Prediction of rainfall time series using modular soft computingmethods

Abstract

In this paper, several soft computing approaches were employed for rainfall prediction. Two aspects were considered to improve the accuracy of rainfall prediction: (1)carrying out a data-preprocessing procedure and (2)adopting a modular modeling method. The proposed preprocessing techniques included moving average (MA) and singular spectrum analysis (SSA). The modular models were composed of local support vectors regression (SVR) models or/and local artificial neural networks (ANN) models. In the process of rainfall forecasting, the ANN was first used to choose data-preprocessing method from MA and SSA. Modular models involved preprocessing the training data into three crisp subsets (low, medium and high levels) according to the magnitudes of the training data, and finally two SVRs were performed in the medium and high-level subsets whereas ANN or SVR was involved in training and predicting the low-level subset. For daily rainfall record, the low-level subset tended to be modeled by the ANN because it was overwhelming in the training data, which is based on the fact that the ANN is very efficient in training large-size samples due to its parallel information processing configuration. Four rainfall time series consisting of two monthly rainfalls and two daily rainfalls from different regions were utilized to evaluate modular models at 1-day, 2-day, and 3-day lead-time with the persistence method and the global ANN as benchmarks. Results showed that the MA was superior to the SSA when they were coupled with the ANN. Comparison results indicated that modular models (referred to as ANN-SVR for daily rainfall simulations and MSVR for monthly rainfall simulations) outperformed other models. The ANN-MA also displayed considerable accuracy in rainfall forecasts compared with the benchmark.

Introduction

An accurate and timely rainfall forecast is crucial for reservoir operation and flooding prevention because it can provide an extension of lead-time of the flow forecast, larger than the response time of the watershed, in particular for small and medium-sized mountainous basins.

Rainfall prediction is a very complex problem. Simulating the response using conventional approaches in modeling rainfall time series is far from a trivial task since the hydrologic processes are complex and involve various inherently complex predictors such as geomorphologic and climatic factors, which are still not well understood. As such, the artificial neural network algorithm becomes an attractive inductive approach in rainfall prediction owing to their highly nonlinearity, flexibility and data-driven learning in building models without any prior knowledge about catchment behavior and flow processes. They are purely based on the information retrieved from the hydro-meteorological data and act as blackbox.

Many studies have been conducted for the quantitative precipitation forecast (QPF) using diverse techniques including numerical weather prediction (NWP) models and remote sensing observations (Davolio et al., 2008, Diomede et al., 2008, Ganguly and Bras, 2003, Sheng et al., 2006, Yates et al., 2000), statistical models (Chan and Shi, 1999, Chu and He, 1995, DelSole and Shukla, 2002, Li and Zeng, 2008, Munot and Kumar, 2007, Nayagam et al., 2008), chaos-based approach (Jayawardena and Lai, 1994), non-parametric nearest-neighbors method (Toth et al., 2000), and soft computing-based methods including artificial neural networks (ANN), support vector regression (SVR) and fuzzy logic (FL) (Brath et al., 2002, Dorum et al., 2010, Guhathakurta, 2008, Nasseri et al., 2008, Pongracz et al., 2001, Sedki et al., 2009, Silverman and Dracup, 2000, Sivapragasam et al., 2001, Surajit and Goutami, 2007, Talei et al., 2010, Toth et al., 2000, Venkatesan et al., 1997). The contemporary studies focused on soft computing-based methods. Several examples of such methods can be mentioned. Venkatesan et al. (1997) employed the ANN to predict the all India summer monsoon rainfall with different meteorological parameters as model inputs. Chattopadhyay and Chattopadhyay (2008a) constructed an ANN model to predict monsoon rainfall in India depending on the rainfall series alone. The fuzzy logic theory was applied to monthly rainfall prediction by Pongracz et al. (2001). Toth et al. (2000) applied three time series models, auto-regressive moving average (ARMA), ANN and k-nearest-neighbors (KNN) method, to short-term rainfall prediction. The results showed that the ANN performed the best in the improvement of the runoff forecasting accuracy when the predicted rainfall was used as inputs of the rainfall-runoff model. ANN has also been applied on general circulation model (GCM). Chadwick et al. (2011) employed an artificial neural network approach to downscale GCM temperature and rainfall fields to regional model scale over Europe. Sachindra et al. (2011) developed a model with various soft computing techniques capable of statistically downscaling monthly GCM outputs to catchment scale monthly streamflows, accounting for the climate change.

Recently, models based on combining concepts have been paid more attention in hydrologic forecasting. Depending on different combination methods, combining models can be categorized into ensemble models and modular (or hybrid) models. The basic idea behind the ensemble models is to build several different or similar models for the same process and to combine them in a combining method (Abrahart and See, 2002, Kim et al., 2006, Shamseldin et al., 1997, Shamseldin and O'Connor, 1999, Xiong et al., 2001). For example, Xiong et al. (2001) used a Takagi-Sugeno fuzzy technique to combine several conceptual rainfall-runoff models. Coulibaly et al. (2005) employed an improved weighted-average method to coalesce forecasted daily reservoir inflows from the KNN model, conceptual model and ANN model. Kim et al. (2006) investigated five combining methods for improving ensemble streamflow prediction.

Physical processes in rainfall and/or runoff are generally composed of a number of sub-processes so that their accurate modeling by the building of a single global model is often not possible. Modular models are therefore proposed where sub-processes are first of all identified and then separate models (also called local or expert model) are established for each of them (Solomatine and Ostfeld, 2008). In these modular models, the split of training data can be soft or crisp. The soft split means the dataset can be overlapped and the overall forecasting output is the weighted-average of each local model (Shrestha and Solomatine, 2006, Zhang and Govindaraju, 2000, Wang et al., 2006, Wu et al., 2008). Zhang and Govindaraju (2000) examined the performance of modular networks in predicting monthly discharges based on the Bayesian concept. Wu et al. (2008) employed a distributed SVR for daily river stage prediction. On the contrary, there is no overlap of data in the crisp split and the final forecasting output is generated explicitly from one of the local models (Corzo and Solomatine, 2007, Jain and Srinivasulu, 2006, See and Openshaw, 2000, Sivapragasam and Liong, 2005, Solomatine and Xue, 2004). Solomatine and Xue (2004) used M5 model trees and neural networks in a flood-forecasting problem. Sivapragasam and Liong (2005) divided the flow range into three regions, and employed different SVR models to predict daily flows in high, medium and low regions.

Apart from the adoption of the modular model, the improvement of predictions may be expected by suitable data preprocessing techniques. Besides the conventional rescaling or standardization of training data, preprocessing methods from the perspective of signal analysis are also crucial because rainfall time series may be also viewed as a quasi-periodic signal, which is contaminated by various noises. Hence techniques such as singular spectrum analysis (SSA) were recently introduced to hydrology field by some researchers (Marques et al., 2006, Partal and Kişi, 2007, Sivapragasam et al., 2001). Sivapragasam et al. (2001) established a hybrid model of support vector machine (SVM) and the SSA for rainfall and runoff predictions. The hybrid model resulted in a considerable improvement in the model performance in comparison with the original SVM model. The application of wavelet analysis to precipitation was undertaken by Partal and Kişi (2007). Their results indicated that the wavelet analysis was highly promising. In addition, the issue of lagged predictions in the ANN model was mentioned by some researchers (Dawson and Wilby, 2001, Jain and Srinivasulu, 2004, De Vos and Rientjes, 2005, Muttil and Chau, 2006). A main reason on lagged predictions was the use of previous observed data as ANN inputs (De Vos and Rientjes, 2005). An effective solution was to obtain new model inputs by moving average over the original data series.

The scope of this study was to investigate the effect of the MA and SSA as data-preprocessing techniques and to couple with modular models in improving model performance for rainfall prediction. The modular model included three local models which were associated with three crisp subsets (low-, medium- and high-intensity rainfall) clustered by fuzzy C-mean (FCM) method. The ANN was first used to choose data-preprocessing method from MA and SSA. Depending on the selected data-preprocessing technique, modular models were employed to perform rainfall prediction. Generally, the ANN is very efficient in processing large-size training samples due to its parallel information processing configuration. The biggest drawback is that the model outputs are variable because of the random initialization of weights and biases. The SVR holds a good generalization and more stable model outputs. However, it is suitable for a small-size training sample (e.g. below 200) because the training time exponentially increases with the size of training samples. For the current rainfall data, the majority of subsets after data split belong to a small-size sample except for the low-intensity daily rainfall. Therefore, three local SVRs (hereafter referred as to MSVR) were employed for monthly rainfall data whereas two local SVRs and one ANN (hereafter referred to as ANN-SVR) were adopted for daily rainfall data. For daily rainfall record, the low-intensity subset was modeled by the ANN because it was overwhelming in the training data. For the comparison purpose, the global ANN and the persistence model were used as benchmarks. To ensure generalization of this study, four cases consisting of two monthly rainfall series and two daily rainfall series from India and China, were explored.