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 hybrid neural network model for typhoon-rainfall forecasting

A hybrid neural network model is proposed in this paper to forecast the typhoon rainfall. Two different types of artificial neural networks, the self-organizing map (SOM) and the multilayer perceptron network (MLPN), are combined to develop the proposed model. In the proposed model, a data analysis technique is developed based on the SOM, which can perform cluster analysis and discrimination analysis in one step. The MLPN is used as the nonlinear regression technique to construct the relationship between the input and output data. First, the input data are analyzed using a SOM-based data analysis technique. Through the SOM-based data analysis technique, input data with different properties are first divided into distinct clusters, which can help the multivariate nonlinear regression of each cluster. Additionally, the topological relationships among data are discovered from which more insight into the typhoon-rainfall process can be revealed. Then, for each cluster, the individual relationship between the input and output data is constructed by a specific MLPN. For evaluating the forecasting performance of the proposed model, an application is conducted. The proposed model is applied to the Tanshui River Basin to forecast the typhoon rainfall. The results show that the proposed model can forecast more precisely than the model developed by the conventional neural network approach.     

基于电磁探测数据的时序分析模型研究

针对电磁探测数据交叉检验时对不同卫星探测数据的时间匹配需求,本文基于DEMETER卫星时序探测数据,分析了国际参考电离层(IRI)模型模拟电子浓度(N_e)数据在不同纬度区域的误差分布特征; 同时,基于自回归移动平均(ARIMA)模型构建了N_e数据时序预测模型. 在此基础上,分析比较IRI模型与ARIMA模型在N_e数据时序预测中的优缺点,结果表明: ARIMA模型模拟预测N_e数据时间序列的相对误差在短期内较低(小于10%),且随着预测时间的增长而增大; 而IRI模型模拟预测N_e数据时间序列的相对误差不会随着预测时间的增长而增大,且在高纬度地区的预测相对误差比在中低纬度地区低.      

BIBLIOGRAPHIE

Abstract

Time series modelling approaches are useful tools for simulating and forecasting hydrological variables and their change through time. Although linear time series models are common in hydrology, the nonlinear time series model, the Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model, has rarely been used in hydrology and water resources engineering. The GARCH model considers the conditional variance remaining in the residuals of the linear time series models, such as an ARMA or an ARIMA model. In the present study, the advantages of a GARCH model against a linear ARIMA model are investigated using three classes of the GARCH approach, namely Power GARCH, Threshold GARCH and Exponential GARCH models. A daily streamflow time series of the Matapedia River, Quebec, Canada, is selected for this study. It is shown that the ARIMA (13,1,4) model is adequate for modelling streamflow time series of Matapedia River, but the Engle test shows the existence of heteroscedasticity in the residuals of the ARIMA model. Therefore, an ARIMA (13,1,4)-GARCH (3,1) error model is fitted to the data. The residuals of this model are examined for the existence of heteroscedasticity. The Engle test indicates that the GARCH model has considerably reduced the heteroscedasticity of the residuals. However, the Exponential GARCH model seems to completely remove the heteroscedasticity from the residuals. The multi-criteria evaluation for model performance also proves that the Exponential GARCH model is the best model among ARIMA and GARCH models. Therefore, the application of a GARCH model is strongly suggested for hydrological time series modelling as the conditional variance of the residuals of the linear models can be removed and the efficiency of the model will be improved.

Editor D. Koutsoyiannis; Associate editor C. Onof

Citation Modarres, R. and Ouarda, T.B.M.J., 2013. Modelling heteroscedasticty of streamflow times series. Hydrological Sciences Journal, 58 (1), 1–11.     

Application of integrated back‐propagation network and self organizing map for flood forecasting

Much of the nonlinearity and uncertainty regarding the flood process is because hydrologic data required for estimation are often tremendously difficult to obtain. This study employed a back‐propagation network (BPN) as the main structure in flood forecasting to learn and to demonstrate the sophisticated nonlinear mapping relationship. However, a deterministic BPN model implies high uncertainty and poor consistency for verification work even when the learning performance is satisfactory for flood forecasting. Therefore, a novel procedure was proposed in this investigation which integrates linear transfer function (LTF) and self‐organizing map (SOM) to efficiently determine the intervals of weights and biases of a flood forecasting neural network to avoid the above problems. A SOM network with classification ability was applied to the solutions and parameters of the BPN model in the learning stage, to classify the network parameter rules and to obtain the winning parameters. The outcomes from the previous stage were then used as the ranges of the parameters in the recall stage. Finally, a case study was carried out in Wu‐Shi basin to demonstrate the effectiveness of the proposal. Copyright © 2009 John Wiley & Sons, Ltd.     

An RBF‐based model with an information processor for forecasting hourly reservoir inflow during typhoons

Inflow forecasting is essential for decision making on reservoir operation during typhoons. In this paper, a radial basis function (RBF)‐based model with an information processor is proposed for more accurate forecasts of hourly reservoir inflow. Firstly, based on the multilayer perceptron neural (MLP) network, an information processor is developed to pre‐process the typhoon information (namely, typhoon characteristics and rainfall) and to produce forecasts of rainfall. The forecasted rainfall and the observed inflow are then used as input to the RBF‐based model, which is a nonlinear function approximator, to produce forecasts of hourly inflow. For parameter estimation of the RBF‐based model, the fully‐supervised learning algorithm is used. Actual applications of the proposed model are performed to yield 1‐ to 6‐h ahead forecasts of inflow. To assess the improvement due to the use of the typhoon information processor, models without the typhoon information processor are constructed and compared with the proposed model. The results show that the proposed model performs the best and is capable of providing improved forecasts of hourly inflow, especially for long lead‐time. In conclusion, the proposed model with a typhoon information processor can extract useful information from typhoon characteristics and rainfall, and consequently improve the forecasting performance. Copyright © 2009 John Wiley & Sons, Ltd.     

Long-range forecasting of suspended sediment

This study examines the employment of two methods, multiple linear regression (MLR) and an artificial neural network (ANN), for multistep ahead forecasting of suspended sediment. The autoregressive integrated moving average (ARIMA) model is considered for one-step ahead forecasting of sediment series in order to provide a comparison with the MLR and ANN methods. For one- and two-step ahead forecasting, the ANN model performance is superior to that of the MLR model. For longer ranges, MLR models provide better accuracy, but there is an important assumption violation. The Durbin-Watson statistics of the MLR models show a noticeable decrease from 1.3 to 0.5, indicating that the residuals are not dependent over time. The scatterplots of the three methods (MLR, ARIMA and ANN) for one-step ahead forecasting for the validation period illustrate close fits with the regression line, with the ANN configuration having a slightly higher R² value.     

Forecasting flows in Apalachicola River using neural networks

Forecasting river flow is important to water resources management and planning. In this study, an artificial neural network (ANN) model was successfully developed to forecast river flow in Apalachicola River. The model used a feed‐forward, back‐propagation network structure with an optimized conjugated training algorithm. Using long‐term observations of rainfall and river flow during 1939–2000, the ANN model was satisfactorily trained and verified. Model predictions of river flow match well with the observations. The correlation coefficients between forecasting and observation for daily, monthly, quarterly and yearly flow forecasting are 0·98, 0·95, 0·91 and 0·83, respectively. Results of the forecasted flow rates from the ANN model were compared with those from a traditional autoregressive integrated moving average (ARIMA) forecasting model. Results indicate that the ANN model provides better accuracy in forecasting river flow than does the ARIMA model. Copyright © 2004 John Wiley & Sons, Ltd.     

Multi-models for SPI drought forecasting in the north of Haihe River Basin,China

Drought is one of the most devastating climate disasters. Hence, drought forecasting plays an important role in mitigating some of the adverse effects of drought. Data-driven models are widely used for drought forecasting such as ARIMA model, artificial neural network (ANN) model, wavelet neural network (WANN) model, support vector regression model, grey model and so on. Three data-driven models (ARIMA model; ANN model; WANN model) are used in this study for drought forecasting based on standard precipitation index of two time scales (SPI; SPI-6 and SPI-12). The optimal data-driven model and time scale of SPI are then selected for effective drought forecasting in the North of Haihe River Basin. The effectiveness of the three data-models is compared by Kolmogorov–Smirnov (K–S) test, Kendall rank correlation, and the correlation coefficients (R²). The forecast results shows that the WANN model is more suitable and effective for forecasting SPI-6 and SPI-12 values in the north of Haihe River Basin.     

水文时间序列概率预报方法的通用架构

在准确揭示水文过程变化特性的基础上开展中长期(月尺度及以上)水文预报,是掌握未来水文情势和演变规律,以及研究解决实际水文水资源问题的重要基础.水文时间序列预报方法是揭示未来水文情势和演变规律的重要技术手段.本文首先梳理了目前常用的各类水文序列预报方法,分析讨论了各方法的基本原理和主要缺陷.然后,通过综合分析相关研究成果,总结得到关于水文序列预报方法的4点重要认识:序列预报前应进行序列分解;序列中确定成分和随机成分应分别建模预报;序列预报结果需要估计不确定性;模型集成效果常常优于单个模型效果.最后,提出一个水文时间序列概率预报方法的通用架构.利用该通用架构能够克服常规模型或方法的缺陷,进行物理成因分析的基础上,针对水文序列中不同特性的确定成分和随机成分别进行分析,既可得到准确的确定性预报结果,又可对预报结果的不确定性进行定量评估,并可提高最终预报结果的合理性和可靠性.     

Author Index 1991

Abstract

Evapotranspiration (ET) is an important process in the hydrological cycle and needs to be accurately quantified for proper irrigation scheduling and optimal water resources systems operation. The time variant characteristics of ET necessitate the need for forecasting ET. In this paper, two techniques, namely a seasonal ARIMA model and Winter's exponential smoothing model, have been investigated for their applicability for forecasting weekly reference crop ET. A seasonal ARIMA model with one autoregressive and one moving average process and with a seasonality of 52 weeks was found to be an appropriate stochastic model. The ARIMA and Winter's models were compared with a simple ET model to assess their performance in forecasting. The forecast errors produced by these models were very small and the models would be promisingly of great use in real-time irrigation management.     

Development of a short-term river flood forecasting method for snowmelt driven floods based on wavelet and cross-wavelet analysis

In this study, a new method of stand-alone short-term spring snowmelt river flood forecasting was developed based on wavelet and cross-wavelet analysis. Wavelet and cross-wavelet analysis were used to decompose flow and meteorological time series data and to develop wavelet based constituent components which were then used to forecast floods 1, 2, and 6 days ahead. The newly developed wavelet forecasting method (WT) was compared to multiple linear regression analysis (MLR), autoregressive integrated moving average analysis (ARIMA), and artificial neural network analysis (ANN) for forecasting daily stream flows with lead-times equal to 1, 2, and 6 days. This comparison was done using data from the Rideau River watershed in Ontario, Canada. Numerical analysis was performed on daily maximum stream flow data from the Rideau River station and on meteorological data (rainfall, snowfall, and snow on ground) from the Ottawa Airport weather station. Data from 1970 to 1997 were used to train the models while data from 1998 to 2001 were used to test the models. The most significant finding of this research was that it was demonstrated that the proposed wavelet based forecasting method can be used with great accuracy as a stand-alone forecasting method for 1 and 2 days lead-time river flood forecasting, assuming that there are no significant trends in the amplitude for the same Julian day year-to-year, and that there is a relatively stable phase shift between the flow and meteorological time series. The best forecasting model for 1 day lead-time was a wavelet analysis model. In testing, it had the lowest RMSE value (13.8229), the highest R² value (0.9753), and the highest EI value (0.9744). The best forecasting model for 2 days lead-time was also a wavelet analysis model. In testing, it had the lowest RMSE value (31.7985), the highest R² value (0.8461), and the second highest EI value (0.8410). It was also shown that the proposed wavelet based forecasting method is not particularly accurate for longer lead-time forecasting such as 6 days, with the ANN method providing more accurate results. The best forecasting model for 6 days lead-time was an ANN model, with the wavelet model not performing as well. In testing, the wavelet model had an RMSE of 57.6917, an R² of 0.4835, and an EI of 0.4366.     

Hydrological time‐series modelling using an adaptive neuro‐fuzzy inference system

Accurate forecasting of hydrological time‐series is a quite important issue for a wise and sustainable use of water resources. In this study, an adaptive neuro‐fuzzy inference system (ANFIS) approach is used to construct a time‐series forecasting system. In particular, the applicability of an ANFIS to the forecasting of the time‐series is investigated. To illustrate the applicability and capability of an ANFIS, the River Great Menderes, located in western Turkey, is chosen as a case study area. The advantage of this method is that it uses the input–output data sets. A total of 5844 daily data sets collected from 1985 to 2000 are used for the time‐series forecasting. Models having various input structures were constructed and the best structure was investigated. In addition, four various training/testing data sets were built by cross‐validation methods and the best data set was obtained. The performance of the ANFIS models in training and testing sets was compared with observations and also evaluated. In order to get an accurate and reliable comparison, the best‐fit model structure was also trained and tested by artificial neural networks and traditional time‐series analysis techniques and the results compared. The results indicate that the ANFIS can be applied successfully and provide high accuracy and reliability for time‐series modelling. Copyright © 2007 John Wiley & Sons, Ltd.     

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.     

Prophet时序预测模型在电离层TEC异常探测中的应用

提出一种基于Facebook 开源的Prophet预测模型进行电离层TEC异常识别的新方法。 首先, 对比分析了该方法与传统时间序列预测方法(ARIMA模型等)预测电离层TEC建模背景值的精度, 以及与经典电离层TEC异常识别方法(滑动四分位法)提取前面对应一致的电离层TEC背景值的精度。 结果表明, Prophet预测模型预测建模背景值的精度要明显优于其他方法, 且预测的建模精度比ARIMA模型等方法高2.55倍左右, 比滑动四分位法高10.74倍左右。 同时, 在最佳预测建模区间时, 其精度值大小比较依次为RMSE_IQR=10.5841>RMSE_ARIMA=3.2780>RMSE_Prophet=0.8469, 说明传统探测法预测建模背景值时具有较大的不足。 随后, 以2017年8月8日九寨沟7.0级地震为例, 利用该方法分析了电离层TEC异常扰动情况, 并对比验证了该方法的有效性和准确性。 实验结果表明: 在震前第10 d和第2 d电离层TEC发生较为明显的负异常, 第7 d电离层TEC发生较为明显的正异常。 对比实验表明, Prophet预测模型的有效性和准确性明显优于滑动四分位法。     

Application of a neural network model in establishing a stage–discharge relationship for a tidal river

This paper presents the applicability of neural network (NN) modelling for forecasting and filtering problems. The multilayer feedforward (MLFF) network was first constructed to forecast the tidal‐level variations at the mouth of the River Chao Phraya in Thailand. Unlike the well‐known conventional harmonic analysis, the NN model uses a set of previous data for learning and then forecasting directly the time‐series of tidal levels. It was found that lead time of 1 to 24 hourly tidal levels can be predicted successfully using only a short‐time hourly learning data. The MLFF network was further used to establish a stage–discharge relationship for the tidal river. The results show a considerably better performance of the NN model over the conventional models. In addition, the stage–discharge relationship obtained by the NN model can indicate reasonably well the important behaviour of the tidal influences. Copyright © 2003 John Wiley & Sons, Ltd.     

Construction of design hyetographs for locations without observed data

A design hyetograph which represents the time distribution of design rainfall depth corresponding to a duration and a return period is essential in hydrologic design. However, for locations without observed data (ungauged sites), construction of design hyetographs is a difficult task because of the lack of data. Hence, an approach based on self‐organizing map (SOM) is proposed in this paper to construct design hyetographs at ungauged sites. SOM, which is a special kind of artificial neural networks (ANNs), is a powerful technique for extracting and visualizing salient features of data and for solving classification problems. The proposed approach is composed of three steps: classification, assignment and construction. First, the SOM‐based classification is performed to analyse gauged sites' design hyetographs. Second, based on the concept of indicator kriging, a method is developed to assign an ungauged site of interest to a certain cluster. Third, based on the spatial information, the clustering results, and the design hyetographs of gauged sites, the design hyetograph at the site of interest is constructed using the reciprocal‐distance‐squared method. An application is conducted to assess the advantages of the proposed approach over the conventional approaches. Moreover, cross‐validation tests are applied to evaluate the performance of the accuracy and the robustness of the proposed approach. The results confirm the improvement in performance by using the proposed approach instead of conventional approaches. The proposed approach is useful for constructing design hyetographs at ungauged sites. Copyright © 2009 John Wiley & Sons, Ltd.     

ARIMA forecasting of ambient air pollutants (O3, NO, NO2 and CO)

In the present study, a stationary stochastic ARMA/ARIMA [Autoregressive Moving (Integrated) Average] modelling approach has been adapted to forecast daily mean ambient air pollutants (O₃, CO, NO and NO₂) concentration at an urban traffic site (ITO) of Delhi, India. Suitable variance stabilizing transformation has been applied to each time series in order to make them covariance stationary in a consistent way. A combination of different information-criterions, namely, AIC (Akaike Information Criterion), HIC (Hannon–Quinn Information Criterion), BIC (Bayesian Information criterion), and FPE (Final Prediction Error) in addition to ACF (autocorrelation function) and PACF (partial autocorrelation function) inspection, has been tried out to obtain suitable orders of autoregressive (p) and moving average (q) parameters for the ARMA(p,q)/ARIMA(p,d,q) models. Forecasting performance of the selected ARMA(p,q)/ARIMA(p,d,q) models has been evaluated on the basis of MAPE (mean absolute percentage error), MAE (mean absolute error) and RMSE (root mean square error) indicators. For 20 out of sample forecasts, one step (i.e., one day) ahead MAPE for CO, NO₂, NO and O₃, have been found to be 13.6, 12.1, 21.8 and 24.1%, respectively. Given the stochastic nature of air pollutants data and in the light of earlier reported studies regarding air pollutants forecasts, the forecasting performance of the present approach is satisfactory and the suggested forecasting procedure can be effectively utilized for short term air quality forewarning purposes.     

Hydro-climatic variability and forest fires in Mexico’s northern temperate forests

Global warming is likely modifying the hydrological cycle of forested watersheds. This report set as objectives to: a) assess the hydrological variables interception loss, I, potential and actual evapo-transpiration, E, Et, runoff, Q, and soil moisture content, θ; b) evaluate whether these variables are presenting consistent trends or oscillations that can be associated to global warming or climate variability; and c) relate θ to the number of wildfires and the burned area in Durango, Mexico. A mass balance approach estimated daily variables of the water cycle using sub-models for I and Et to calculate Q and θ for a time series from 1945 to 2007. Regression and auto-regressive and moving averaging (ARIMA) techniques evaluated the statistical significance of trends. The cumulative standardized z value magnified and ARIMA models projected statistically similar monthly and annual time series data of all variables of the water cycle. Regression analysis and ARIMA models showed monthly and annual P, I, E, and Et, Q, and θ do not follow consistent up or downward linear tendencies over time with statistical significance; they rather follow oscillations that could be adequately predicted by ARIMA models (r² ≥ 0.70). There was a consistent statistical association (p ≤ 0.05) of θ with the number of wildfires and the area burned regardless of the different spatial scales used in evaluating these variables. The analysis shows seasonal variability is increasing over time as magnifying pulses of dryness and wetness, which may be the response of the hydrological cycle to climate change. Further research must center on using longer time series data, testing seasonal variability with additional statistical analysis, and incorporating new variables in the analysis.     

Prediction of the impact of climate change on drought: an evaluation of six UK catchments using two stochastic approaches

Under future climate scenarios, possible changes of drought patterns pose new challenges for water resources management. For quantifying and qualifying drought characteristics in the UK, the drought severity indices of six catchments are investigated and modelled by two stochastic methods: autoregressive integrated moving average (ARIMA) models and the generalized linear model (GLM) approach. From the ARIMA models, autocorrelation structures are first identified for the drought index series, and the unexplained variance of the series is used to establish empirical relationships between drought and climate variables. Based on the ARIMA results, mean sea level pressure and possibly the North Atlantic Oscillation index are found to be significant climate variables for seasonal drought forecasting. Using the GLM approach, occurrences and amounts of rainfall are simulated with conditioning on climate variables. From the GLM‐simulated rainfall for the 1980s and 2080s, the probabilistic characteristics of the drought severity are derived and assessed. Results indicate that the drought pattern in the 2080s is less certain than for the 1961–1990 period, based on the Shannon entropy, but that droughts are expected to be more clustered and intermittent. The 10th and 50th quantiles of drought are likely higher in the 2080s scenarios, but there is no evidence showing the changes in the 90th quantile extreme droughts. Copyright © 2012 John Wiley & Sons, Ltd.