Streamflow forecasting using least-squares support vector machines

Abstract

This paper investigates the ability of a least-squares support vector machine (LSSVM) model to improve the accuracy of streamflow forecasting. Cross-validation and grid-search methods are used to automatically determine the LSSVM parameters in the forecasting process. To assess the effectiveness of this model, monthly streamflow records from two stations, Tg Tulang and Tg Rambutan of the Kinta River in Perak, Peninsular Malaysia, were used as case studies. The performance of the LSSVM model is compared with the conventional statistical autoregressive integrated moving average (ARIMA), the artificial neural network (ANN) and support vector machine (SVM) models using various statistical measures. The results of the comparison indicate that the LSSVM model is a useful tool and a promising new method for streamflow forecasting.

Editor D. Koutsoyiannis; Associate editor L. See

Citation Shabri, A. and Suhartono, 2012. Streamflow forecasting using least-squares support vector machines. Hydrological Sciences Journal, 57 (7), 1275–1293.     

Long‐lead seasonal rainfall forecasting using time‐delay recurrent neural networks: a case study

A temporal artificial neural network‐based model is developed and applied for long‐lead rainfall forecasting. Tapped delay lines and recurrent connections are two different components that are used along with a static multilayer perceptron network to design a time‐delay recurrent neural network. The proposed model is, in fact, a combination of time‐delay and recurrent neural networks. The model is applied in three case studies of the Northwest, West, and Southwest basins of Iran. In addition, an autoregressive moving average with exogenous inputs (ARMAX) model is used as a baseline in order to be compared with the time‐delay recurrent neural networks developed in this study. Large‐scale climate signals, such as sea‐level pressure, that affect the rainfall of the study area are used as the predictors in the models, as well as the persistence between rainfall data. The results of winter‐spring rainfall forecasts are discussed thoroughly. It is demonstrated that in all cases the proposed neural network results in better forecasts in comparison with the statistical ARMAX model. Moreover, it is found that in two of three case studies the time‐delay recurrent neural networks perform better than either recurrent or time‐delay neural networks. The results demonstrate that the proposed method can significantly improve the long‐lead forecast by utilizing a non‐linear relationship between climatic predictors and rainfall in a region. Copyright © 2007 John Wiley & Sons, Ltd.     

支持向量机在储层厚度预测和计算中的应用

本文通过对油田储层结构的分析,运用支持向量机的理论和方法,建立了用于预测和计算储层厚度的支持向量机回归模型,并对该模型从参数变化范围、核函数选择、误差评价的标准等多方面进行了探讨,找出了建立储层厚度预测模型的一种有效方法,通过对实际储层厚度的预测,证明该方法在预测和计算储层厚度中具有较高的参考价值.     

Integrative stochastic model standardization with genetic algorithm for rainfall pattern forecasting in tropical and semi-arid environments

ABSTRACT

Climate patterns, including rainfall prediction, is one of the most complex problems for hydrologist. It is inherited by its natural and stochastic phenomena. In this study, a new approach for rainfall time series forecasting is introduced based on the integration of three stochastic modelling methods, including the seasonal differencing, seasonal standardization and spectral analysis, associated with the genetic algorithm (GA). This approach is specially tailored to eradicate the periodic pattern effects notable on the rainfall time series stationarity behaviour. Two different climates are selected to evaluate the proposed methodology, in tropical and semi-arid regions (Malaysia and Iraq). The results show that the predictive model registered an acceptable result for the forecasting of rainfall for both the investigated regions. The attained determination coefficient (R²) for the investigated stations was approx. 0.91, 0.90 and 0.089 for Mosul, Baghdad and Basrah (Iraq), and 0.80, 0.87 and 0.94 for Selangor, Negeri Sembilan and Johor (Malaysia).     

最小二乘支持向量回归滤波系统性能分析

支持向量机(Support Vector Machine: SVM)一直作为机器学习方法在统计学习理论基础上被研究和发展,本文从信号与系统的角度出发,证明了平移不变核最小二乘支持向量机(Least Squares SVM: LS-SVM)是一个线性时不变系统.以Ricker子波核为例,探讨了不同参数对最小二乘支持向量回归(Least Squares Support Vector Regression: LS-SVR)滤波器频率响应特性的影响,这些参数的不同选择相应地控制着滤波器通带上升沿的陡峭性、通带的中心频率、通带带宽以及信号能量的衰减,即滤波器长度越长通带的上升沿越陡,核参数值越大通带的中心频率越高,且通带带宽越宽,正则化参数值越小,通带带宽越窄(但通带中心频率基本保持恒定),有效信号幅度衰减越严重.合成地震记录的仿真实验结果表明,Ricker子波核LS-SVR滤波器在处理地震勘探信号的应用中,滤波性能优于径向基函数(Radial Basic Function: RBF)核LS-SVR滤波器以及小波变换滤波和Wiener滤波方法.     

Real‐time recurrent learning neural network for stream‐flow forecasting

Various types of neural networks have been proposed in previous papers for applications in hydrological events. However, most of these applied neural networks are classified as static neural networks, which are based on batch processes that update action only after the whole training data set has been presented. The time variate characteristics in hydrological processes have not been modelled well. In this paper, we present an alternative approach using an artificial neural network, termed real‐time recurrent learning (RTRL) for stream‐flow forecasting. To define the properties of the RTRL algorithm, we first compare the predictive ability of RTRL with least‐square estimated autoregressive integrated moving average models on several synthetic time‐series. Our results demonstrate that the RTRL network has a learning capacity with high efficiency and is an adequate model for time‐series prediction. We also investigated the RTRL network by using the rainfall–runoff data of the Da‐Chia River in Taiwan. The results show that RTRL can be applied with high accuracy to the study of real‐time stream‐flow forecasting networks. Copyright © 2002 John Wiley & Sons, Ltd.     

Support vector machine method for forecasting future strong earthquakes in Chinese mainland

Statistical learning theory is for small-sample statistics. And support vector machine is a new machine learning method based on the statistical learning theory. The support vector machine not only has solved certain problems in many learning methods, such as small sample, over fitting, high dimension and local minimum, but also has a higher generalization （forecasting） ability than that of artificial neural networks. The strong earthquakes in Chinese mainland are related to a certain extent to the intensive seismicity along the main plate boundaries in the world, however, the relation is nonlinear. In the paper, we have studied this unclear relation by the support vector machine method for the purpose of forecasting strong earthquakes in Chinese mainland.     

Wavelet regression model as an alternative to neural networks for monthly streamflow forecasting

The accuracy of the wavelet regression (WR) model in monthly streamflow forecasting is investigated in the study. The WR model is improved combining the two methods—the discrete wavelet transform (DWT) model and the linear regression (LR) model—for 1‐month‐ahead streamflow forecasting. In the first part of the study, the results of the WR model are compared with those of the single LR model. Monthly flow data from two stations, Gerdelli Station on Canakdere River and Isakoy Station on Goksudere River, in Eastern Black Sea region of Turkey are used in the study. The comparison results reveal that the WR model could increase the forecast accuracy of the LR model. In the second part of the study, the accuracy of the WR model is compared with those of the artificial neural networks (ANN) and auto‐regressive (AR) models. On the basis of the results, the WR is found to be better than the ANN and AR models in monthly streamflow forecasting. Copyright © 2009 John Wiley & Sons, Ltd.     

Potential of support vector regression for prediction of monthly streamflow using endogenous property

In the recent past, a variety of statistical and other modelling approaches have been developed to capture the properties of hydrological time series for their reliable prediction. However, the extent of complexity hinders the applicability of such traditional models in many cases. Kernel‐based machine learning approaches have been found to be more popular due to their inherent advantages over traditional modelling techniques including artificial neural networks(ANNs ). In this paper, a kernel‐based learning approach is investigated for its suitability to capture the monthly variation of streamflow time series. Its performance is compared with that of the traditional approaches. Support vector machines (SVMs) are one such kernel‐based algorithm that has given promising results in hydrology and associated areas. In this paper, the application of SVMs to regression problems, known as support vector regression (SVR), is presented to predict the monthly streamflow of the Mahanadi River in the state of Orissa, India. The results obtained are compared against the results derived from the traditional Box–Jenkins approach. While the correlation coefficient between the observed and predicted streamflows was found to be 0·77 in case of SVR, the same for different auto‐regressive integrated moving average (ARIMA) models ranges between 0·67 and 0·69. The superiority of SVR as compared to traditional Box‐Jenkins approach is also explained through the feature space representation. Copyright © 2009 John Wiley & Sons, Ltd.     

A hybrid approach of artificial neural network and multiple regression to forecast typhoon rainfall and groundwater-level change

ABSTRACT

A forecasting model is developed using a hybrid approach of artificial neural network (ANN) and multiple regression analysis (MRA) to predict the total typhoon rainfall and groundwater-level change in the Zhuoshui River basin. We used information from the raingauge stations in eastern Taiwan and open source typhoon data to build the ANN model for forecasting the total rainfall and the groundwater level during a typhoon event; then we revised the predictive values using MRA. As a result, the average accuracy improved up to 80% when the hybrid model of ANN and MRA was applied, even where insufficient data were available for model training. The outcome of this research can be applied to forecasts of total rainfall and groundwater-level change before a typhoon event reaches the Zhuoshui River basin once the typhoon has made landfall on the east coast of Taiwan.     

Performance of an artificial neural network on forecasting the daily occurrence and annual depth of rainfall at a tropical site

Performance of a feed‐forward back‐propagation artificial neural network on forecasting the daily occurrence and annual depth of rainfall at a single meteorological station is presented. Both short‐term and long‐term forecasting was attempted, with ground level data collected by the meteorological station in Colombo, Sri Lanka (79° 52′E, 6° 54′N) during two time periods, 1994–2003 and 1869–2003. Two neural network models were developed; a one‐day‐ahead model for predicting the rainfall occurrence of the next day, which was able to make predictions with a 74·3% accuracy, and one‐year‐ahead model for yearly rainfall depth predictions with an 80·0% accuracy within a ± 5% error bound. Each of these models was extended to make predictions several time steps into the future, where accuracies were found to decrease rapidly with the number of time steps. The success rates and rainfall variability within the north‐east and south‐west monsoon seasons are also discussed. Copyright © 2007 John Wiley & Sons, Ltd.     

A combined rotated general regression neural network method for river flow forecasting

ABSTRACT

This study focused on the performance of the rotated general regression neural network (RGRNN), as an enhancement of the general regression neural network (GRNN), in monthly-mean river flow forecasting. The study of forecasting of monthly mean river flows in Heihe River, China, was divided into two steps: first, the performance of the RGRNN model was compared with the GRNN model, the feed-forward error back-propagation (FFBP) model and the soil moisture accounting and routing (SMAR) model in their initial model forms; then, by incorporating the corresponding outputs of the SMAR model as an extra input, the combined RGRNN model was compared with the combined FFBP and combined GRNN models. In terms of model efficiency index, R², and normalized root mean squared error, NRMSE, the performances of all three combined models were generally better than those of the four initial models, and the RGRNN model performed better than the GRNN model in both steps, while the FFBP and the SMAR were consistently the worst two models. The results indicate that the combined RGRNN model could be a useful river flow forecasting tool for the chosen arid and semi-arid region in China.

Editor D. Koutsoyiannis; Associate editor not assigned     

地下水观测数据拟合与预测的支持向量机方法

影响地下水位变化因素有很多,在正常情况下,地下水位的变化实际上反应了气压、固体潮和降雨这些因素的变化,但是这些影响因子与地下水位之间有着较强的非线性关系。该文使用支持向量机方法建立起崇明中学观测站地下水位与气压、固体潮和降雨这些因素之间的非线性关系模型,并用于地下水观测数据拟合与预测,得到了较理想的结果,明显优于逐步回归方法。研究结果表明,支持向量机方法在地震前兆数据处理中有着广泛的应用前景。文中还对支持向量机方法在实际应用中的有关问题进行了讨论。     

Short‐term inflow forecasting using an artificial neural network model

The primary objective of this study is to investigate the possibility of including more temporal and spatial information on short‐term inflow forecasting, which is not easily attained in the traditional time‐series models or conceptual hydrological models. In order to achieve this objective, an artificial neural network (ANN) model for short‐term inflow forecasting is developed and several issues associated with the use of an ANN model are examined in this study. The formulated ANN model is used to forecast 1‐ to 7‐h ahead inflows into a hydropower reservoir. The root‐mean‐squared error (RMSE), the Nash–Sutcliffe coefficient (NSC), the A information criterion (AIC), B information criterion (BIC) of the 1‐ to 7‐h ahead forecasts, and the cross‐correlation coefficient between the forecast and observed inflows are estimated. Model performance is analysed and some quantitative analysis is presented. The results obtained are satisfactory. Perceived strengths of the ANN model are the capability for representing complex and non‐linear relationships as well as being able to include more information in the model easily. Although the results obtained may not be universal, they are expected to reveal some possible problems in ANN models and provide some helpful insights in the development and application of ANN models in the field of hydrology and water resources. Copyright © 2002 John Wiley & Sons, Ltd.     

Prediction of flow rate of karstic springs using support vector machines

Complex void space structure and flow patterns in karstic aquifers render behaviour prediction of karstic springs difficult. Four support vector regression-based models are proposed to predict flow rates from two adjacent karstic springs in Greece (Mai Vryssi and Pera Vryssi). Having no accurate estimates of the groundwater flow pattern, we used four kernels: linear, polynomial, Gaussian radial basis function and exponential radial basis function (ERBF). The data used for training and testing included daily and mean monthly precipitation, and spring flow rates. The support vector machine (SVM) performance depends on hyper-parameters, which were optimized using a grid search approach. Model performance was evaluated using root mean square error and correlation coefficient. Polynomial kernel performed better for Mai Vryssi and the ERBF for Pera Vryssi. All models except one performed better for Pera Vryssi. Our models performed better than generalized regression neural network, radial basis function neural network and ARIMA models.     

Improving the forecasts of extreme streamflow by support vector regression with the data extracted by self‐organizing map

During typhoons or storms, accurate forecasts of hourly streamflow are necessary for flood warning and mitigation. However, hourly streamflow is difficult to forecast because of the complex physical process and the high variability in time. Furthermore, under the global warming scenario, events with extreme streamflow may occur that leads to more difficulties in forecasting streamflows. Hence, to obtain more accurate hourly streamflow forecasts, an improved streamflow forecasting model is proposed in this paper. The computational kernel of the proposed model is developed on the basis of support vector machine (SVM). Additionally, self‐organizing map (SOM) is used to analyse observed data to extract data with specific properties, which are capable of providing valuable information for streamflow forecasting. After reprocessing, these extracted data and the observed data are used to construct the SVM‐based model. An application is conducted to clearly demonstrate the advantage of the proposed model. The comparison between the proposed model and the conventional SVM model, which is constructed without SOM, is performed. The results indicate that the proposed model is better performed than the conventional SVM model. Moreover, as regards the extreme events, the result shows that the proposed model reduces the forecasting error, especially the error of peak streamflow. It is confirmed that because of the use of data extracted by SOM, the improved forecasting performance is obtained. The proposed model, which can produce accurate forecasts, is expected to be useful to support flood warning systems. Copyright © 2012 John Wiley & Sons, Ltd.     

A two‐step‐ahead recurrent neural network for stream‐flow forecasting

In many engineering problems, such as flood warning systems, accurate multistep‐ahead prediction is critically important. The main purpose of this study was to derive an algorithm for two‐step‐ahead forecasting based on a real‐time recurrent learning (RTRL) neural network that has been demonstrated as best suited for real‐time application in various problems. To evaluate the properties of the developed two‐step‐ahead RTRL algorithm, we first compared its predictive ability with least‐square estimated autoregressive moving average with exogenous inputs (ARMAX) models on several synthetic time‐series. Our results demonstrate that the developed two‐step‐ahead RTRL network has efficient ability to learn and has comparable accuracy for time‐series prediction as the refitted ARMAX models. We then investigated the two‐step‐ahead RTRL network by using the rainfall–runoff data of the Da‐Chia River in Taiwan. The results show that the developed algorithm can be successfully applied with high accuracy for two‐step‐ahead real‐time stream‐flow forecasting. Copyright © 2003 John Wiley & Sons, Ltd.     

Regional flood frequency analysis using support vector regression in arid and semi-arid regions of Iran

Regional flood frequency analysis (RFFA) was carried out on data for 55 hydrometric stations in Namak Lake basin, Iran, for the period 1992–2012. Flood discharge of specific return periods was computed based on the log Pearson Type III distribution, selected as the best regional distribution. Independent variables, including physiographic, meteorological, geological and land-use variables, were derived and, using three strategies – gamma test (GT), GT plus classification and expert opinion – the best input combination was selected. To select the best technique for regionalization, support vector regression (SVR), adaptive neuro-fuzzy inference system (ANFIS), artificial neural network (ANN) and nonlinear regression (NLR) techniques were applied to predict peak flood discharge for 2-, 5-, 10-, 25-, 50- and 100-year return periods. The GT + ANFIS and GT + SVR models gave better performance than the ANN and NLR models in the RFFA. The results of the input variable selection showed that the GT technique improved the model performance.     

An ANN‐based model for spatiotemporal groundwater level forecasting

This paper evaluates the feasibility of using an artificial neural network (ANN) methodology for estimating the groundwater levels in some piezometers placed in an aquifer in north‐western Iran. This aquifer is multilayer and has a high groundwater level in urban areas. Spatiotemporal groundwater level simulation in a multilayer aquifer is regarded as difficult in hydrogeology due to the complexity of the different aquifer materials. In the present research the performance of different neural networks for groundwater level forecasting is examined in order to identify an optimal ANN architecture that can simulate the piezometers water levels. Six different types of network architectures and training algorithms are investigated and compared in terms of model prediction efficiency and accuracy. The results of different experiments show that accurate predictions can be achieved with a standard feedforward neural network trained usung the Levenberg–Marquardt algorithm. The structure and spatial regressions of the ANN parameters (weights and biases) are then used for spatiotemporal model presentation. The efficiency of the spatio‐temporal ANN (STANN) model is compared with two hybrid neural‐geostatistics (NG) and multivariate time series‐geostatistics (TSG) models. It is found in this study that the ANNs provide the most accurate predictions in comparison with the other models. Based on the nonlinear intrinsic ANN approach, the developed STANN model gives acceptable results for the Tabriz multilayer aquifer. Copyright © 2008 John Wiley & Sons, Ltd.     

Ricker子波核最小二乘支持向量回归滤波方法的稳健性研究

除了信噪比、有效子波畸变等,稳健性(Robustness)也是度量滤波方法效果的一个重要的物理量,它刻画了滤波系统应对异常点值的能力.一般用影响函数作为评价稳健性的工具.支持向量机方法已较成功地应用于信号与图像的滤波中,尤其Ricker子波核方法更适于地震勘探信号处理.通过考察Ricker子波核最小二乘支持向量回归(LS-SVR:least squares support vector regression)滤波方法的影响函数,可以证明该方法的稳健性较差,本文用加权方法改善该方法的稳健性.经过大量理论实验得到一种改进的权函数,使加权之后的方法具有比较理想的稳健性.进一步用这个权函数辅助的加权Ricker子波LS-SVR处理含噪的合成与实际地震记录,都得到较好的效果.由具有平方损失函数的LS-SVR信号处理系统的无界影响函数出发,本文所提出的权函数可以有效地应用于具有相似损失函数的处理过程,如消噪、信号检测、提高分辨率与预测等问题.