In addition, Typhoons Zeb (1998) and Nari (2001) were selected for comparison between the MM5 model output and the developed statistical models. Results showed that the MM5 tended to overestimate the peak and cumulative rainfall amounts while the statistical models were inclined to yield underestimations. 1. Introduction forecasts (Jian et al. 2003). Microphysical schemes, used only in research before the 1990s, are now being adopted In meteorology and the atmospheric sciences, the by operational numerical weather prediction models. prediction of rainfall at landfall during tropical cyclones Furthermore, tremendous growth in computer capabil- (TCs) is an important research topic that has attracted ity in recent years has led to significant improvements in much interest. TCs, also known as typhoons, often de- forecasts of cloud condition and precipitation. To un- velop in the western North Pacific region. As soon as a typhoon makes landfall, the upstream watershed re- derstand the complicated physical mechanisms that oc- ceives voluminous rainfall within a short time, which cur during typhoon attacks in Taiwan, some insightful quickly converges downstream. The heavy precipitation real-case numerical studies (see section 2) have been un- can easily lead to floodwater exceeding the downstream dertaken (Businger et al. 1990; Jian et al. 2003). However, embankments, causing considerable economic losses and the physically based model is mathematically a highly casualties (Wei and Hsu 2009). Therefore, an accurate complicated, nonlinear numerical model in space and quantitative precipitation forecast for TC events is one time, and an accurate quantitative precipitation forecast of the most difficult challenges in meteorology (Businger remains one of the most difficult tasks (Lee et al. 2006). et al. 1990; Lonfat et al. 2004). Forecasting the behavior of complex systems has been High-resolution mesoscale numerical models hold a broad application domain for artificial intelligence or promise for enhancing the accuracy of precipitation machine learning. In weather forecasting, the prediction of rainfall during typhoons by statistical approaches has received much attention in recent years (see section 2). Corresponding author address: Chih-Chiang Wei, Dept. of In- formation Management, Toko University, No. 51, Sec. 2, Univer- As is well known, support vector machines (SVMs) pro- sity Rd., Pu-Tzu City, Chia-Yi County 61363, Taiwan. posed by V. Vapnik and his group at AT&T Bell Lab- E-mail: [email protected] oratories offer new and promising classification and DOI: 10.1175/WAF-D-11-00004.1 Ó 2012 American Meteorological Society Unauthenticated | Downloaded 09/28/21 07:32 PM UTC APRIL 2012 W E I 439 regression techniques (Cortes and Vapnik 1995). SVMs Li et al. 2005). Comparison of performance between the are developed from the idea of structural risk minimiza- above-mentioned statistical models and MM5 (Li et al. tion, which shows that the generalization error is bounded 2005) was made in terms of the prediction of typhoon by the sum of training errors (Hao 2008). SVMs learn floods (Typhoons Zeb in 1998 and Nari in 2001) at the from a separating hyperplane to maximize the margin Shihmen Reservoir watershed. and to produce good generalization ability (Burges 1998). Recent theoretical research has solved the existing diffi- 2. Statistical and numerical approaches culties in practical applications of SVMs (Joachims 1999; Platt 1999). In recent years, statistical and numerical approaches On the other hand, wavelet transforms have proven have been successfully applied to typhoon precipitation to be very popular and effective in regression and pat- prediction. For the statistical approaches, Yeh (2002) tern recognition applications and the wavelet technique used empirical orthogonal function analysis including shows promise for both nonstationary signal approxi- the climatology average method, deviation persistence mations and classifications (Zhang and Benveniste 1992; method, and regression equations to forecast the 6-h ac- Szu et al. 1992; Chen and Xie 2007). Hence, it is of value cumulated typhoon rainfall over Taiwan. Lee et al. (2006) to explore whether better performance could be ob- employed a climatology model for forecasting typhoon tained if the wavelet technique is combined with SVMs rainfall in Taiwan. The proposed model used a simple (Zhang et al. 2004). In recent years, the combination of statistical approach to estimate reasonable cumulative wavelet theories and SVMs, called wavelet support vec- rainfall for each river basin. Lonfat et al. (2007) devel- tor machines (WSVMs; see section 3) has drawn con- oped a parametric hurricane rainfall prediction scheme, siderable attention owing to its high predictive ability which applied the rainfall climatology and persistence for a wide range of applications and its better perfor- model to forecasting rainfall accumulations. Using the mance compared with other traditional leaning machines skills of the artificial intelligence/machine learning, Lin (Kivanc et al. 2003). For example, Chen and Xie (2007) and Chen (2005) developed a neural network with two used the dual-tree complex wavelet features and SVMs hidden layers for typhoon rainfall forecasting. The model for pattern recognition. Yang and Wang (2008) applied configuration is evaluated using typhoon characteristics. the WSVM to distributed denial of service intrusion Fan and Lee (2007) developed a Bayesian mixture re- detections. Widodo and Yang (2008) established an gression model where the data of the nonnegative re- intelligent system for fault detection and classification sponse variable contain many zero measurements. The of induction motors using WSVM. Wu (2009) proposed model was applied to typhoon rainfall predictions in new WSVMs for setting up a nonlinear system of Taipei, Taiwan. Sheng et al. (2008) used TC data (po- product sale series. Yao et al. (2010) presented a method sition, pressure, and wind) to establish the distribution that used WSVM for chatter identification. Chen et al. functions of TC rainfall and ran the SVM regression (2010) proposed an improved voice activity detection models for TC rainfall forecast in Jiaxing, in eastern algorithm using WSVM. At present, the WSVM tech- China. nique has not been applied to typhoon precipitation For the numerical approaches, Yang and Houze (1995) forecast. indicated that the simulated rainfall amount, distribu- This study aims to develop SVM-based models, which tion, and internal mesoscale structure were highly sensi- include the traditional Gaussian radial basis function tive to the hydrometeor types and microphysical schemes kernel SVMs (GSVM) and the advanced WSVM, for implemented in the model. Liu et al. (1997) successfully forecasting hourly precipitation during typhoon events. simulated the track, storm intensity, and detailed inner- Comparison of performance between these developed core structure of Hurricane Andrew in 1992, using MM5 models and linear regressions (regression) was made in with a grid nesting down to a 6-km grid size and a so- terms of precipitation forecasts at the Shihmen Reservoir phisticated explicit-scale cloud microphysics scheme. watershed in Taiwan. Wang (2002) further indicated that the detailed cloud Moreover, this study also compares the above statis- structures of an idealized TC showed various cloud mi- tical models with the fifth-generation Pennsylvania State crophysics schemes. Jian et al. (2003) simulated precipi- University–National Center for Atmospheric Research tation associated with Typhoon Sinlaku over Taiwan (PSU–NCAR) Mesoscale Model (MM5; Grell et al. 1994). using MM5 initialized diabatically with the Local Anal- MM5 has been widely used by the mesoscale and mi- ysis and Prediction System (LAPS). Li et al. (2005) used croscale meteorology communities. It has also been em- a physically based distributed hydrological model to ployed to