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.     

Comparison of static-feedforward and dynamic-feedback neural networks for rainfall–runoff modeling

A systematic comparison of two basic types of neural network, static and dynamic, is presented in this study. Two back-propagation (BP) learning optimization algorithms, the standard BP and conjugate gradient (CG) method, are used for the static network, and the real-time recurrent learning (RTRL) algorithm is used for the dynamic-feedback network. Twenty-three storm-events, about 1632 rainfall and runoff data sets, of the Lan-Yang River in Taiwan are used to demonstrate the efficiency and practicability of the neural networks for one hour ahead streamflow forecasting. In a comparison of searching algorithms for a static network, the results show that the CG method is superior to the standard BP method in terms of the efficiency and effectiveness of the constructed network's performance. For a comparison of the static neural network using the CG algorithm with the dynamic neural network using RTRL, the results show that (1) the static-feedforward neural network could produce satisfactory results only when there is a sufficient and adequate training data set, (2) the dynamic neural network generally could produce better and more stable flow forecasting than the static network, and (3) the RTRL algorithm helps to continually update the dynamic network for learning—this feature is especially important for the extraordinary time-varying characteristics of rainfall–runoff processes.     

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.     

Instance‐based learning compared to other data‐driven methods in hydrological forecasting

Data‐driven techniques based on machine learning algorithms are becoming popular in hydrological modelling, in particular for forecasting. Artificial neural networks (ANNs) are often the first choice. The so‐called instance‐based learning (IBL) has received relatively little attention, and the present paper explores the applicability of these methods in the field of hydrological forecasting. Their performance is compared with that of ANNs, M5 model trees and conceptual hydrological models. Four short‐term flow forecasting problems were solved for two catchments. Results showed that the IBL methods often produce better results than ANNs and M5 model trees, especially if used with the Gaussian kernel function. The study showed that IBL is an effective data‐driven method that can be successfully used in hydrological forecasting. Copyright © 2007 John Wiley & Sons, Ltd.     

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.     

Using recurrent neural networks to reconstruct rainfall‐runoff processes

Many novel techniques for reconstructing rainfall‐runoff processes require hydrometeorologic and geomorphologic information for modelling. However, certain information is not always measurable. In this paper, we employ a special recurrent neural network to reconstruct the rainfall‐runoff process by using collected rainfall data. In addition, we propose an indirect system identification to overcome the drawback of a traditional, time‐consuming trial‐and‐error search. The indirect system identification is an efficient method to recognize the structure of a recurrent neural network. The unit hydrograph can be derived directly from the weights of the network due to a state‐space form embedded in the recurrent neural network. This improves the link between the weights of the network and the physical concepts that most neural networks fail to connect. The case studies of 41 events from 1966 to 1997 have been implemented in Taiwan's Wu‐Tu watershed, where the runoff path‐lines are short and steep. Two recurrent neural networks and one state‐space model are utilized to simulate the rainfall‐runoff processes for comparison. The results are validated by four criteria: coefficient of efficiency; peak discharge error; time to peak arrival error; total discharge volume error. The resulting data from the recurrent neural network reveal that the neural network proposed herein is appropriate for hydrological systems. Copyright © 2005 John Wiley & Sons, Ltd.     

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.     

Predicting catchment flow in a semi‐arid region via an artificial neural network technique

A model of rainfall–runoff relationships is an essential tool in the process of evaluation of water resources projects. In this paper, we applied an artificial neural network (ANN) based model for flow prediction using the data for a catchment in a semi‐arid region in Morocco. Use of this method for non‐linear modelling has been demonstrated in several scientific fields such as biology, geology, chemistry and physics. The performance of the developed neural network‐based model was compared against multiple linear regression‐based model using the same observed data. It was found that the neural network model consistently gives superior predictions. Based on the results of this study, artificial neural network modelling appears to be a promising technique for the prediction of flow for catchments in semi‐arid regions. Accordingly, the neural network method can be applied to various hydrological systems where other models may be inappropriate. Copyright © 2004 John Wiley & Sons, Ltd.     

Uncertainties in real‐time flood forecasting with neural networks

Although artificial neural networks (ANNs) have been applied in rainfall runoff modelling for many years, there are still many important issues unsolved that have prevented this powerful non‐linear tool from wide applications in operational flood forecasting activities. This paper describes three ANN configurations and it is found that a dedicated ANN for each lead‐time step has the best performance and a multiple output form has the worst result. The most popular form with multiple inputs and single output has the average performance. In comparison with a linear transfer function (TF) model, it is found that ANN models are uncompetitive against the TF model in short‐range predictions and should not be used in operational flood forecasting owing to their complicated calibration process. For longer range predictions, ANN models have an improved chance to perform better than the TF model; however, this is highly dependent on the training data arrangement and there are undesirable uncertainties involved, as demonstrated by bootstrap analysis in the study. To tackle the uncertainty issue, two novel approaches are proposed: distance analysis and response analysis. Instead of discarding the training data after the model's calibration, the data should be retained as an integral part of the model during its prediction stage and the uncertainty for each prediction could be judged in real time by measuring the distances against the training data. The response analysis is based on an extension of the traditional unit hydrograph concept and has a very useful potential to reveal the hydrological characteristics of ANN models, hence improving user confidence in using them in real time. Copyright © 2006 John Wiley & Sons, Ltd.     

Neural network time series prediction of environmental variables in a small upland headwater in NE Scotland

Short‐term prediction of environmental variables such as stream flow rate is useful to members of the general public and environmental scientists alike, providing the ability to predict environmental disasters or scientifically interesting events. Here, a neural‐network based method is presented, which is capable of providing advance flood warnings or the prediction of high stream flow events for research purposes in a small upland headwater in NE Scotland. This method relies on training from past time series data acquired in the field, and provides the ability to predict a range of hydrological and meteorological variables up to 24 h ahead using feedback of predicted values at time t as new inputs for the next time step t + 1. The system is rapid and effective, relies on standard neural network training methods, and has the potential to be implemented in a web‐based monitoring and prediction package. The model design could be implemented at any study site where time series data has been gathered, and is sufficiently flexible to accept whatever data is available. Copyright © 2007 John Wiley & Sons, Ltd.     

Flow network derivation from a high resolution DEM in a low relief,agrarian landscape

Digital flow networks derived from digital elevation models (DEMs) sensitively react to errors due to measurement, data processing and data representation. Since high‐resolution DEMs are increasingly used in geomorphological and hydrological research, automated and semi‐automated procedures to reduce the impact of such errors on flow networks are required. One such technique is stream‐carving, a hydrological conditioning technique to ensure drainage connectivity in DEMs towards the DEM edges. Here we test and modify a state‐of‐the‐art carving algorithm for flow network derivation in a low‐relief, agricultural landscape characterized by a large number of spurious, topographic depressions. Our results show that the investigated algorithm reconstructs a benchmark network insufficiently in terms of carving energy, distance and a topological network measure. The modification to the algorithm that performed best, combines the least‐cost auxiliary topography (LCAT) carving with a constrained breaching algorithm that explicitly takes automatically identified channel locations into account. We applied our methods to a low relief landscape, but the results can be transferred to flow network derivation of DEMs in moderate to mountainous relief in situations where the valley bottom is broad and flat and precise derivations of the flow networks are needed. Copyright © 2013 John Wiley & Sons, Ltd.     

Estimation of river flow by artificial neural networks and identification of input vectors susceptible to producing unreliable flow estimates

Reliable river flow estimates are crucial for appropriate water resources planning and management. River flow forecasting can be conducted by conceptual or physical models, or data-driven black box models. Development of physically-based models requires an understanding of all the physical processes which impact a natural process and the interactions among them. Since identification of the relationships among these physical processes is very difficult, data-driven approaches have recently been utilized in hydrological modeling. Artificial neural networks are one of the widely used data-driven approaches for modeling hydrological processes. In this study, estimation of future monthly river flows for Guvenc River, Ankara is conducted using various artificial neural network models. Success of artificial neural network models relies on the availability of adequate data sets. A direct mapping from inputs to outputs without consideration of the complex relationships among the dependent and independent variables of the hydrological process is identified. In this study, past precipitation, river flow data, and the associated month are used to predict future river flows for Guvenc River. Impacts of various input patterns, number of training cycles, and initial values assigned to the weights of the connections are investigated. One of the major weaknesses of artificial neural networks is that they may fail to generate good estimates for extreme events, i.e. events that do not occur at all or often enough in the training data set. It is very important to be able to identify such unlikely events. A fuzzy c-means algorithm is used in this study to cluster the training and validation input vectors into regular and extreme events so that the user will have an idea about the risk of the artificial neural network model to generate unreliable results.     

Basin‐scale stream‐flow forecasting using the information of large‐scale atmospheric circulation phenomena

It is well recognized that the time series of hydrologic variables, such as rainfall and streamflow are significantly influenced by various large‐scale atmospheric circulation patterns. The influence of El Niño‐southern oscillation (ENSO) on hydrologic variables, through hydroclimatic teleconnection, is recognized throughout the world. Indian summer monsoon rainfall (ISMR) has been proved to be significantly influenced by ENSO. Recently, it was established that the relationship between ISMR and ENSO is modulated by the influence of atmospheric circulation patterns over the Indian Ocean region. The influences of Indian Ocean dipole (IOD) mode and equatorial Indian Ocean oscillation (EQUINOO) on ISMR have been established in recent research. Thus, for the Indian subcontinent, hydrologic time series are significantly influenced by ENSO along with EQUINOO. Though the influence of these large‐scale atmospheric circulations on large‐scale rainfall patterns was investigated, their influence on basin‐scale stream‐flow is yet to be investigated. In this paper, information of ENSO from the tropical Pacific Ocean and EQUINOO from the tropical Indian Ocean is used in terms of their corresponding indices for stream‐flow forecasting of the Mahanadi River in the state of Orissa, India. To model the complex non‐linear relationship between basin‐scale stream‐flow and such large‐scale atmospheric circulation information, artificial neural network (ANN) methodology has been opted for the present study. Efficient optimization of ANN architecture is obtained by using an evolutionary optimizer based on a genetic algorithm. This study proves that use of such large‐scale atmospheric circulation information potentially improves the performance of monthly basin‐scale stream‐flow prediction which, in turn, helps in better management of water resources. Copyright © 2007 John Wiley & Sons, Ltd.     

Enforced self‐organizing map neural networks for river flood forecasting

Self‐organizing maps (SOMs) have been successfully accepted widely in science and engineering problems; not only are their results unbiased, but they can also be visualized. In this study, we propose an enforced SOM (ESOM) coupled with a linear regression output layer for flood forecasting. The ESOM re‐executes a few extra training patterns, e.g. the peak flow, as recycling input data increases the mapping space of peak flow in the topological structure of SOM, and the weighted sum of the extended output layer of the network improves the accuracy of forecasting peak flow. We have investigated an ESOM neural network by using the flood data of the Da‐Chia River, Taiwan, and evaluated its performance based on the results obtained from a commonly used back‐propagation neural network. The results demonstrate that the ESOM neural network has great efficiency for clustering, especially for the peak flow, and super capability of modelling the flood forecast. The topology maps created from the ESOM are interesting and informative. Copyright © 2007 John Wiley & Sons, Ltd.     

Forecasting monthly precipitation using sequential modelling

In the hydrological cycle, rainfall is a major component and plays a vital role in planning and managing water resources. In this study, new generation deep learning models, recurrent neural network (RNN) and long short-term memory (LSTM), were applied for forecasting monthly rainfall, using long sequential raw data for time series analysis. “All-India” monthly average precipitation data for the period 1871–2016 were taken to build the models and they were tested on different homogeneous regions of India to check their robustness. From the results, it is evident that both the trained models (RNN and LSTM) performed well for different homogeneous regions of India based on the raw data. The study shows that a deep learning network can be applied successfully for time series analysis in the field of hydrology and allied fields to mitigate the risks of climatic extremes.     

Automated calibration applied to watershed‐scale flow simulations

Complexity in simulating the hydrological response in large watersheds over long times has prompted a significant need for procedures for automatic calibration. Such a procedure is implemented in the basin‐scale hydrological model (BSHM), a physically based distributed parameter watershed model. BSHM simulates the most important basin‐scale hydrological processes, such as overland flow, groundwater flow and stream–aquifer interaction in watersheds. Here, the emphasis is on estimating the groundwater parameters with water levels in wells and groundwater baseflows selected as the calibration targets. The best set of parameters is selected from within plausible ranges of parameters by adjusting the values of hydraulic conductivity, storativity, groundwater recharge and stream bed permeability. The baseflow is determined from stream flow hydrographs by using an empirical scheme validated using a chemical approach to hydrograph separation. Field studies determined that the specific conductance for components of the composite hydrograph were sufficiently unique to make the chemical approach feasible. The method was applied to the Big Darby Creek Watershed, Ohio. The parameter set selected for the groundwater system provides a good fit with the estimated baseflow and observed water well data. Copyright © 1999 John Wiley & Sons, Ltd.     

High‐frequency streamflow acquisition and bed level/flow angle estimates in a mountainous river using shallow‐water acoustic tomography

The acquisition of reliable discharge estimates is crucial in hydrological studies. This study demonstrates a promising acoustic method for measuring streamflow at high sampling rate for a long period using the fluvial acoustic tomography system (FATS). The FATS recently emerged as an innovative technique for continuous measurements of streamflow. In contrast to the traditional point/transect measurements of discharge, the FATS enables the depth‐averaged and range‐averaged flow velocity along the ray path to be measured in a fraction of a second. The field test was conducted in a shallow gravel‐bed river (0.9 m deep under low‐flow conditions, 115 m wide) for 1 month. The parameters (stream direction and bottom elevation) required for calculating the streamflow were deduced by a nonlinear regression to the discharge data from the well‐established rating curve. The cross‐sectional average velocities were automatically calculated from the acoustic data, which were collected on both riverbanks every 30 s. The FATS was connected to the internet so that the real‐time flow data could be obtained. The FATS captured discharge variations at a cut‐off frequency of approximately 70 day^?1. The stream exhibited temporal discharge changes at multiple time scales ranging from a few tens of minutes to days. Copyright © 2016 John Wiley & Sons, Ltd.     

Bivariate frequency analysis of nonstationary low‐flow series based on the time‐varying copula

Many studies have analysed the nonstationarity in single hydrological variables due to changing environments. Yet, few researches have been done to investigate how the dependence structure between different individual hydrological variables is affected by changing environments. To investigate how the reservoirs have altered the dependence structure between river flows at different locations on the Hanjiang River, a time‐varying copula model, which takes the nonstationarity in the marginal distribution and/or the time variation in dependence structure between different hydrological series into consideration, is presented in this paper to perform a bivariate frequency analysis for the low‐flow series from two neighbouring hydrological gauges. The time‐varying moments model with either time or reservoir index as explanatory variables is applied to build the time‐varying marginal distributions of the two low‐flow series. It's found that both marginal distributions are nonstationary, and the reservoir index yields better performance than the time index in describing the nonstationarities in the marginal distributions. Then, the copula with the dependence parameter expressed as a function of either time or reservoir index is applied to model the variable dependence between the two low‐flow series. The copula with reservoir index as the explanatory variable of the dependence parameter has a better fitting performance than the copula with the constant or the time‐trend dependence parameter. Finally, the effect of the time variation in the joint distribution on three different types of joint return periods (i.e. AND, OR and Kendall) of low flows at two neighbouring hydrological gauges is presented. Copyright © 2014 John Wiley & Sons, Ltd.     

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.     

An approach to hydrograph classification

The stream hydrograph is an integration of spatial and temporal variations in water input, storage and transfer processes within a catchment. For glacier basins in particular, inferences concerning catchment‐scale processes have been developed from the varying form and magnitude of the diurnal hydrograph in the proglacial river. To date, however, such classifications of proglacial diurnal hydrographs have developed in a relatively subjective manner. This paper develops an objective approach to the classification of diurnal discharge hydrograph ‘shape’ and ‘magnitude’ using a combination of principal components analysis and cluster analysis applied to proglacial discharge time‐series and to diurnal bulk flow indices. The procedure is applied to discharge time‐series from two different glacier basins and four separate ablation seasons representing a gradient of increasing hydrological perturbation as a result of (i) variable water inputs generated by rainstorm activity and (ii) variable location and response of hydrological stores through a systematic decrease in catchment glacierized area. The potential of the technique for application in non‐glacial hydrological contexts is discussed. Copyright © 2000 John Wiley & Sons, Ltd.