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.     

Rainfall‐runoff analysis based on competing linear impulse responses: decomposition of rainfall‐runoff processes

Many recent studies have successfully used neural networks for non‐linear rainfall‐runoff modelling. Due to fundamental limitation of linear structures, approaches employing linear models have been generally considered inferior to the neural network approaches in this area. However, the authors believe that with an appropriate extension, the concept of linear impulse responses can be a viable tool since it enables one to understand underlying dynamics of rainfall‐runoff processes. In this paper, the use of competing impulse responses for rainfall‐runoff analysis is proposed. The proposed method is based on the switch over of competing linear impulse‐responses, each of which satisfies the constraints of non‐negativity and uni‐modality. The computational analyses performed for the rainfall‐runoff data in the Seolma‐Chun experimental basin, Korea showed that the proposed method can yield promising results. Considering the basin characteristics as well as the results from this study, it may be concluded that three impulse responses are enough for rainfall‐runoff analysis. 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.     

A fusion-based neural network methodology for monthly reservoir inflow prediction using MODIS products

ABSTRACT

A model fusion approach was developed based on five artificial neural networks (ANNs) and MODIS products. Static and dynamic ANNs – the multi-layer perceptron (MLP) with one and two hidden layers, general regression neural network (GRNN), radial basis function (RBF) and nonlinear autoregressive network with exogenous inputs (NARX) – were used to predict the monthly reservoir inflow in Mollasadra Dam, Fars Province, Iran. Leaf area index and snow cover from MODIS, and rainfall and runoff data were used to identify eight different combinations to train the models. Statistical error indices and the Borda count method were used to verify and rank the identified combinations. The best results for individual ANNs were combined with MODIS products in a fusion model. The results show that using MODIS products increased the accuracy of predictions, with the MLP with two hidden layers giving the best performance. Also, the fusion model was found to be superior to the best individual ANNs.     

Comparative study of neural network,fuzzy logic and linear transfer function techniques in daily rainfall‐runoff modelling under different input domains

This paper compares artificial neural network (ANN), fuzzy logic (FL) and linear transfer function (LTF)‐based approaches for daily rainfall‐runoff modelling. This study also investigates the potential of Takagi‐Sugeno (TS) fuzzy model and the impact of antecedent soil moisture conditions in the performance of the daily rainfall‐runoff models. Eleven different input vectors under four classes, i.e. (i) rainfall, (ii) rainfall and antecedent moisture content, (iii) rainfall and runoff and (iv) rainfall, runoff and antecedent moisture content are considered for examining the effects of input data vector on rainfall‐runoff modelling. Using the rainfall‐runoff data of the upper Narmada basin, Central India, a suitable modelling technique with appropriate model input structure is suggested on the basis of various model performance indices. The results show that the fuzzy modelling approach is uniformly outperforming the LTF and also always superior to the ANN‐based models. Copyright © 2010 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.     

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.     

A systematic approach to the input determination for neural network rainfall–runoff models

Input determination has a great influence on the performance of artificial neural network (ANN) rainfall–runoff models. To improve the performance of ANN models, a systematic approach to the input determination for ANN models is proposed. In the proposed approach, the irrelevant inputs are removed. Then an adequate ANN model, which only includes highly relevant inputs, is constructed. Unlike the trial‐and‐error procedure, the proposed approach is more systematic and avoids unnecessary trials. To demonstrate the effectiveness of the proposed approach, an application to actual typhoon events is presented. The results show that the proposed ANN model, which is constructed by the proposed approach, has advantages over those obtained by the trial‐and‐error procedure. The proposed ANN model has a simpler architecture, needs less training time, and performs better. The proposed ANN model is recommended as an alternative to existing rainfall–runoff ANN models. Copyright © 2007 John Wiley & Sons, Ltd.     

Comparison of artificial neural network models for hydrologic predictions at multiple gauging stations in an agricultural watershed

This paper reports on an evaluation of the use of artificial neural network (ANN) models to forecast daily flows at multiple gauging stations in Eucha Watershed, an agricultural watershed located in north‐west Arkansas and north‐east Oklahoma. Two different neural network models, the multilayer perceptron (MLP) and the radial basis neural network (RBFNN), were developed and their abilities to predict stream flow at four gauging stations were compared. Different scenarios using various combinations of data sets such as rainfall and stream flow at various lags were developed and compared for their ability to make flow predictions at four gauging stations. The input vector selection for both models involved quantification of the statistical properties such as cross‐, auto‐ and partial autocorrelation of the data series that best represented the hydrologic response of the watershed. Measured data with 739 patterns of input–output vector were divided into two sets: 492 patterns for training, and the remaining 247 patterns for testing. The best performance based on the RMSE, R² and CE was achieved by the MLP model with current and antecedent precipitation and antecedent flow as model inputs. The MLP model testing resulted in R² values of 0·86, 0·86, 0·81, and 0·79 at the four gauging stations. Similarly, the testing R² values for the RBFNN model were 0·60, 0·57, 0·58, and 0·56 for the four gauging stations. Both models performed satisfactorily for flow predictions at multiple gauging stations, however, the MLP model outperformed the RBFNN model. The training time was in the range 1–2 min for MLP, and 5–10 s for RBFNN on a Pentium IV processor running at 2·8 GHz with 1 MB of RAM. The difference in model training time occurred because of the clustering methods used in the RBFNN model. The RBFNN uses a fuzzy min‐max network to perform the clustering to construct the neural network which takes considerably less time than the MLP model. Results show that ANN models are useful tools for forecasting the hydrologic response at multiple points of interest in agricultural watersheds. Copyright © 2008 John Wiley & Sons, Ltd.     

The strategy of building a flood forecast model by neuro‐fuzzy network

A methodology is proposed for constructing a flood forecast model using the adaptive neuro‐fuzzy inference system (ANFIS). This is based on a self‐organizing rule‐base generator, a feedforward network, and fuzzy control arithmetic. Given the rainfall‐runoff patterns, ANFIS could systematically and effectively construct flood forecast models. The precipitation and flow data sets of the Choshui River in central Taiwan are analysed to identify the useful input variables and then the forecasting model can be self‐constructed through ANFIS. The analysis results suggest that the persistent effect and upstream flow information are the key effects for modelling the flood forecast, and the watershed's average rainfall provides further information and enhances the accuracy of the model performance. For the purpose of comparison, the commonly used back‐propagation neural network (BPNN) is also examined. The forecast results demonstrate that ANFIS is superior to the BPNN, and ANFIS can effectively and reliably construct an accurate flood forecast model. Copyright © 2005 John Wiley & Sons, Ltd.     

A Modified Neural Network for Improving River Flow Prediction/Un Réseau de Neurones Modifié pour Améliorer la Prévision de L'Écoulement Fluvial

Abstract

Artificial neural network (ANN) models provide huge potential for simulating nonlinear behaviour of hydrological systems. However, the potential of ANN is yet to be fully exploited due to the problems associated with improving the model generalization performance. Generalization refers to the ability of a neural network to correctly process input data that have not been used for calibrating the neural network model. In the hydrological context, better generalization performance implies higher precision of forecasting. The primary objectives of this study are to explore new measures for improving the generalization performance of an ANN-based rainfall–runoff model, and to evaluate the applicability of the new measures. A modified neural network model (entitled goal programming (GP) neural network) for modelling the rainfall–runoff process has been developed, in which three enhancements are made as compared to the widely-used backpropagation (BP) network. The three enhancements are (a) explicit integration of hydrological prior knowledge into the neural network learning; (b) incorporation of a modified training objective function; and (c) reduction of network sensitivity to input errors. Seven watersheds across a range of climatic conditions and watershed areas in China were selected for examining the alternative networks. The results demonstrate that the GP consistently outperformed the BP both in the calibration and verification periods and three proposed measures yielded improvement of performance.     

Identification of physical processes inherent in artificial neural network rainfall runoff models

The emergence of artificial neural network (ANN) technology has provided many promising results in the field of hydrology and water resources simulation. However, one of the major criticisms of ANN hydrologic models is that they do not consider/explain the underlying physical processes in a watershed, resulting in them being labelled as black‐box models. This paper discusses a research study conducted in order to examine whether or not the physical processes in a watershed are inherent in a trained ANN rainfall‐runoff model. The investigation is based on analysing definite statistical measures of strength of relationship between the disintegrated hidden neuron responses of an ANN model and its input variables, as well as various deterministic components of a conceptual rainfall‐runoff model. The approach is illustrated by presenting a case study for the Kentucky River watershed. The results suggest that the distributed structure of the ANN is able to capture certain physical behaviour of the rainfall‐runoff process. The results demonstrate that the hidden neurons in the ANN rainfall‐runoff model approximate various components of the hydrologic system, such as infiltration, base flow, and delayed and quick surface flow, etc., and represent the rising limb and different portions of the falling limb of a flow hydrograph. Copyright © 2004 John Wiley & Sons, Ltd.     

Multi-layer perceptrons with Levenberg-Marquardt training algorithm for suspended sediment concentration prediction and estimation / Prévision et estimation de la concentration en matières en suspension avec des perceptrons multi-couches et l’algorithme d’apprentissage de Levenberg-Marquardt

Abstract

Abstract The prediction and estimation of suspended sediment concentration are investigated by using multi-layer perceptrons (MLP). The fastest MLP training algorithm, that is the Levenberg-Marquardt algorithm, is used for optimization of the network weights for data from two stations on the Tongue River in Montana, USA. The first part of the study deals with prediction and estimation of upstream and down-stream station sediment data, separately, and the second part focuses on the estimation of downstream suspended sediment data by using data from both stations. In each case, the MLP test results are compared to those of generalized regression neural networks (GRNN), radial basis function (RBF) and multi-linear regression (MLR) for the best-input combinations. Based on the comparisons, it was found that the MLP generally gives better suspended sediment concentration estimates than the other neural network techniques and the conventional statistical method (MLR). However, for the estimation of maximum sediment peak, the RBF was mostly found to be better than the MLP and the other techniques. The results also indicate that the RBF and GRNN may provide better performance than the MLP in the estimation of the total sediment load.     

An evaluation of a traditional and a neural net modelling approach to flood forecasting for an upland catchment

This study evaluates two (of the many) modelling approaches to flood forecasting for an upland catchment (the River South Tyne at Haydon Bridge, England). The first modelling approach utilizes ‘traditional’ hydrological models. It consists of a rainfall–runoff model (the probability distributed model, or PDM) for flow simulation in the upper catchment. Those flows are then routed to the lower catchment using two kinematic wave (KW) routing models. When run in forecast‐mode, the PDM and KW models utilize model updating procedures. The second modelling approach uses neural network models, which use a ‘pattern‐matching’ process to produce model forecasts.Following calibration, the models are evaluated in terms of their fit to continuous stage data and flood event magnitudes and timings within a validation period. Forecast times of 1 h, 2 h and 4 h are selected (the catchment has a response time of approximately 4 h). The ‘traditional’ models generally perform adequately at all three forecast times. The neural networks produce reasonable forecasts of small‐ to medium‐sized flood events but have difficulty in forecasting the magnitude of the larger flood events in the validation period. Possible modifications to the latter approach are discussed. © Crown copyright 2002. Reproduced with the permission of Her Majesty's stationery office. Published by John Wiley & Sons, Ltd.     

Analytical model for a geomorphological instantaneous unit hydrograph

The rainfall‐runoff modelling of a river basin can be divided into two processes: the production function and the transfer function. The production function determines the proportion of gross rainfall actually involved in the runoff. The transfer function spreads the net rainfall over time and space in the river basin. Such a transfer function can be modelled using the approach of the geomorphological instantaneous unit hydrograph (GIUH). The effectiveness of geomorphological models is actually revealed in rainfall‐runoff modelling, where hydrologic data are desperately lacking, just as in ungauged basins. These models make it possible to forecast the hydrograph shape and runoff variation versus time at the basin outlet. This article is an introduction to a new GIUH model that proves to be simple and analytical. Its geomorphological parameters are easily available on a map or from a digital elevation model. This model is based on general hypotheses on symmetry that provide it with multiscale versatile characteristics. After having validated the model in river basins of very different nature and size, we present an application of this model for rainfall‐runoff modelling. Since parameters are determined relying on real geomorphological data, no calibration is necessary, and it is then possible to carry out rainfall‐runoff simulations in ungauged river basins. Copyright © 2006 John Wiley & Sons, Ltd.     

Regionalizing mean annual flow and daily flow variability for basin‐scale sediment and nutrient modelling

River discharges vary strongly through time and space, and quantifying this variability is fundamental to understanding and modelling river processes. The river basin is increasingly being used as the unit for natural resource planning and management; to facilitate this, basin‐scale models of material supply and transport are being developed. For many basin‐scale planning activities, detailed rainfall‐runoff modelling is neither necessary nor tractable, and models that capture spatial patterns of material supply and transport averaged over decades are sufficient. Nevertheless, the data to describe the spatial variability of river discharge across large basins for use in such models are often limited, and hence models to predict river discharge at the basin scale are required. We describe models for predicting mean annual flow and a non‐dimensional measure of daily flow variability for every river reach within a drainage network. The models use sparse river gauging data, modelled grid surfaces of mean annual rainfall and mean annual potential evapotranspiration, and a network accumulation algorithm. We demonstrate the parameterization and application of the models using data for the Murrumbidgee basin, in southeast Australia, and describe the use of these predictions in modelling sediment transport through the river network. The regionalizations described contain less uncertainty, and are more sensitive to observed spatial variations in runoff, than regionalizations based on catchment area and rainfall alone. Copyright © 2006 John Wiley & Sons, Ltd.     

A hybrid machine learning ensemble approach based on a Radial Basis Function neural network and Rotation Forest for landslide susceptibility modeling: A case study in the Himalayan area,India

In this paper, a hybrid machine learning ensemble approach namely the Rotation Forest based Radial Basis Function (RFRBF) neural network is proposed for spatial prediction of landslides in part of the Himalayan area (India). The proposed approach is an integration of the Radial Basis Function (RBF) neural network classifier and Rotation Forest ensemble, which are state-of-the art machine learning algorithms for classification problems. For this purpose, a spatial database of the study area was established that consists of 930 landslide locations and fifteen influencing parameters (slope angle, road density, curvature, land use, distance to road, plan curvature, lineament density, distance to lineaments, rainfall, distance to river, profile curvature, elevation, slope aspect, river density, and soil type). Using the database, training and validation datasets were generated for constructing and validating the model. Performance of the model was assessed using the Receiver Operating Characteristic (ROC) curve, area under the ROC curve (AUC), statistical analysis methods, and the Chi square test. In addition, Logistic Regression (LR), Multi-layer Perceptron Neural Networks (MLP Neural Nets), Naïve Bayes (NB), and the hybrid model of Rotation Forest and Decision Trees (RFDT) were selected for comparison. The results show that the proposed RFRBF model has the highest prediction capability in comparison to the other models (LR, MLP Neural Nets, NB, and RFDT); therefore, the proposed RFRBF model is promising and should be used as an alternative technique for landslide susceptibility modeling.     

Daily pan evaporation modelling using multi‐layer perceptrons and radial basis neural networks

This paper reports on investigations of the abilities of three different artificial neural network (ANN) techniques, multi‐layer perceptrons (MLP), radial basis neural networks (RBNN) and generalized regression neural networks (GRNN) to estimate daily pan evaporation. Different MLP models comprising various combinations of daily climatic variables, that is, air temperature, solar radiation, wind speed, pressure and humidity were developed to evaluate the effect of each of these variables on pan evaporation. The MLP estimates are compared with those of the RBNN and GRNN techniques. The Stephens‐Stewart (SS) method is also considered for the comparison. The performances of the models are evaluated using root mean square errors (RMSE), mean absolute error (MAE) and determination coefficient (R²) statistics. Based on the comparisons, it was found that the MLP and RBNN computing techniques could be employed successfully to model the evaporation process using the available climatic data. The GRNN was found to perform better than the SS method. Copyright © 2008 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.     

The potential of different ANN techniques in evapotranspiration modelling

The potential of three different artificial neural network (ANN) techniques, the multi‐layer perceptrons (MLPs), radial basis neural networks (RBNNs) and generalized regression neural networks (GRNNs), in modelling of reference evapotranspiration (ET₀) is investigated in this paper. Various daily climatic data, that is, solar radiation, air temperature, relative humidity and wind speed from two stations, Pomona and Santa Monica, in Los Angeles, USA, are used as inputs to the ANN techniques so as to estimate ET₀ obtained using the FAO‐56 Penman–Monteith (PM) equation. In the first part of the study, a comparison is made between the estimates provided by the MLP, RBNN and GRNN and those of the following empirical models: The California Irrigation Management Information System (CIMIS) Penman (1985), Hargreaves (1985) and Ritchie (1990). In this part of the study, the empirical models are calibrated using the standard FAO‐56 PM ET₀ values. The estimates of the ANN techniques are also compared with those of the calibrated empirical models. Mean square errors, mean absolute errors and determination coefficient statistics are used as comparing criteria for the evaluation of the models' performances. Based on the comparisons, it is found that the MLP and RBNN techniques could be employed successfully in modelling the ET₀ process. In the second part of the study, the potential of ANN techniques and the empirical methods in ET₀ estimation using nearby station data is investigated. Among the models, the calibrated Hargreaves model is found to perform better than the others. Copyright © 2007 John Wiley & Sons, Ltd.