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.     

Daily streamflow forecasting using a wavelet transform and artificial neural network hybrid models

Abstract

New wavelet and artificial neural network (WA) hybrid models are proposed for daily streamflow forecasting at 1, 3, 5 and 7 days ahead, based on the low-frequency components of the original signal (approximations). The results show that the proposed hybrid models give significantly better results than the classical artificial neural network (ANN) model for all tested situations. For short-term (1-day ahead) forecasts, information on higher-frequency signal components was essential to ensure good model performance. However, for forecasting more days ahead, lower-frequency components are needed as input to the proposed hybrid models. The WA models also proved to be effective for eliminating the lags often seen in daily streamflow forecasts obtained by classical ANN models. 

Editor D. Koutsoyiannis; Associate editor L. See

Citation Santos, C.A.G. and Silva, G.B.L., 2013. Daily streamflow forecasting using a wavelet transform and artificial neural network hybrid models. Hydrological Sciences Journal, 59 (2), 312–324.     

River flow modelling: comparison of performance and evaluation of uncertainty using data-driven models and conceptual hydrological model

Hydrological and statistical models are playing an increasing role in hydrological forecasting, particularly for river basins with data of different temporal scales. In this study, statistical models, e.g. artificial neural networks, adaptive network-based fuzzy inference system, genetic programming, least squares support vector machine, multiple linear regression, were developed, based on parametric optimization methods such as particle swarm optimization (PSO), genetic algorithm (GA), and data-preprocessing techniques such as wavelet decomposition (WD) for river flow modelling using daily streamflow data from four hydrological stations for a period of 1954–2009. These models were used for 1-, 3- and 5-day streamflow forecasting and the better model was used for uncertainty evaluation using bootstrap resampling method. Meanwhile, a simple conceptual hydrological model GR4J was used to evaluate parametric uncertainty based on generalized likelihood uncertainty estimation method. Results indicated that: (1) GA and PSO did not help improve the forecast performance of the model. However, the hybrid model with WD significantly improved the forecast performance; (2) the hybrid model with WD as a data preprocessing procedure can clarify hydrological effects of water reservoirs and can capture peak high/low flow changes; (3) Forecast accuracy of data-driven models is significantly influenced by the availability of streamflow data. More human interferences from the upper to the lower East River basin can help to introduce greater uncertainty in streamflow forecasts; (4) The structure of GR4J may introduce larger parametric uncertainty at the Longchuan station than at the Boluo station in the East river basin. This study provides a theoretical background for data-driven model-based streamflow forecasting and a comprehensive view about data and parametric uncertainty in data-scarce river basins.     

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 effective drought index using a wavelet extreme learning machine (W-ELM) model

A drought forecasting model is a practical tool for drought-risk management. Drought models are used to forecast drought indices (DIs) that quantify drought by its onset, termination, and subsequent properties such as the severity, duration, and peak intensity in order to monitor and evaluate the impacts of future drought. In this study, a wavelet-based drought model using the extreme learning machine (W-ELM) algorithm where the input data are first screened through the wavelet pre-processing technique for better accuracy is developed to forecast the monthly effective DI (EDI). The EDI is an intensive index that considers water accumulation with a weighting function applied to rainfall data with the passage of time in order to analyze the drought-risk. Determined by the autocorrelation function (ACF) and partial ACFs, the lagged EDI signals for the current and past months are used as significant inputs for 1 month lead-time EDI forecasting. For drought model development, 97 years of data for three hydrological stations (Bathurst Agricultural, Wilsons Promontory and Merredin in Australia) are partitioned in approximately 90:5:5 ratios for training, cross-validation and test purposes, respectively. The discrete wavelet transformation (DWT) is applied to the predictor datasets to decompose inputs into their time–frequency components that capture important information on periodicities. DWT sub-series are used to develop new EDI sub-series as inputs for the W-ELM model. The forecasting capability of W-ELM is benchmarked with ELM, artificial neural network (ANN), least squares support vector regression (LSSVR) and their wavelet-equivalent (W-ANN, W-LSSVR) models. Statistical metrics based on agreement between the forecasted and observed EDI, including the coefficient of determination, Willmott’s index, Nash–Sutcliffe coefficient, percentage peak deviation, root-mean-square error, mean absolute error, and model execution time are used to assess the effectiveness of the models. The results demonstrate enhanced forecast skill of the drought models that use wavelet pre-processing of the predictor dataset. Based on statistical measures, W-ELM outperformed traditional ELM, LSSVR, ANN and their wavelet-equivalent counterparts (W-ANN, W-LSSVR). It is found that the W-ELM model is computationally efficient as shown by a faster running time with the majority of forecasting errors in lower frequency bands. The results demonstrate the usefulness of W-ELM over W-ANN and W-LSSVR models and the benefits of wavelet transformation of input data to improve the performance of drought forecasting models.     

Using large‐scale climatic patterns for improving long lead time streamflow forecasts for Gunnison and San Juan River Basins

In a water‐stressed region, such as the western United States, it is essential to have long lead times for streamflow forecasts used in reservoir operations and water resources management. Current water supply forecasts provide a 3‐month to 6‐month lead time, depending on the time of year. However, there is a growing demand from stakeholders to have forecasts that run lead times of 1 year or more. In this study, a data‐driven model, the support vector machine (SVM) based on the statistical learning theory, was used to predict annual streamflow volume with a 1‐year lead time. Annual average oceanic–atmospheric indices consisting of the Pacific decadal oscillation, North Atlantic oscillation (NAO), Atlantic multidecadal oscillation, El Niño southern oscillation (ENSO), and a new sea surface temperature (SST) data set for the ‘Hondo’ region for the period of 1906–2006 were used to generate annual streamflow volumes for multiple sites in the Gunnison River Basin and San Juan River Basin, both located in the Upper Colorado River Basin. Based on the performance measures, the model showed very good forecasts, and the forecasts were in good agreement with measured streamflow volumes. Inclusion of SST information from the Hondo region improved the model's forecasting ability; in addition, the combination of NAO and Hondo region SST data resulted in the best streamflow forecasts for a 1‐year lead time. The results of the SVM model were found to be better than the feed‐forward, back propagation artificial neural network and multiple linear regression. The results from this study have the potential of providing useful information for the planning and management of water resources within these basins. Copyright © 2012 John Wiley & Sons, Ltd.     

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.     

Investigating the extrapolation performance of neural network models in suspended sediment data

Suspended sediment modelling is a quite significant issue in hydrology. The prediction of suspended sediment has taken the attention of several scientists in water resources. With extrapolation, the forecasting ability of the employed forecasting model beyond the calibration range is investigated. In the present study, different smoothing parameters are used to differentiate the kurtosis of the local critical points (local minima and maxima). The two models used are an artificial neural network (ANN) model and a multiple linear regression (MLR) model for prediction in order to examine the model extrapolation ability. The ANN model provides closer estimations to the observed peaks, being higher than the corresponding MLR ones. For the local minima, the ANN predictions are higher than the MLR predictions. As there are limited local points, all the remaining ANN predictions are lower than the MLR ones except for one point.     

River flow forecasting using wavelet and cross‐wavelet transform models

In this study, short‐term river flood forecasting models based on wavelet and cross‐wavelet constituent components were developed and evaluated for forecasting daily stream flows with lead times equal to 1, 3, and 7 days. These wavelet and cross‐wavelet models were compared with artificial neural network models and simple perseverance models. This was done using data from the Skrwa Prawa River watershed in Poland. Numerical analysis was performed on daily maximum stream flow data from the Parzen station and on meteorological data from the Plock weather station in Poland. Data from 1951 to 1979 was used to train the models while data from 1980 to 1983 was used to test the models. The study showed that forecasting models based on wavelet and cross‐wavelet constituent components can be used with great accuracy as a stand‐alone forecasting method for 1 and 3 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. It was also shown that forecasting models based on wavelet and cross‐wavelet constituent components for forecasting river floods are not accurate for longer lead time forecasting such as 7 days, with the artificial neural network models providing more accurate results. Copyright © 2008 John Wiley & Sons, Ltd.     

Comparison of local and global approximators in multivariate chaotic forecasting of daily streamflow

ABSTRACT

Although it is conceptually assumed that global models are relatively ineffective in modelling the highly unstable structure of chaotic hydrologic dynamics, there is not a detailed study of comparing the performances of local and global models in a hydrological context, especially with new emerging machine learning models. In this study, the performance of a local model (k-nearest neighbour, k-nn) and, as global models, several recent machine learning models – artificial neural network (ANN), least square-support vector regression (LS-SVR), random forest (RF), M5 model tree (M5), multivariate adaptive regression splines (MARS) – was analysed in multivariate chaotic forecasting of streamflow. The models were developed for Australia’s largest river, the River Murray. The results indicate that the k-nn model was more successful than the global models in capturing the streamflow dynamics. Furthermore, coupled with the multivariate phase-space, it was shown that the global models can be successfully used for obtaining reliable uncertainty estimates for streamflow.     

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.     

Artificial neural network models for forecasting monthly precipitation in Jordan

Forecasting precipitation in arid and semi-arid regions, in Jordan in the Middle East for example, has particular importance since precipitation is the unique source of water in such regions. In this study, 1-month ahead precipitation forecasts are made using artificial neural network (ANN) models. Feed forward back propagation (FFBP), radial basis function (RBF) and generalized regression type ANNs are used and compared with a simple multiple linear regression (MLR) model. The models are tested on monthly total precipitation recorded at three meteorological stations (Baqura, Amman and Safawi) from different climatological regions in Jordan. For the three stations, it is found that the best calibrated model is FFBP with respect to all performance criteria used in the study, including determination coefficient, mean square error, mean absolute error, the slope and the intercept in the best-fit linear line of the scatter diagram. In the validation stage, FFBP is again the best model in Baqura and Amman. However, in Safawi, the driest station, not only FFBP but also RBF and MLR perform equally well depending on the performance criterion under consideration.     

Streamflow predictability in the Saskatchewan/Nelson River basin given macroscale estimates of the initial soil moisture status

Abstract

Soil moisture estimates obtained over large spatial areas will become increasingly available through current and upcoming satellite missions and from numerous land surface parameterization schemes run at global- and continental-scale resolutions. The goal of this research was to evaluate the potential for using macroscale estimates of soil moisture for enhancing streamflow forecasts. Towards this research objective, monthly streamflow estimates were obtained from over 50 gauge locations within the Nelson basin, Canada, for the period 1979–1999. For each streamflow record, multiple linear regression models were used to remove components of the streamflow signal related to previous streamflow, climate teleconnections (e.g. ENSO and AO) and snow water equivalence. Correlations were then assessed between the macroscale soil moisture estimates and the residuals of the multiple linear regression analysis over lead times of one, two and three months. At the one- and two-month lead time, statistically significant relationships between soil moisture and the residuals of streamflow are observed over a large proportion of the gauging locations. The number of catchments with statistically significant relationships decreases significantly after two months and particularly in the months of April—June. This study demonstrates that available macroscale estimates of soil moisture have the potential to enhance streamflow prediction, although further study is suggested to improve upon the soil moisture estimates and their application in a forecast system.     

Adjusting wavelet‐based multiresolution analysis boundary conditions for long‐term streamflow forecasting

We propose a novel technique for improving a long‐term multi‐step‐ahead streamflow forecast. A model based on wavelet decomposition and a multivariate Bayesian machine learning approach is developed for forecasting the streamflow 3, 6, 9, and 12 months ahead simultaneously. The inputs of the model utilize only the past monthly streamflow records. They are decomposed into components formulated in terms of wavelet multiresolution analysis. It is shown that the model accuracy can be increased by using the wavelet boundary rule introduced in this study. A simulation study is performed to evaluate the effects of different wavelet boundary rules using synthetic and real streamflow data from the Yellowstone River in the Uinta Basin in Utah. The model based on the combination of wavelet and Bayesian machine learning regression techniques is compared with that of the wavelet and artificial neural networks‐based model. The robustness of the models is evaluated. Copyright © 2015 John Wiley & Sons, Ltd.     

Monthly streamflow forecasting using neuro-wavelet techniques and input analysis

ABSTRACT

Combinations of low-frequency components (also known as approximations) resulting from the wavelet decomposition are tested as inputs to an artificial neural network (ANN) in a hybrid approach, and compared to classical ANN models for flow forecasting for 1, 3, 6 and 12 months ahead. In addition, the inputs are rewritten in terms of the flow, revealing what type of information was being provided to the network, in order to understand the effect of the approximations on the forecasting performance. The results show that the hybrid approach improved the accuracy of all tested models, especially for 1, 3 and 6 months ahead. The input analyses show that high-frequency components are more important for shorter forecast horizons, while for longer horizons, they may worsen the model accuracy.     

Comparison of data-driven modelling techniques for river flow forecasting

Abstract

Accurate forecasting of streamflow is essential for the efficient operation of water resources systems. The streamflow process is complex and highly nonlinear. Therefore, researchers try to devise alterative techniques to forecast streamflow with relative ease and reasonable accuracy, although traditional deterministic and conceptual models are available. The present work uses three data-driven techniques, namely artificial neural networks (ANN), genetic programming (GP) and model trees (MT) to forecast river flow one day in advance at two stations in the Narmada catchment of India, and the results are compared. All the models performed reasonably well as far as accuracy of prediction is concerned. It was found that the ANN and MT techniques performed almost equally well, but GP performed better than both these techniques, although only marginally in terms of prediction accuracy in normal and extreme events.

Citation Londhe, S. & Charhate, S. (2010) Comparison of data-driven modelling techniques for river flow forecasting. Hydrol. Sci. J. 55(7), 1163–1174.     

Monthly total sediment forecasting using adaptive neuro fuzzy inference system

Accurate forecasting of sediment is an important issue for reservoir design and water pollution control in rivers and reservoirs. In this study, an adaptive neuro-fuzzy inference system (ANFIS) approach is used to construct monthly sediment forecasting system. To illustrate the applicability of ANFIS method the Great Menderes basin is chosen as the study area. The models with various input structures are constructed for the purpose of identification of the best structure. The performance of the ANFIS models in training and testing sets are compared with the observed data. To get more accurate evaluation of the results ANFIS models, the best fit model structures are also tested by artificial neural networks (ANN) and multiple linear regression (MLR) methods. The results of three methods are compared, and it is observed that the ANFIS is preferable and can be applied successfully because it provides high accuracy and reliability for forecasting of monthly total sediment.     

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.     

Stream flow forecasting using neuro‐wavelet technique

This paper proposes the application of a neuro‐wavelet technique for modelling monthly stream flows. The neuro‐wavelet model is improved by combining two methods, discrete wavelet transform and multi‐layer perceptron, for one‐month‐ahead stream flow forecasting and results are compared with those of the single multi‐layer perceptron (MLP), multi‐linear regression (MLR) and auto‐regressive (AR) models. Monthly flow data from two stations, Gerdelli Station on Canakdere River and Isakoy Station on Goksudere River, in the Eastern Black Sea region of Turkey are used in the study. The comparison results revealed that the suggested model could increase the forecast accuracy and perform better than the MLP, MLR and AR models. Copyright © 2008 John Wiley & Sons, Ltd.     

Evaluation of nonlinear models for precipitation forecasting

Prediction of factors affecting water resources systems is important for their design and operation. In hydrology, wavelet analysis (WA) is known as a new method for time series analysis. In this study, WA was combined with an artificial neural network (ANN) for prediction of precipitation at Varayeneh station, western Iran. The results obtained were compared with the adaptive neural fuzzy inference system (ANFIS) and ANN. Moreover, data on relative humidity and temperature were employed in addition to rainfall data to examine their influence on precipitation forecasting. Overall, this study concluded that the hybrid WANN model outperformed the other models in the estimation of maxima and minima, and is the best at forecasting precipitation. Furthermore, training and transfer functions are recommended for similar studies of precipitation forecasting.