M5 model tree application in daily river flow forecasting in Sohu Stream, Turkey

This study investigate the potential of M5 model tree in predicting daily stream flows in Sohu river located within the municipal borders of Ankara, Turkey. The results of the M5 model tree was compared with support vector machines. Both modelling approaches were used to forecast up to 7-day ahead stream flow. A comparison of correlation coefficient and root mean square value indicates that M5 model tree approach works equally well to the SVM for same day discharge prediction. The M5 model tree also works well up to 7-day ahead discharge forecasting in comparison of SVM with this data set. An advantage of using M5 model tree approach is the availability of simple linear models to predict the discharge as well use of less computational time.     

Enhancing streamflow forecasting using the augmenting ensemble procedure coupled machine learning models: case study of Aswan High Dam

ABSTRACT

The potential of the most recent pre-processing tool, namely, complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), is examined for providing AI models (artificial neural network, ANN; M5-model tree, M5-MT; and multivariate adaptive regression spline, MARS) with more informative input–output data and, thence, evaluate their forecasting accuracy. A 130-year inflow dataset for Aswan High Dam, Egypt, is considered for training, validating and testing the proposed models to forecast the reservoir inflow up to six months ahead. The results show that, after the pre-processing analysis, there is a significant enhancement in the forecasting accuracy. The MARS model combined with CEEMDAN gave superior performance compared to the other models – CEEMDAN-ANN and CEEMDAN-M5-MT – with an increase in accuracy of, respectively, about 13–25% and 6–20% in terms of the root mean square error.     

River temperature forecasting: case study for Little Southwest Miramichi River (New Brunswick,Canada)

River temperature models play an increasingly important role in the management of fisheries and aquatic resources. Among river temperature models, forecasting models remain relatively unused compared to water temperature simulation models. However, water temperature forecasting is extremely important for in-season management of fisheries, especially when short-term forecasts (a few days) are required. In this study, forecast and simulation models were applied to the Little Southwest Miramichi River (New Brunswick, Canada), where water temperatures can regularly exceed 25–29°C during summer, necessitating associated fisheries closures. Second- and third-order autoregressive models (AR2, AR3) were calibrated and validated using air temperature as the exogenous variable to predict minimum, mean and maximum daily water temperatures. These models were then used to predict river temperatures in forecast mode (1-, 2- and 3-day forecasts using real-time data) and in simulation mode (using only air temperature as input). The results showed that the models performed better when used to forecast rather than simulate water temperatures. The AR3 model slightly outperformed the AR2 in the forecasting mode, with root mean square errors (RMSE) generally between 0.87°C and 1.58°C. However, in the simulation mode, the AR2 slightly outperformed the AR3 model (1.25°C < RMSE < 1.90°C). One-day forecast models performed the best (RMSE ~ 1°C) and model performance decreased as time lag increased (RMSE close to 1.5°C after 3 days). The study showed that marked improvement in the modelling can be accomplished using forecasting models compared to water temperature simulations, especially for short-term forecasts.

EDITOR M.C. Acreman ASSOCIATE EDITOR S. Huang     

Incorporating synoptic-scale climate signals for streamflow modelling over the Mediterranean region using machine learning models

ABSTRACT

Understanding streamflow patterns by incorporating climate signal information can contribute remarkably to the knowledge of future local environmental flows. Three machine learning models, the multivariate adaptive regression splines (MARS), the M5 Model Tree and the least squares support vector machine (LSSVM) are established to predict the streamflow pattern over the Mediterranean region of Turkey (Besiri and Baykan stations). The structure of the predictive models is built using synoptic-scale climate signal information and river flow data from antecedent records. The predictive models are evaluated and assessed using quantitative and graphical statistics. The correlation analysis demonstrates that the North Pacific (NP) and the East Central Tropical Pacific Sea Surface Temperature (Niño3.4) indices have a substantial influence on the streamflow patterns, in addition to the historical information obtained from the river flow data. The model results reveal the utility of the LSSVM model over the other models through incorporating climate signal information for modelling streamflow.     

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.     

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.     

Fuzzy computing based rainfall–runoff model for real time flood forecasting

This paper analyses the skills of fuzzy computing based rainfall–runoff model in real time flood forecasting. The potential of fuzzy computing has been demonstrated by developing a model for forecasting the river flow of Narmada basin in India. This work has demonstrated that fuzzy models can take advantage of their capability to simulate the unknown relationships between a set of relevant hydrological data such as rainfall and river flow. Many combinations of input variables were presented to the model with varying structures as a sensitivity study to verify the conclusions about the coherence between precipitation, upstream runoff and total watershed runoff. The most appropriate set of input variables was determined, and the study suggests that the river flow of Narmada behaves more like an autoregressive process. As the precipitation is weighted only a little by the model, the last time‐steps of measured runoff are dominating the forecast. Thus a forecast based on expected rainfall becomes very inaccurate. Although good results for one‐step‐ahead forecasts are received, the accuracy deteriorates as the lead time increases. Using the one‐step‐ahead forecast model recursively to predict flows at higher lead time, however, produces better results as opposed to different independent fuzzy models to forecast flows at various lead times. Copyright © 2004 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.     

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.     

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 daily streamflow forecasts using extreme learning machines and the random forest method

ABSTRACT

Daily streamflow forecasting is a challenging and essential task for water resource management. The main goal of this study was to compare the accuracy of five data-driven models: extreme learning machine (basic ELM), extreme learning machine with kernels (ELM-kernel), random forest (RF), back-propagation neural network (BPNN) and support vector machine (SVR). The results show that the ELM-kernel model provided a superior alternative to the other models, and the basic ELM model had the poorest performance. To further evaluate the predictive capacities of the five models, the estimations of low flow and high flow in the testing dataset were compared. The RF model was slightly superior to the other models in predicting the peak flows, and the ELM-kernel model showed the highest prediction precision of low flows. There was no single model that showed obvious advantages over the other models in this study. Therefore, further exploration is required for the hydrological forecasting problems.     

Impact of complexity on daily and multi-step forecasting of streamflow with chaotic,stochastic, and black-box models

Despite significant research advances achieved during the last decades, seemingly inconsistent forecasting results related to stochastic, chaotic, and black-box approaches have been reported. Herein, we attempt to address the entropy/complexity resulting from hydrological and climatological conditions. Accordingly, mutual information function, correlation dimension, averaged false nearest neighbor with E1 and E2 quantities, and complexity analysis that uses sample entropy coupled with iterative amplitude adjusted Fourier transform were employed as nonlinear deterministic identification tools. We investigated forecasting of daily streamflow for three climatologically different Swedish rivers, Helge, Ljusnan, and Kalix Rivers using self-exciting threshold autoregressive (SETAR), k-nearest neighbor (k-nn), and artificial neural networks (ANN). The results suggest that the streamflow in these rivers during the 1957–2012 period exhibited dynamics from low to high complexity. Specifically, (1) lower complexity lead to higher predictability at all lead-times and the models’ worst performances were obtained for the most complex streamflow (Ljusnan River), (2) ANN was the best model for 1-day ahead forecasting independent of complexity, (3) SETAR was the best model for 7-day ahead forecasting by means of performance indices, especially for less complexity, (4) the largest error propagation was obtained with the k-nn and ANN and thus these models should be carefully used beyond 2-day forecasting, and (5) higher number input variables except for the dominant variables made insignificant impact on forecasting performances for ANN and k-nn models.     

A recurrent support vector regression model in rainfall forecasting

To minimize potential loss of life and property caused by rainfall during typhoon seasons, precise rainfall forecasts have been one of the key subjects in hydrological research. However, rainfall forecast is made difficult by some very complicated and unforeseen physical factors associated with rainfall. Recently, support vector regression (SVR) models and recurrent SVR (RSVR) models have been successfully employed to solve time‐series problems in some fields. Nevertheless, the use of RSVR models in rainfall forecasting has not been investigated widely. This study attempts to improve the forecasting accuracy of rainfall by taking advantage of the unique strength of the SVR model, genetic algorithms, and the recurrent network architecture. The performance of genetic algorithms with different mutation rates and crossover rates in SVR parameter selection is examined. Simulation results identify the RSVR with genetic algorithms model as being an effective means of forecasting rainfall amount. Copyright © 2006 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.     

A comparison of performance of several artificial intelligence methods for forecasting monthly discharge time series

Developing a hydrological forecasting model based on past records is crucial to effective hydropower reservoir management and scheduling. Traditionally, time series analysis and modeling is used for building mathematical models to generate hydrologic records in hydrology and water resources. Artificial intelligence (AI), as a branch of computer science, is capable of analyzing long-series and large-scale hydrological data. In recent years, it is one of front issues to apply AI technology to the hydrological forecasting modeling. In this paper, autoregressive moving-average (ARMA) models, artificial neural networks (ANNs) approaches, adaptive neural-based fuzzy inference system (ANFIS) techniques, genetic programming (GP) models and support vector machine (SVM) method are examined using the long-term observations of monthly river flow discharges. The four quantitative standard statistical performance evaluation measures, the coefficient of correlation (R), Nash–Sutcliffe efficiency coefficient (E), root mean squared error (RMSE), mean absolute percentage error (MAPE), are employed to evaluate the performances of various models developed. Two case study river sites are also provided to illustrate their respective performances. The results indicate that the best performance can be obtained by ANFIS, GP and SVM, in terms of different evaluation criteria during the training and validation phases.     

Improving flow forecasting by error correction modelling in altered catchment conditions

Despite human is an increasingly significant component of the hydrologic cycle in many river basins, most hydrologic models are still developed to accurately reproduce the natural processes and ignore the effect of human activities on the watershed response. This results in non‐stationary model forecast errors and poor predicting performance every time these models are used in non‐pristine watersheds. In the last decade, the representation of human activities in hydrological models has been extensively studied. However, mathematical models integrating the human and the natural dimension are not very common in hydrological applications and nearly unknown in the day‐to‐day practice. In this paper, we propose a new simple data‐driven flow forecast correction method that can be used to simultaneously tackle forecast errors from structural, parameter and input uncertainty, and errors that arise from neglecting human‐induced alterations in conceptual rainfall–runoff models. The correction system is composed of two layers: (i) a classification system that, based on the current flow condition, detects whether the source of error is natural or human induced and (ii) a set of error correction models that are alternatively activated, each tailored to the specific source of errors. As a case study, we consider the highly anthropized Aniene river basin in Italy, where a flow forecasting system is being established to support the operation of a hydropower dam. Results show that, even by using very basic methods, namely if‐then classification rules and linear correction models, the proposed methodology considerably improves the forecasting capability of the original hydrological model. Copyright © 2013 John Wiley & Sons, Ltd.     

River suspended sediment load prediction based on river discharge information: application of newly developed data mining models

ABSTRACT

Suspended sediment load (SSL) is one of the essential hydrological processes that affects river engineering sustainability. Sediment has a major influence on the operation of dams and reservoir capacity. This investigation is aimed at exploring a new version of machine learning models (i.e. data mining), including M5P, attribute selected classifier (AS M5P), M5Rule (M5R), and K Star (KS) models for SSL prediction at the Trenton meteorological station on the Delaware River, USA. Different input scenarios were examined based on the river flow discharge and sediment load database. The performance of the applied data mining models was evaluated using various statistical metrics and graphical presentation. Among the applied data mining models, the M5P model gave a superior prediction result. The current and one-day lead time river flow and sediment load were the influential predictors for one-day-ahead SSL prediction. Overall, the applied data mining models achieved excellent predictions of the SSL process.     

Multiple model combination methods for annual maximum water level prediction during river ice breakup

The Athabasca River is the largest unregulated river in Alberta, Canada, with ice jams frequently occurring in the vicinity of Fort McMurray. Modelling tools are desired to forecast ice‐related flood events. Multiple model combination methods can often obtain better predictive performances than any member models due to possible variance reduction of forecast errors or correction of biases. However, few applications of this method to river ice forecasting are reported. Thus, a framework of multiple model combination methods for maximum breakup water level (MBWL) Prediction during river ice breakup is proposed. Within the framework, the member models describe the relations between the MBWL (predicted variable) and their corresponding indicators (predictor variables); the combining models link the relations between the predicted MBWL by each member model and the observed MBWL. Especially, adaptive neuro‐fuzzy inference systems, artificial neural networks, and multiple linear regression are not only employed as member models but also as combining models. Simple average methods (SAM) are selected as the basic combining model due to simple calculations. In the SAM, an equal weight (1/n) is assigned to n member models. The historical breakup data of the Athabasca River at Fort McMurray for the past 36 years (1980 to 2015) are collected to facilitate the comparison of models. These models are examined using the leave‐one‐out cross validation and the holdout validation methods. A SAM, which is the average output from three optimal member models, is selected as the best model as it has the optimal validation performance (lowest average squared errors). In terms of lowest average squared errors, the SAM improves upon the optimal artificial neural networks, adaptive neuro‐fuzzy inference systems, and multiple linear regression member models by 21.95%, 30.97%, and 24.03%, respectively. This result sheds light on the effectiveness of combining different forecasting models when a scarce river ice data set is investigated. The indicators included in the SAM may indicate that the MBWL is affected by water flow conditions just after freeze‐up, overall freezing conditions during winter, and snowpack conditions before breakup.     

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.