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.     

Multi-step water quality forecasting using a boosting ensemble multi-wavelet extreme learning machine model

The use of electrical conductivity (EC) as a water quality indicator is useful for estimating the mineralization and salinity of water. The objectives of this study were to explore, for the first time, extreme learning machine (ELM) and wavelet-extreme learning machine hybrid (WA-ELM) models to forecast multi-step-ahead EC and to employ an integrated method to combine the advantages of WA-ELM models, which utilized the boosting ensemble method. For comparative purposes, an adaptive neuro-fuzzy inference system (ANFIS) model, and a WA-ANFIS model, were also developed. The study area was the Aji-Chay River at the Akhula hydrometric station in Northwestern Iran. A total of 315 monthly EC (µS/cm) datasets (1984–2011) were used, in which the first 284 datasets (90% of total datasets) were considered for training and the remaining 31 (10% of total datasets) were used for model testing. Autocorrelation function (ACF) and partial autocorrelation function (PACF) demonstrated that the 6-month lags were potential input time lags. The results illustrated that the single ELM and ANFIS models were unable to forecast the multi-step-ahead EC in terms of root mean square error (RMSE), coefficient of determination (R²) and Nash–Sutcliffe model efficiency coefficient (NSC). To develop the hybrid WA-ELM and WA-ANFIS models, the original time series of lags as inputs, and time series of 1, 2 and 3 month-step-ahead EC values as outputs, were decomposed into several sub-time series using different maximal overlap discrete wavelet transform (MODWT) functions, namely Daubechies, Symlet, Haar and Coiflet of different orders at level three. These sub-time series were then used in the ELM and ANFIS models as an input dataset to forecast the multi-step-ahead EC. The results indicated that single WA-ELM and WA-ANFIS models performed better than any ELM and ANFIS models. Also, WA-ELM models outperformed WA-ANFIS models. To develop the boosting multi-WA-ELM and multi-WA-ANFIS ensemble models, a least squares boosting (LSBoost) algorithm was used. The results showed that boosting multi-WA-ELM and multi-WA-ANFIS ensemble models outperformed the individual WA-ELM and WA-ANFIS models.     

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.     

Seasonal Short‐Term Prediction of Dissolved Oxygen in Rivers via Nature‐Inspired Algorithms

This study challenges the use of three nature‐inspired algorithms as learning frameworks of the adaptive‐neuro‐fuzzy inference system (ANFIS) machine learning model for short‐term modeling of dissolved oxygen (DO) concentrations. Particle swarm optimization (PSO), butterfly optimization algorithm (BOA), and biogeography‐based optimization (BBO) are employed for developing predictive ANFIS models using seasonal 15 min data collected from the Rock Creek River in Washington, DC. Four independent variables are used as model inputs including water temperature (T), river discharge (Q), specific conductance (SC), and pH. The Mallow's Cp and R² parameters are used for choosing the best input parameters for the models. The models are assessed by several statistics such as the coefficient of determination (R²), root‐mean‐square error (RMSE), Nash–Sutcliffe efficiency, mean absolute error, and the percent bias. The results indicate that the performance of all‐nature‐inspired algorithms is close to each other. However, based on the calculated RMSE, they enhance the accuracy of standard ANFIS in the spring, summer, fall, and winter around 13.79%, 15.94%, 6.25%, and 12.74%, respectively. Overall, the ANFIS‐PSO and ANFIS‐BOA provide slightly better results than the other ANFIS models.     

Forecasting streamflow by combination of a genetic input selection algorithm and wavelet transforms using ANFIS models

ABSTRACT

In this study, a data-driven streamflow forecasting model is developed, in which appropriate model inputs are selected using a binary genetic algorithm (GA). The process involves using a combination of a GA input selection method and two adaptive neuro-fuzzy inference systems (ANFIS): subtractive (Sub)-ANFIS and fuzzy C-means (FCM)-ANFIS. Moreover, the application of wavelet transforms coupled with these models is tested. Long-term data for the Lighvan and Ajichai basins in Iran are used to develop the models. The results indicate considerable improvements when GA selection and wavelet methods are used in both models. For example, the Nash-Sutcliffe efficiency (NSE) coefficient for Lighvan using FCM-ANFIS is 0.74. However, when GA selection is applied, the NSE is improved to 0.85. Moreover, when the wavelet method is added, the performance of new hybrid models shows noticeable enhancements. The NSE value of wavelet-FCM-ANFIS is improved to 0.97 for Lighvan basin.

Editor D. Koutsoyiannis Associate editor E. Toth     

Biological assessment of the Zayandeh Rud River, Iran, using benthic macroinvertebrates

Benthic macroinvertebrate communities from the middle of Zayandeh Rud River were analyzed monthly during 1 year at 8 stations, in order to assess changes in their diversity and richness in relation to water quality. Two major groups of sites based on similarity between macroinvertebrate communities were identified by cluster analysis. The performances of the original and revised BMWP score systems were assessed by comparing the community structure indices of benthic macroinvertebrates along with physico-chemical parameters of the water. The biotic indices (BMWP, ASPT, revised BMWP and ASPT) showed better correlation with water quality parameters than that of the richness and diversity indices. The revised ASPT had the highest correlation with water quality parameters. It seems that the application of the revised BMWP score system could be useful for assessment of the water quality in Zayandeh Rud River.     

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     

Identifying complexity of annual precipitation variation in Iran during 1960–2010 based on information theory and discrete wavelet transform

The hydrologic process and dynamic system of precipitation is influenced by many physical factors which are excessively complex and variable. Present study used a wavelet transform based multiscale entropy (WME) and wavelet-based multiscale relative entropy (WMRE) approach in order to analyze and gage the complexity of the precipitation series and spatially classify the raingauges in Iran. For this end, historical annual precipitation data of 51 years (1960–2010) from 31 raingauges was decomposed using WT in which smooth Daubechies (db) mother wavelet (db5–db10), optimal level of decomposition and boundary extensions were considered. Next, entropy concept was applied for components obtained from WT to measure of dispersion, uncertainty, disorderliness and diversification in a multi-scale form. Spatial classification of raingauges was performed using WME and WMRE values as input data to SOM and k-means approaches. Three validity indices namely Davis Bouldin (DB), Silhouette coefficient (SC) and Dunn index were used to validate the proposed model’s efficiency. Based on results, it was observed that k-means approach had better performance in determining homogenous areas with SC = 0.337, DB = 0.769 and Dunn = 1.42. Finally, spatial structure of precipitation variation in latitude and longitude directions demonstrated that WME and WMRE values had a decreasing trend with latitude, however, it was seen that WME and WMRE had an increasing relationship with longitude in Iran.     

Modelling of infiltration using artificial intelligence techniques in semi-arid Iran

ABSTRACT

Infiltration plays a fundamental role in streamflow, groundwater recharge, subsurface flow, and surface and subsurface water quality and quantity. In this study, adaptive neuro-fuzzy inference system (ANFIS), support vector machine (SVM) and random forest (RF) models were used to determine cumulative infiltration and infiltration rate in arid areas in Iran. The input data were sand, clay, silt, density of soil and soil moisture, while the output data were cumulative infiltration and infiltration rate, the latter measured using a double-ring infiltrometer at 16 locations. The results show that SVM with radial basis kernel function better estimated cumulative infiltration (RMSE = 0.2791 cm) compared to the other models. Also, SVM with M4 radial basis kernel function better estimated the infiltration rate (RMSE = 0.0633 cm/h) than the ANFIS and RF models. Thus, SVM was found to be the most suitable model for modelling infiltration in the study area.     

Regional flood frequency analysis using support vector regression in arid and semi-arid regions of Iran

Regional flood frequency analysis (RFFA) was carried out on data for 55 hydrometric stations in Namak Lake basin, Iran, for the period 1992–2012. Flood discharge of specific return periods was computed based on the log Pearson Type III distribution, selected as the best regional distribution. Independent variables, including physiographic, meteorological, geological and land-use variables, were derived and, using three strategies – gamma test (GT), GT plus classification and expert opinion – the best input combination was selected. To select the best technique for regionalization, support vector regression (SVR), adaptive neuro-fuzzy inference system (ANFIS), artificial neural network (ANN) and nonlinear regression (NLR) techniques were applied to predict peak flood discharge for 2-, 5-, 10-, 25-, 50- and 100-year return periods. The GT + ANFIS and GT + SVR models gave better performance than the ANN and NLR models in the RFFA. The results of the input variable selection showed that the GT technique improved the model performance.     

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.     

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.     

New data on the zoogeography of Aphanius sophiae (Teleostei: Cyprinodontidae) in the Central Zagros (Southwest Iran)

The clade of the Iranian freshwater Aphanius species from endorheic and exorheic drainage basins contains three subclades, of which the Aphanius sophiae subclade with seven species is the most specious one. Recently, two previously not known populations of Aphanius were discovered in two isolated basins; one in the Arjan Wetland (Helleh subbasin), and the other in the Semirom spring (Karun Basin), both are located in the Central Zagros Mountains (SW Iran). The objective of this study is to investigate their taxonomic status, to elucidate their phylogenetic relationships and to contribute to future conservation strategies and habitat management of the freshwater species of Aphanius in Iran. Methods include analysis of genetic data based on mtDNA (cyt b), combined with meristics, morphometrics, scale sizes (J-indices) and otolith data. The results based on cyt b clearly indicate that two species are present in the Arjan Wetland, one is closely related to A. sophiae (currently thought to be restricted to the Kor Basin), the other represents Aphanius shirini (previously only known from its type locality Paselari spring). However, significant phenotypic differences are not present between these two species. The second population from the Semirom spring is sister to A. sophiae (Kor Basin) according to cyt b data, but differs significantly from this species with regard to the phenotype. The presence of A. shirini in the Arjan Wetland is most likely be explained by man-made introduction because of the recent droughts. The similarity of the two species present in the Arjan Wetland may be due to phenotypic plasticity, but also hybridization could have played a role. The isolation of populations of A. sophiae is discussed in the context of the active geological history and climate change, and it is likely that their divergence happened in the Early or Middle Holocene (c. 11,700–4000 y. ago). The presence of A. sophiae in the Helleh subbasin and Karun Basin extends the currently known zoogeographic range of this species, which previously has only been reported from the Kor Basin. Such knowledge is important for future conservation strategies and habitat management.     

Effects of long-term wastewater irrigation on soil physical properties and performance of selected infiltration models in a semi-arid region

ABSTRACT

In many arid and semi-arid countries, wastewater irrigation is becoming a common practice in agriculture. In this study, the effect of long-term (40 years) wastewater irrigation on selected physical and hydraulic properties of soil in different parts of a landscape was investigated. The performance of some infiltration models, including Philip (Ph), Kostiakov (Kos), Kostiakov-Lewis (Kos-L), Horton (Ho), Huggins and Monke (Hug-M), and linear and nonlinear Smith-Parlange (S-P(L) and S-P(NL)), was compared. This study was performed in the Urmia region, Iran, where flooding wastewater irrigation has been practised for at least 40 years. Five paired sites, each of which contained a measurement location at the wastewater-irrigated (WWI) and adjacent control area were studied. Accuracy of the infiltration models was evaluated using several statistical criteria, including root mean square error (RMSE) and Akaike information criterion (AIC). The models were classified into groups using cluster analysis based on level of similarity in their performance. The cumulative water infiltration into soils after 1 h (I_1h) was calculated using the selected most accurate models and introduced so as to use only one term to compare the infiltration behaviour of soils. Based on RMSE and AIC, the performance of the Ph, Ho, Kos and Kos-L models was considerably better than that of Hug-M, S-P(L) and S-P(NL). The ranking of the models in terms of their AIC values was: Kos-L > Ho > Kos > Ph > S-P(L) > Hug-M > S-P(NL). The models were classified into two distinct groups. The similarity among Ph, Ho, Kos and Kos-L models was more than 80% and for Hug-M, S-P(L), and S-P(NL) models, it was more than 79%. However, the similarity between these two groups of models was less than 58%.

Editor M.C. Acreman; Associate editor not assigned     

Deep learning approaches for improving prediction of daily stream temperature in data-scarce,unmonitored, and dammed basins

Basin-centric long short-term memory (LSTM) network models have recently been shown to be an exceptionally powerful tool for stream temperature (T_s) temporal prediction (training in one period and predicting in another period at the same sites). However, spatial extrapolation is a well-known challenge to modelling T_s and it is uncertain how an LSTM-based daily T_s model will perform in unmonitored or dammed basins. Here we compiled a new benchmark dataset consisting of >400 basins across the contiguous United States in different data availability groups (DAG, meaning the daily sampling frequency) with and without major dams, and studied how to assemble suitable training datasets for predictions in basins with or without temperature monitoring. For prediction in unmonitored basins (PUB), LSTM produced a root-mean-square error (RMSE) of 1.129°C and an R² of 0.983. While these metrics declined from LSTM's temporal prediction performance, they far surpassed traditional models' PUB values, and were competitive with traditional models' temporal prediction on calibrated sites. Even for unmonitored basins with major reservoirs, we obtained a median RMSE of 1.202°C and an R² of 0.984. For temporal prediction, the most suitable training set was the matching DAG that the basin could be grouped into (for example, the 60% DAG was most suitable for a basin with 61% data availability). However, for PUB, a training dataset including all basins with data was consistently preferred. An input-selection ensemble moderately mitigated attribute overfitting. Our results indicate there are influential latent processes not sufficiently described by the inputs (e.g., geology, wetland covers), but temporal fluctuations can still be predicted well, and LSTM appears to be a highly accurate T_s modelling tool even for spatial extrapolation.     

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.     

Effect of ENSO on annual maximum floods and volume over threshold in the southwestern region of Iran

In this paper, the effects of the El Niño-Southern Oscillation (ENSO) on the annual maximum flood (AMF) and volume over threshold (VOT) in two major neighbouring river basins in southwest Iran are investigated. The basins are located upstream of the Dez and Karun-I dams and cover over 40?000 km² in total area. The effects of ENSO on the frequency, magnitude and severity (frequency times magnitude) of flood characteristics over the March–April period were analysed. ENSO indices were also correlated with both AMF and VOT. The results indicate that, in the Dez and Karun basins, the El Niño phenomenon intensifies March–April floods compared with neutral conditions. The opposite is true in La Niña conditions. The degree of the effect is more intense in the El Niño period.     

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.     

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.     

Monthly total sediment forecasting using adaptive neuro fuzzy inference system

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