Hybrid denoising-jittering data pre-processing approach to enhance multi-step-ahead rainfall–runoff modeling

Successful modeling of stochastic hydro-environmental processes widely relies on quantity and quality of accessible data and noisy data might effect on the functioning of the modeling. On the other hand in training phase of any Artificial Intelligence based model, each training data set is usually a limited sample of possible patterns of the process and hence, might not show the behavior of whole population. Accordingly in the present article first, wavelet-based denoising method was used in order to smooth hydrological time series and then small normally distributed noises with the mean of zero and various standard deviations were generated and added to the smoothed time series to form different denoised-jittered training data sets, for Artificial Neural Network (ANN) and Adaptive Neuro-Fuzzy Inference System (ANFIS) modeling of daily and multi-step-ahead rainfall–runoff process of the Milledgeville station of the Oconee River and the Pole Saheb station of the Jighatu River watersheds, respectively located in USA and Iran. The proposed hybrid data pre-processing approach in the present study is used for the first time in modeling of time series and especially in modeling of hydrological processes. Furthermore, the impacts of denoising (smoothing) and noise injection (jittering) have been simultaneously investigated neither in hydrology nor in any other engineering fields. To evaluate the modeling performance, the outcomes were compared with the results of multi linear regression and Auto Regressive Integrated Moving Average models. Comparing the achieved results via the trained ANN and ANFIS models using denoised-jittered data showed that the proposed data pre-processing approach which serves both denoising and jittering techniques could improve performance of the ANN and ANFIS based single-step-ahead rainfall–runoff modeling of the Milledgeville station up to 14 and 12% and of the Pole Saheb station up to 22 and 16% in the verification phase. Also the results of multi-step-ahead modeling using the proposed data pre-processing approach showed improvement of modeling for both watersheds.     

Water quality variations in different climates of Iran: toward modeling total dissolved solid using soft computing techniques

In present paper, wavelet analysis of total dissolved solid that monitored at Nazlu Chay (northwest of Iran), Tajan (north of Iran), Zayandeh Rud (central of Iran) and Helleh (south of Iran) basins with various climatic conditions, have been studied. Daubechies wavelet at suitable level (db4) has been calculated for TDS of each selected basins. The performance of artificial neural networks (ANN), two different adaptive-neurofuzzy inference system (ANFIS) including ANFIS with grid partition (ANFIS-GP) and ANFIS with subtractive clustering (ANFIS-SC), gene expression programming (GEP), wavelet-ANN, wavelet-ANFIS and wavelet-GEP in predicting TDS of mentioned basins were assessed over a period of 20 years at twelve different hydrometric stations. EC (μmhos/cm), Na (meq L^?1) and Cl (meq L^?1) parameters were selected (based on Pearson correlation) as input variables to forecast amount of TDS in four studied basins. To develop hybrid wavelet-AI models, the original observed data series was decomposed into sub-time series using Daubechies wavelets at suitable level for each basin. Based on the statistical criteria of correlation coefficient (R), root mean square error (RMSE) and mean absolute error (MAE), the hybrid wavelet-AI models performance were better than single AI models in all basins. A comparison was made between these artificial intelligence approaches which emphasized the superiority of wavelet-GEP over the other intelligent models with amount of RMSE 18.978, 6.774, 9.639 and 318.363 mg/l, in Nazlu Chay, Tajan, Zayandeh Rud and Helleh basins, respectively.     

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.     

The data‐driven approach as an operational real‐time flood forecasting model

Accurate water level forecasts are essential for flood warning. This study adopts a data‐driven approach based on the adaptive network–based fuzzy inference system (ANFIS) to forecast the daily water levels of the Lower Mekong River at Pakse, Lao People's Democratic Republic. ANFIS is a hybrid system combining fuzzy inference system and artificial neural networks. Five ANFIS models were developed to provide water level forecasts from 1 to 5 days ahead, respectively. The results show that although ANFIS forecasts of water levels up to three lead days satisfied the benchmark, four‐ and five‐lead‐day forecasts were only slightly better in performance compared with the currently adopted operational model. This limitation is imposed by the auto‐ and cross‐correlations of the water level time series. Output updating procedures based on the autoregressive (AR) and recursive AR (RAR) models were used to enhance ANFIS model outputs. The RAR model performed better than the AR model. In addition, a partial recursive procedure that reduced the number of recursive steps when applying the AR or the RAR model for multi‐step‐ahead error prediction was superior to the fully recursive procedure. The RAR‐based partial recursive updating procedure significantly improved three‐, four‐ and five‐lead‐day forecasts. Our study further shows that for long lead times, ANFIS model errors are dominated by lag time errors. Although the ANFIS model with the RAR‐based partial recursive updating procedure provided the best results, this method was able to reduce the lag time errors significantly for the falling limbs only. Improvements for the rising limbs were modest. Copyright © 2011 John Wiley & Sons, Ltd.     

Extreme learning machine for the displacement prediction of landslide under rainfall and reservoir level

Landslide prediction is always the emphasis of landslide research. Using global positioning system GPS technologies to monitor the superficial displacements of landslide is a very useful and direct method in landslide evolution analysis. In this paper, an EEMD–ELM model [ensemble empirical mode decomposition (EEMD) based extreme learning machine (ELM) ensemble learning paradigm] is proposed to analysis the monitoring data for landslide displacement prediction. The rainfall data and reservoir level fluctuation data are also integrated into the study. The rainfall series, reservoir level fluctuation series and landslide accumulative displacement series are all decomposed into the residual series and a limited number of intrinsic mode functions with different frequencies from high to low using EEMD technique. A novel neural network technique, ELM, is employed to study the interactions of these sub-series at different frequency affecting landslide occurrence. Each sub-series extracted from accumulative displacement of landslide is forecasted respectively by establishing appropriate ELM model. The final prediction result is obtained by summing up the calculated predictive displacement value of each sub. The EEMD–ELM model shows the best accuracy comparing with basic artificial neural network models through forecasting the displacement of Baishuihe landslide in the Three Gorges reservoir area of China.     

Application of wavelet-artificial intelligence hybrid models for water quality prediction: a case study in Aji-Chay River,Iran

The accuracy of Artificial Neural Network (ANN), Adaptive Neuro-Fuzzy Inference System (ANFIS), wavelet-ANN and wavelet-ANFIS in predicting monthly water salinity levels of northwest Iran’s Aji-Chay River was assessed. The models were calibrated, validated and tested using different subsets of monthly records (October 1983 to September 2011) of individual solute (Ca²⁺, Mg²⁺, Na⁺, SO₄ ^2? and Cl^?) concentrations (input parameters, meq L^?1), and electrical conductivity-based salinity levels (output parameter, µS cm^?1), collected by the East Azarbaijan regional water authority. Based on the statistical criteria of coefficient of determination (R²), normalized root mean square error (NRMSE), Nash–Sutcliffe efficiency coefficient (NSC) and threshold statistics (TS) the ANFIS model was found to outperform the ANN model. To develop coupled wavelet-AI models, the original observed data series was decomposed into sub-time series using Daubechies, Symlet or Haar mother wavelets of different lengths (order), each implemented at three levels. To predict salinity input parameter series were used as input variables in different wavelet order/level-AI model combinations. Hybrid wavelet-ANFIS (R² = 0.9967, NRMSE = 2.9 × 10^?5 and NSC = 0.9951) and wavelet-ANN (R² = 0.996, NRMSE = 3.77 × 10^?5 and NSC = 0.9946) models implementing the db4 mother wavelet decomposition outperformed the ANFIS (R² = 0.9954, NRMSE = 3.77 × 10^?5 and NSC = 0.9914) and ANN (R² = 0.9936, NRMSE = 3.99 × 10^?5 and NSC = 0.9903) models.     

Comparative analysis of fuzzy inference systems for water consumption time series prediction

Two types of fuzzy inference systems (FIS) are used for predicting municipal water consumption time series. The FISs used include an adaptive neuro-fuzzy inference system (ANFIS) and a Mamdani fuzzy inference systems (MFIS). The prediction models are constructed based on the combination of the antecedent values of water consumptions. The performance of ANFIS and MFIS models in training and testing phases are compared with the observations and the best fit model is identified according to the selected performance criteria. The results demonstrated that the ANFIS model is superior to MFIS models and can be successfully applied for prediction of water consumption time series.     

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.     

Linear and non-linear approaches to predict the Darcy-Weisbach friction factor of overland flow using the extreme learning machine approach

In modeling of overland flow and erosion, the overland flow friction factor (f), is a crucial factor. Due to the importance of a good understanding of f and its variability, the current study aimed to investigate the capability of non-linear approaches to estimate the Darcy-Weisbach friction factor of overland flow and its components (sediment transport, wave, form, and grain friction factors) through the Extreme Learning Machine (ELM) approach. Four datasets were used herein which were obtained from flume experiments done by different researchers. In order to investigate the effects of different parameters on the friction factor, numerous models consisting of various parameters were utilized to predict the friction factor using the ELM approach. The modeling procedure was established in two stages; the first stage aimed to model the overland flow friction factor and investigate the effect of the different parameters on the friction factor using non-linear separation via the ELM approach. In the second stage, the friction factor was linearly separated into different types of friction factors and then the separate components were estimated. Sensitivity analysis results confirmed the key role of Froude number (Fr) values for most of the models. On the other hand, the results obtained for estimated values of the friction factor were acceptable and outperformed available empirical approaches.     

A modelling approach for estimating suspended sediment concentrations for multiple rivers influenced by agriculture

A data-driven model based on an adaptive neuro-fuzzy inference system (ANFIS) was tested for the estimation of suspended sediment concentrations within watersheds influenced by agriculture. ANFIS models were developed using different combinations of inputs such as precipitation, streamflow, surface runoff and the watershed vulnerability index. A multi-watershed ANFIS model was also developed combining the datasets from all studied watersheds. The best results were obtained from a combination of precipitation, streamflow and watershed vulnerability index as input variables. Nash-Sutcliffe coefficients were improved for the multi-watershed ANFIS compared to watershed-specific ANFIS models. The introduction of the erosion vulnerability index significantly improved the ability of the ANFIS model to estimate suspended sediment concentrations within the watersheds. Furthermore, the inclusion of this index opens the possibility of using the ANFIS model to investigate the impact of land-use changes on sediment delivery.     

Multiple linear regression,multi-layer perceptron network and adaptive neuro-fuzzy inference system for forecasting precipitation based on large-scale climate signals

ABSTRACT

Nowadays, mathematical models are widely used to predict climate processes, but little has been done to compare the models. In this study, multiple linear regression (MLR), multi-layer perceptron (MLP) network and adaptive neuro-fuzzy inference system (ANFIS) models were compared for precipitation forecasting. The large-scale climate signals were considered as inputs to the applied models. After selecting the most effective climate indices, the effects of large-scale climate signals on the seasonal standardized precipitation index (SPI) of the Maharlu-Bakhtaran catchment, Iran, simultaneously and with a delay, was analysed using a cross-correlation function. Hence, the SPI time series was forecasted up to four time intervals using MLR, MLP and ANFIS. The results showed that most of the indices were significant with SPI of different lag times. Comparison of the SPI forecast results by MLR, MLP and ANFIS models showed better performance for the MLP network than the other two models (RMSE = 0.86, MAE = 0.74 for the first step ahead of SPI forecasting).

Editor D. Koutsoyiannis; Associate editor F. Pappenberger     

Wavelet-ANFIS models for forecasting monsoon flows: Case study for the Gandak River (India)

WANFIS, a conjunction model of discreet wavelet transform (DWT) and adaptive neuro-fuzzy inference system (ANFIS) was developed for forecasting the current-day flow in a river when only available data are historical flows. Discreet wavelet transform decomposed the observed flow time series (OFTS) into wavelet components which captured useful information on three resolution levels. A smoothened flow time series (SFTS) was formed by filtering out the noise wavelet components and recombining the effective wavelet components. WANFIS model is essentially an ANFIS model with SFTS hydrograph as the input, while ANFIS and autoregression (AR) models, developed for comparison purpose, use OFTS hydrograph as input. For performance evaluation, the developed models were utilized for predicting daily monsoon flows for the Gandak River in Bihar state of India. During monsoon (June–October), this river carries large flows making the entire North Bihar unsafe for habitation or cultivation. Based on various performance indices, it was concluded that WANFIS models simulate the monsoon flows in the Gandak more reliably than ANFIS and AR models. The best performing WANFIS model, with four previous days’ flows as input, predicted the current-day Gandak flows with 80.7% accuracy while ANFIS and AR models predicted it with only 71.8 and 51.2% accuracies.     

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.     

Application of different data-driven methods for the prediction of total dissolved solids in the Zarinehroud basin

A total dissolved solid (TDS) is an important indicator for water quality assessment. Since the composition of mineral salts and discharge affects the TDS of water, it is important to understand the relationship of mineral salt composition with TDS. In the present study, four artificial intelligence approaches, namely artificial neural networks (ANNs), two different adaptive-neuro-fuzzy inference system (ANFIS) including ANFIS with grid partition (ANFIS-GP) and ANFIS with subtractive clustering (ANFIS-SC), and gene expression programming (GEP) were applied to forecast TDS in river water over a period of 18 years at seven different sites. Five different GEP, ANFIS and ANN models comprising various combinations of water quality and flow variables from Zarinehroud basin in northwest of Iran were developed to forecast TDS variations. The correlation coefficient (R), root mean square error and mean absolute error statistics were used for evaluating the accuracy of models. Based on the comparisons, it was found that the GEP, ANFIS-GP, ANFIS-SC and ANN models could be employed successfully in forecasting TDS variations. A comparison was made between these artificial intelligence approaches which emphasized the superiority of GEP over the other intelligent models.     

Ensemble prediction of regional droughts using climate inputs and the SVM–copula approach

In this study, the climate teleconnections with meteorological droughts are analysed and used to develop ensemble drought prediction models using a support vector machine (SVM)–copula approach over Western Rajasthan (India). The meteorological droughts are identified using the Standardized Precipitation Index (SPI). In the analysis of large‐scale climate forcing represented by climate indices such as El Niño Southern Oscillation, Indian Ocean Dipole Mode and Atlantic Multidecadal Oscillation on regional droughts, it is found that regional droughts exhibits interannual as well as interdecadal variability. On the basis of potential teleconnections between regional droughts and climate indices, SPI‐based drought forecasting models are developed with up to 3 months' lead time. As traditional statistical forecast models are unable to capture nonlinearity and nonstationarity associated with drought forecasts, a machine learning technique, namely, support vector regression (SVR), is adopted to forecast the drought index, and the copula method is used to model the joint distribution of observed and predicted drought index. The copula‐based conditional distribution of an observed drought index conditioned on predicted drought index is utilized to simulate ensembles of drought forecasts. Two variants of drought forecast models are developed, namely a single model for all the periods in a year and separate models for each of the four seasons in a year. The performance of developed models is validated for predicting drought time series for 10 years' data. Improvement in ensemble prediction of drought indices is observed for combined seasonal model over the single model without seasonal partitions. The results show that the proposed SVM–copula approach improves the drought prediction capability and provides estimation of uncertainty associated with drought predictions. Copyright © 2013 John Wiley & Sons, Ltd.     

Adaptive neural-based fuzzy inference system (ANFIS) approach for modelling hydrological time series

Abstract

The main aim of this study is to develop a flow prediction method, based on the adaptive neural-based fuzzy inference system (ANFIS) coupled with stochastic hydrological models. An ANFIS methodology is applied to river flow prediction in Dim Stream in the southern part of Turkey. Application is given for hydrological time series modelling. Synthetic series, generated through autoregressinve moving-average (ARMA) models, are then used for training data sets of the ANFIS. It is seen that the extension of input and output data sets in the training stage improves the accuracy of forecasting by using ANFIS.     

Modelling long-term groundwater fluctuations by extreme learning machine using hydro-climatic data

The ability of the extreme learning machine (ELM) is investigated in modelling groundwater level (GWL) fluctuations using hydro-climatic data obtained for Hormozgan Province, southern Iran. Monthly precipitation, evaporation and previous GWL data were used as model inputs. Developed ELM models were compared with the artificial neural networks (ANN) and radial basis function (RBF) models. The models were also compared with the autoregressive moving average (ARMA), and evaluated using mean square errors, mean absolute error, Nash-Sutcliffe efficiency and determination coefficient statistics. All the data-driven models had better accuracy than the ARMA, and the ELM model’s performance was superior to that of the ANN and RBF models in modelling 1-, 2- and 3-month-ahead GWL. The RMSE accuracy of the ANN model was increased by 37, 34 and 52% using ELM for the 1-, 2- and 3-month-ahead forecasts, respectively. The accuracy of the ELM models was found to be less sensitive to increasing lead time.     

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.     

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     

Estimating uncertainty of streamflow measurements with moving-boat acoustic Doppler current profilers

A theoretical and a semi-empirical model are presented for estimating the uncertainty of streamflow measurements made with an acoustic Doppler current profiler (ADCP) mounted on a moving platform. Both models are based on the statistical analysis of ADCP ensemble discharge time series collected during a transect; therefore, they account for all random error sources associated with the measurement at a site. The theoretical model is developed based on the law of propagation of variance; it explores the theoretical relationship between the variables involved in the problem. The semi-empirical model is developed based on the theory of dimensional analysis; it explores the empirical relationship between the variables. The semi-empirical model is calibrated using 205 transect datasets and verified with an additional 382 transect datasets. It provides a useful tool for the uncertainty analysis and uncertainty-based measurement quality control of moving-boat ADCP streamflow measurements.