A hybrid neural network model for typhoon-rainfall forecasting
Introduction
Taiwan is situated in one of the main paths of northwestern Pacific typhoons. There are about four typhoons invading Taiwan each year. During the typhoon season (generally from July to October), heavy rainfall often causes floods and results in loss of life and property damage. Precise forecasts of typhoon rainfall are needed for issuing flood warnings. Therefore, to improve the accuracy of typhoon-rainfall forecasts is always an important task of flood management in Taiwan. However, typhoon rainfall is a complex component of the hydrologic cycle. It is not easy to develop a physically based model for typhoon-rainfall forecasting because of the lack of knowledge about its physical process. It is also difficult to construct a statistically based model using traditional regression techniques owing to various factors involved and their great variability in space and time.
Artificial neural networks (ANNs) have been proven to be very successful in dealing with highly-complicated problems. Due to their powerful capability to model nonlinear systems without the need to make any assumptions, ANNs have found increasing applications for modeling hydrological processes. A review of ANNs in hydrology was presented by the ASCE Task Committee on Application of Artificial Neural Networks in Hydrology, 2000a, ASCE Task Committee on Application of Artificial Neural Networks in Hydrology, 2000b. Additionally, some studies were performed to examine the potential of combining ANNs with other computing algorithms (Lin and Chen, 2005b, Wu and Chau, 2006, Muttil and Chau, 2006, Xie et al., 2006). Various applications of ANNs for hydrologic forecasting (Lin and Chen, 2004a, Ramirez et al., 2005, Pulido-Calvo and Portela, 2007, Partal and Cigizoglu, 2008) were studied in recent years. As regards the rainfall forecasting by ANNs, the multilayer perceptron network (MLPN) is the most commonly used (French et al., 1992, Luk et al., 2000, Luk et al., 2001, Lin and Chen, 2005a). By using the back-propagation algorithm to network parameter estimation, the MLPN can approximate complicated nonlinear functions to arbitrary accuracy (Govindaraju and Rao, 2000). Hence, the MLPN is used herein to construct the nonlinear relationship between the influential factors and the typhoon-rainfall depth.
However, to determine the appropriate model inputs is an important task when the MLPN is used for forecasting. If the appropriate inputs are used, the performance of ANN model can be improved (Bowden et al., 2005, Lin and Chen, 2008). Thus, the determination of the appropriate model inputs is also considered in this paper. For rainfall forecasting, Luk et al. (2000) used the spatial rainfall information from nearby rain gauges as input data and indicated that the inclusion of spatial information improves the accuracy of forecasts. But it is not easy to determine the optimal number of nearby rain gauges, especially in the situation that there are many rain gauges in the study area. A geostatistical analysis method, the semivariogram, is applied to help the determination of the optimal number of nearby rain gauges (Lin and Chen, 2005a). In addition to the spatial rainfall information, the typhoon characteristics (namely, the latitude and longitude of the typhoon center, the maximum wind speed near the center, the atmospheric pressure of the center, the radius of winds over 15 m/s, the typhoon moving speed, the typhoon moving direction, and the distance of the typhoon center from a rain gauge) also affect the rainfall during a typhoon event. Although these characteristics are too complex to model directly, they are still the helpful information to typhoon-rainfall forecasting. Hence, both the typhoon characteristics and the spatial rainfall information from nearby rain gauges are used as input to the MLPN. However, the input of MLPN becomes high-dimensional and complex. If used carelessly, the MLPN easily learns irrelevant information, which will reduce the performance of forecasting. In order to improve the typhoon-rainfall forecasting, one needs a data analysis method to analyze the input data before the development of the MLPN.
Self organizing map (SOM) proposed by Kohonen is a special class of ANN. It can project high-dimensional input space on a low-dimensional topology to demonstrate the topological relationships among input patterns, which helps users to discover the information. Hence, SOM can provide features that facilitate insight into the hydrological processes (Hsu et al., 2002). The property has rendered the SOM an attractive alternative for clustering massive and complex data which traditionally have been the domain of conventional clustering methods. The superior performance of SOM in clustering has been discussed in the literature (Mangiameli et al., 1996, Michaelides et al., 2001, Lin and Chen, 2006, Lin and Wu, 2007). In addition to cluster analysis, discrimination analysis can also be performed by the identical SOM (Lin and Wang, 2006). Lin and Wang (2006) indicate that SOM has great potential for developing a data analysis technique. Hence, in this paper, the SOM is adopted to develop a data analysis method which in turn helps the development of MLPN. There are two advantages of using SOM to develop the data analysis technique. First, the SOM-based data analysis technique can cluster data without specifying the number of clusters in advance. This property helps users determine the number of clusters more objectively. Second, the SOM-based data analysis technique can integrate cluster analysis with discrimination analysis together, which allows users to obtain the information more directly.
The objective of this paper is to propose a hybrid neural network model which combines the SOM with the MLPNs to improve the accuracy of typhoon-rainfall forecasts. With the advantages of the data analysis technique developed by SOM and the capability of nonlinear function approximation of MLPNs, the proposed model is expected to be useful for typhoon-rainfall forecasting. The performance of the proposed model is examined by actual applications to the Tanshui River Basin in northern Taiwan. In addition, the proposed model is compared with a forecasting model developed by the conventional neural network approach (hereafter referred to as the conventional model). In contrast to the proposed model, the conventional model is constructed by only one MLPN which uses non-grouped data as input.
Section snippets
Methodology
The proposed model is illustrated in Fig. 1. The basic concept of the proposed model is that data with significant different properties should be separated into different clusters before the nonlinear regression is developed by MLPN. In other words, the proposed model can be regarded as a piecewise nonlinear multivariable regression model. Hence, a data analysis technique is developed herein to perform cluster analysis as well as discrimination analysis of the input data. For each cluster, the
The study area and data
The study area of this paper is the Tanshui River Basin located in northern Taiwan. The basin has an area of 2726 km2 and an average river slope of 1/45. The average annual rainfall of the basin is 2966 mm, 63.5% of which occurs during the wet season (from May to October). The study area and the locations of rain gauges are shown in Fig. 3. In this basin, heavy typhoon rainfall often causes serious natural hazards such as floods and debris flow. Typhoon-rainfall forecasting can extend the time to
Results and discussions
The comparison test on the forecast accuracy is made among three MLPNs which use different time lags of typhoon characteristics as input. The three MLPNs are formulated aswhere the fi [ ] represents the ith MLPN, r(t + 1) is the rainfall depth at time t + 1, and Ty(t), Ty(t − 1) and Ty(t − 2) are the typhoon characteristics at time t, t − 1 and t − 2, respectively. Table 1 summarizes the results of the
Summary and conclusions
A hybrid artificial neural network model which combines the SOM with the MLPNs is proposed in this paper to forecast the typhoon rainfall. Firstly, the input determination is performed. By using a comparison test, the present and the past one-hour typhoon characteristics are decided as the optimal input factors. In addition, the semivariogram method is used to help determine the required number of nearby rain gauges whose rainfall records are used as the spatial information and involved in
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