Daily Mean Streamflow Prediction in Perennial and Non-Perennial Rivers Using Four Data Driven Techniques

This study examines and compares the performance of four new attractive artificial intelligence techniques including artificial neural network (ANN), hybrid wavelet-artificial neural network (WANN), Genetic expression programming (GEP), and hybrid wavelet-genetic expression programming (WGEP) for daily mean streamflow prediction of perennial and non-perennial rivers located in semi-arid region of Zagros mountains in Iran. For this purpose, data of daily mean streamflow of the Behesht-Abad (perennial) and Joneghan (non-perennial) rivers as well as precipitation information of 17 meteorological stations for the period 1999–2008 were used. Coefficient of determination (R²) and root mean square error (RMSE) were used for evaluating the applicability of developed models. This study showed that although the GEP model was the most accurate in predicting peak flows, but in overall among the four mentioned models in both perennial and non-perennial rivers, WANN had the best performance. Among input patterns, flow based and coupled precipitation-flow based patterns with negligible difference to each other were determined to be the best patterns. Also this study confirmed that combining wavelet method with ANN and GEP and developing WANN and WGEP methods results in improving the performance of ANN and GEP models.     

Estimation of Peak Flood Discharges at Ungauged Sites Across Turkey

The reliable forecasting of the peak flood discharge at river basins is a common problem, and it becomes more complicated when there is inadequate recorded data. The statistical methods commonly used for the estimation of peak flood discharges are generally considered to be inadequate because of the complexity of this problem. Recently, genetic programming (GP) which is a branch of soft computing methods has attracted the attention of the hydrologists. In this study, gene-expression programming (GEP) and linear genetic programming (LGP), which are extensions to GP, in addition to logistic regression (LR) were employed in order to forecast peak flood discharges. The study covered 543 ungauged sites across Turkey. Drainage area, elevation, latitude, longitude, and return period were used as the inputs while the peak flood discharge was the output. Model comparison results revealed that GEP predicted the peak flood discharges with R ²?=?57.4?% correlation, LGP with 56?% and LR model with 42.3?%, respectively. The peak flood discharges in all river basins can now be determined using the single equation provided by the GEP model.     

Stream Flow Forecasting of Poorly Gauged Mountainous Watershed by Least Square Support Vector Machine,Fuzzy Genetic Algorithm and M5 Model Tree Using Climatic Data from Nearby Station

Forecasting stream flow is a very importance issue in water resources planning and management. The ability of three soft computing methods, least square support vector machine (LSSVM), fuzzy genetic algorithm (FGA) and M5 model tree (M5T), in forecasting daily and monthly stream flows of poorly gauged mountainous watershed using nearby hydro-meteorological data is investigated in the current study. In the first application, monthly stream flows of Hunza river are forecasted using local stream flow data of Hunza and precipitation and temperature data of nearby station. LSSVM provides slightly better forecasts than the FGA and M5T models. Stream flow and temperature inputs generally give better forecasts compared to other inputs. In the second application, daily stream flows of Hunza river are forecasted using local stream flow data of Hunza and precipitation and temperature data of nearby station. Better results are obtained from the models comprising only stream flow inputs. In general, a better accuracy is obtained from LSSVM models in relative to the FGA and M5T. The results indicate that the monthly and daily stream flows of Hunza can be accurately forecasted by using only nearby climatic data. In the third application, daily stream flows of Hunza river are forecasted using local stream flow and climatic data and the models’ accuracy is slightly increased in relative to the previous applications. LSSVM generally performs superior to the FGA and M5T in forecasting daily stream flow of Hunza river using local stream flow and climatic inputs.     

A Comparative Study of Autoregressive,Autoregressive Moving Average,Gene Expression Programming and Bayesian Networks for Estimating Monthly Streamflow

In the recent years, artificial intelligence techniques have attracted much attention in hydrological studies, while time series models are rarely used in this field. The present study evaluates the performance of artificial intelligence techniques including gene expression programming (GEP), Bayesian networks (BN), as well as time series models, namely autoregressive (AR) and autoregressive moving average (ARMA) for estimation of monthly streamflow. In addition, simple multiple linear regression (MLR) was also used. To fulfill this objective, the monthly streamflow data of Ponel and Toolelat stations located on Shafarood and Polrood Rivers, respectively in Northern Iran were used for the period of October 1964 to September 2014. In order to investigate the models’ accuracy, root mean square error (RMSE), mean absolute error (MAE) and coefficient of determination (R²) were employed as the error statistics. The obtained results demonstrated that the single AR and ARMA time series models had better performance in comparison with the single GEP, BN and MLR methods. Furthermore, in this study, six hybrid models known as GEP-AR, GEP-ARMA, BN-AR, BN-ARMA, MLR-AR and MLR-ARMA were developed to enhance the estimation accuracy of the monthly streamflow. It was concluded that the developed hybrid models were more accurate than the corresponding single artificial intelligence and time series models. The obtained results confirmed that the integration of time series models and artificial intelligence techniques could be of use to improve the accuracy of single models in modeling purposes related to the hydrological studies.     

改进GEP方法在边坡非圆临界滑动面搜索中的应用

基因表达式编程(Genetic Expression Programming,简称GEP)是模拟生物遗传进化过程的一种新型优化方法,其结合遗传算法(GA)和遗传编程(GP)各自的优点,使编码更为方便、简单。为了进一步改善GEP方法的局部搜索能力和克服“早熟”现象,将局部搜索能力很强的单纯形法和回溯机制引入GEP中,提出了混合GEP方法。以安全系数为目标函数,将混合GEP法和不平衡推力法结合,提出确定非圆弧临界滑动面的新方法。2个经典算例的计算结果表明:该新方法可以准确地搜索到边坡非圆临界滑动面及相应的安全系数,且混合GEP方法的局部搜索精度和全局搜索能力均优于标准GEP方法,同时收敛速度得到明显提高。     

New Approaches for Estimation of Monthly Rainfall Based on GEP-ARCH and ANN-ARCH Hybrid Models

Accurate estimation of rainfall has an important role in the optimal water resources management, as well as hydrological and climatological studies. In the present study, two novel types of hybrid models, namely gene expression programming-autoregressive conditional heteroscedasticity (GEP-ARCH) and artificial neural networks-autoregressive conditional heteroscedasticity (ANN-ARCH) are introduced to estimate monthly rainfall time series. To fulfill this purpose, five stations with various climatic conditions were selected in Iran. The lagged monthly rainfall data was utilized to develop the different GEP and ANN scenarios. The performance of proposed hybrid models was compared to the GEP and ANN models using root mean square error (RMSE) and coefficient of determination (R²). The results show that the proposed GEP-ARCH and ANN-ARCH models give a much better performance than the GEP and ANN in all of the studied stations with various climates. Furthermore, the ANN-ARCH model generally presents better performance in comparison with the GEP-ARCH model.     

Gene-expression programming for flip-bucket spillway scour

During the last two decades, researchers have noticed that the use of soft computing techniques as an alternative to conventional statistical methods based on controlled laboratory or field data, gave significantly better results. Gene-expression programming (GEP), which is an extension to genetic programming (GP), has nowadays attracted the attention of researchers in prediction of hydraulic data. This study presents GEP as an alternative tool in the prediction of scour downstream of a flip-bucket spillway. Actual field measurements were used to develop GEP models. The proposed GEP models are compared with the earlier conventional GP results of others (Azamathulla et al. 2008b; RMSE = 2.347, δ = 0.377, R = 0.842) and those of commonly used regression-based formulae. The predictions of GEP models were observed to be in strictly good agreement with measured ones, and quite a bit better than conventional GP and the regression-based formulae. The results are tabulated in terms of statistical error measures (GEP1; RMSE = 1.596, δ = 0.109, R = 0.917) and illustrated via scatter plots.     

Estimation of Suspended Sediment Yield in Natural Rivers Using Machine-coded Linear Genetic Programming

Estimation of suspended sediment yield is subject to uncertainty and bias. Many methods have been developed for estimating sediment yield but they still lack accuracy and robustness. This paper investigates the use of a machine-coded linear genetic programming (LGP) in daily suspended sediment estimation. The accuracy of LGP is compared with those of the Gene-expression programming (GEP), which is another branch of GP, and artificial neural network (ANN) technique. Daily streamflow and suspended sediment data from two stations on the Tongue River in Montana, USA, are used as case studies. Root mean square error (RMSE) and determination coefficient (R²) statistics are used for evaluating the accuracy of the models. Based on the comparison of the results, it is found that the LGP performs better than the GEP and ANN techniques. The GEP was also found to be better than the ANN. For the upstream and downstream stations, it is found that the LGP models with RMSE = 175 ton/day, R² = 0.941 and RMSE = 254 ton/day, R² = 0.959 in test period is superior in estimating daily suspended sediments than the best accurate GEP model with RMSE = 231 ton/day, R² = 0.941 and RMSE = 331 ton/day, R² = 0.934, respectively.     

基于多种混合模型的径流预测研究

变化环境下径流的波动不断加大,给径流的精准预报带来新的挑战。基于"分解-合成"策略的混合径流预报模型来提高预报精度是当前研究的热点之一。以往研究聚焦在单一的混合预报模型而忽视了它们的适用性研究。基于此,以渭河流域为例,在优选多元线性回归(MLR)、人工神经网络(ANN)和支持向量机(SVM)单一预报模型的基础上,分别基于经验模态分解(EMD)、集合经验模态分解(EEMD)和小波分解(WD)构建了多种混合模型,并融合了大气环流异常因子的信息。结果表明:(1)SVM模型预测精度高于ANN和MLR;(2)混合预测模型预测精度均高于单一模型,混合模型中WD-SVM的预测精度优于EMD-SVM和EEMD-SVM;(3)融合大气环流异常因子后WD-SVM模型预测精度最高,对极值预报精度的提高较为明显。     

Hybrid SSA-ARIMA-ANN Model for Forecasting Daily Rainfall

Rainfall, which is one of the most important hydrologic processes, is influenced by many meteorological factors like climatic change, atmospheric temperature, and atmospheric pressure. Even though there are several stochastic and data driven hydrologic models, accurate forecasting of rainfall, especially smaller time step rainfall forecasting, still remains a challenging task. Effective modelling of rainfall is puzzling due to its inherent erratic nature. This calls for an efficient model for accurately forecasting daily rainfall. Singular Spectrum Analysis (SSA) is a time series analysis tool, which is found to be a very successful data pre-processing algorithm. SSA decomposes a given time series into a finite number of simpler and decipherable components. This study proposes integration of Singular Spectrum Analysis (SSA), Auto Regressive Integrated Moving Average (ARIMA) and Artificial Neural Network (ANN) into a hybrid model (SSA-ARIMA-ANN), which can yield reliable daily rainfall forecasts in a river catchment. In the present study, spatially averaged daily rainfall data over Koyna catchment, Maharashtra has been used. In this study SSA is proposed as a data pre-processing tool to separate stationary and non-stationary components from the rainfall data. Correlogram and Kwiatkowski–Phillips–Schmidt–Shin (KPSS) test has been used to validate the stationary and non-stationary components. In the developed hybrid model, the stationary components of rainfall data are modelled using ARIMA method and non-stationary components are modelled using ANN. The study of statistical performance of the model shows that the hybrid SSA-ARIMA-ANN model could forecast the daily rainfall of the catchment with reliable accuracy.

     

An expert system for predicting shear stress distribution in circular open channels using gene expression programming

The shear stress distribution in circular channels was modeled in this study using gene expression programming (GEP). 173 sets of reliable data were collected under four flow conditions for use in the training and testing stages. The effect of input variables on GEP modeling was studied and 15 different GEP models with individual, binary, ternary, and quaternary input combinations were investigated. The sensitivity analysis results demonstrate that dimensionless parameter y/P, where y is the transverse coordinate, and P is the wetted perimeter, is the most influential parameter with regard to the shear stress distribution in circular channels. GEP model 10, with the parameter y/P and Reynolds number (Re) as inputs, outperformed the other GEP models, with a coefficient of determination of 0.7814 for the testing data set. An equation was derived from the best GEP model and its results were compared with an artificial neural network (ANN) model and an equation based on the Shannon entropy proposed by other researchers. The GEP model, with an average RMSE of 0.0301, exhibits superior performance over the Shannon entropy-based equation, with an average RMSE of 0.1049, and the ANN model, with an average RMSE of 0.2815 for all flow depths.     

A Hybrid Wavelet and Neuro-Fuzzy Model for Forecasting the Monthly Streamflow Data

Researchers have studied to forecast the streamflow in order to develop the water usage policy. They have used not only traditional methods, but also computer aided methods. Some black-box models, like Adaptive Neuro Fuzzy Inference Systems (ANFIS), became very popular for the hydrologic engineering, because of their rapidity and less variation requirements. Wavelet Transform has become a useful tool for the analysis of the variations in time series. In this study, a hybrid model, Wavelet-Neuro Fuzzy (WNF), has been used to forecast the streamflow data of 5 Flow Observation Stations (FOS), which belong to Sakarya Basin in Turkey. In order to evaluate the accuracy performance of the model, Auto Regressive Integrated Moving Average (ARIMA) model has been used with the same data sets. The comparison has been made by Root Mean Squared Errors (RMSE) of the models. Results showed that hybrid WNF model forecasts the streamflow more accurately than ARIMA model.     

Daily Runoff Forecasting Using a Hybrid Model Based on Variational Mode Decomposition and Deep Neural Networks

Accurate and reliable runoff forecasting plays an increasingly important role in the optimal management of water resources. To improve the prediction accuracy, a hybrid model based on variational mode decomposition (VMD) and deep neural networks (DNN), referred to as VMD-DNN, is proposed to perform daily runoff forecasting. First, VMD is applied to decompose the original runoff series into multiple intrinsic mode functions (IMFs), each with a relatively local frequency range. Second, predicted models of decomposed IMFs are established by learning the deep feature values of the DNN. Finally, the ensemble forecasting result is formulated by summing the prediction sub-results of the modelled IMFs. The proposed model is demonstrated using daily runoff series data from the Zhangjiashan Hydrological Station in Jing River, China. To fully illustrate the feasibility and superiority of this approach, the VMD-DNN hybrid model was compared with EMD-DNN, EEMD-DNN, and multi-scale feature extraction -based VMD-DNN, EMD-DNN and EEMD-DNN. The results reveal that the proposed hybrid VMD-DNN model produces the best performance based on the Nash-Sutcliffe efficiency (NSE?=?0.95), root mean square error (RMSE?=?9.92) and mean absolute error (MAE?=?3.82) values. Thus the proposed hybrid VMD-DNN model is a promising new method for daily runoff forecasting.

     

Improving Ann‐Based Short‐Term and Long‐Term Seasonal River Flow Forecasting with Signal Processing Techniques

One of the key elements in achieving sustainable water resources and environmental management is forecasting the future condition of the surface water resources. In this study, the performance of a river flow forecasting model is improved when different input combinations and signal processing techniques are applied on multi‐layer backpropagation neural networks. Haar, Coiflet and Daubechies wavelet analysis are coupled with backpropagation neural networks model to develop hybrid wavelet neural networks models. Different models with different input selections and structures are developed for daily, weekly and monthly river flow forecasting in Ellen Brook River, Western Australia. Comparison of the performance of the hybrid approach with that of the original neural networks indicates that the hybrid models produce significantly better results. The improvement is more substantial for peak values and longer‐term forecasting, in which the Nash–Sutcliffe coefficient of efficiency for monthly river flow forecasting is improved from 0.63 to 0.89 in this study. Copyright © 2014 John Wiley & Sons, Ltd.     

Wavelet Bootstrap Multiple Linear Regression Based Hybrid Modeling for Daily River Discharge Forecasting

A new hybrid model, the wavelet–bootstrap–multiple linear regression (WBMLR) is proposed to explore the potential of wavelet analysis and bootstrap resampling techniques for daily discharge forecasting. The performance of the developed WBMLR model is also compared with five more models: multiple linear regression (MLR), artificial neural network (ANN), wavelet-based MLR (WMLR), wavelet-based ANN (WANN) and wavelet–bootstrap–ANN (WBANN) models. Seven years of discharge data from seven gauging stations in the middle reaches of Mahanadi river basin in India are applied in this study. Significant input vectors are decomposed into discrete wavelet components (DWCs) using discrete wavelet transformation (DWT) to generate wavelet sub time series that are used as inputs to the MLR and ANN models to develop the WMLR and WANN models, respectively. Effective wavelets are selected by considering several types of wavelets with different vanishing moments. WBMLR and WBANN models are developed as ensemble of different WMLR and WANN models, respectively, developed using different realizations of the training dataset generated using bootstrap resampling technique. The results show that the wavelet bootstrap hybrid models (i.e. WBMLR and WBANN) produce significantly better results than the traditional MLR and ANN models. Hybrid models based on MLR (WMLR, WBMLR) perform better than the ANN based hybrid models (WBANN, WANN). The WBMLR and WMLR models simulate the peak discharges better than the WBANN, WANN, MLR and ANN models, whereas the overall performance of WBMLR model is found to be more accurate and reliable than the remaining five models.     

Forecasting of Multi-Step Ahead Reference Evapotranspiration Using Wavelet- Gaussian Process Regression Model

Evapotranspiration is one of the most important components in the optimization of water use in agriculture and water resources management. In recent years, artificial intelligence methods and wavelet based hybrid model have been used for forecasting of hydrological parameters. In present study the application of the Gaussian Process Regression (GPR) and Wavelet-GPR models to forecast multi step ahead daily (1–30 days ahead) reference evapotranspiration at the synoptic station of Zanjan (Iran) were investigated. For this purpose a 10-year statistical period (2000–2009) was considered, 7 years (2000–2006) for training and the final three years (2007–2009) for testing the various models. Various combinations of input data (various lag times) and different kinds of mother wavelets were evaluated. Results showed that, compared to the GPR model, the hybrid model Wavelet-GPR had greater ability and accuracy in forecasting of daily evapotranspiration. Moreover, the use of yearly lag times in the GPR and wavelet-GPR model increased its accuracy. Investigation of various kinds of mother wavelets also indicated that the Meyer wavelet was the most suitable mother wavelet for forecasting of daily reference evapotranspiration. The results showed that by increasing the forecasting time period from 1 to 30 days, the accuracy of the models is reduced (RMSE = 0.068 mm/day for one day ahead and RMSE = 0.816 mm/day for 30 days ahead). Application of the proposed model to summer season showed that the performance of the model at summer season is better than its performance throughout the year.     

Gene-Expression Programming for Short-Term Forecasting of Daily Reference Evapotranspiration Using Public Weather Forecast Information

This study aimed to forecast the daily reference evapotranspiration (ETo) using a gene-expression programming (GEP) algorithm with limited public weather forecast information over Gaoyou station, located in Jiangsu province, China. To calibrate and validate the gene-expression code, important meteorological data and weather forecast information were collected from the local meteorological station and public weather media, respectively. The GEP algebraic formulation was successfully constructed based only on daily minimum and maximum air temperature using the true FAO56 Penman-Monteith (PM) set as reference values. The performance of the models was then assessed using the correlation coefficient (R), root mean squared error (RMSE), root relative squared error (RRSE) and mean absolute error (MAE). The study demonstrated that GEP is able to calibrate ETo (all errors ≤0.990 mm/day, R = 0.832–0.866) and forecast the daily ETo with good accuracy (RMSE = 1.207 mm/day, MAE = 0.902 mm/day, RRSE = 0.629 mm/day, R = 0.777). The model accuracies slightly decreased over a 7-day forecast lead-time. These results suggest that the GEP algorithm can be considered as a deployable tool for ETo forecast to anticipate decision on short-term irrigation schedule in the study zone.     

新安江模型和改进BP神经网络模型在闽江水文预报中的应用

精确的水文预报是防洪减灾中重要的非工程措施,水文模型是开展水文预报最有力的工具。采用LM算法改进了的BP神经网络水文预报模型,以闽江富屯溪流域为例,进行了BP模型和新安江模型在日流量模拟预报中的应用比较。结果表明:两个模型总体均达到水文预报的精度要求,水文预报合格率可达到90%以上;新安江模型在丰水年模拟效果较好,相比而言,BP神经网络模型的模拟精度更高一些;两个模型均可用于闽江流域的水文预报研究。     

Solving Complex Rainfall-Runoff Processes in Semi-Arid Regions Using Hybrid Heuristic Model

In the current research, a hybrid model was proposed to solve the complexity of rainfall-runoff models in semi-arid regions. The proposed hybrid model structure consists of linking two data mining models, namely, Group Method of Data Handling (GMDH) and Generalized Linear Model (GLM). The proposed hybrid model structure consists of two phases. The GMDH model was used in the first phase of the hybrid model to predict daily streamflow. The first phase consists of two sections. In the first section a predictive model is developed using the time series of the daily streamflow. In the second section the rainfall-runoff model was developed. The outputs of the first phase of the hybrid model are used as inputs to the second phase of the hybrid model. The second phase of the hybrid model was developed using the GLM model. The Gomel River in Iraq was selected as a case study. The daily rainfall data and daily streamflow data for the period from January 1, 2004 to December 19, 2016 were used to train and validate the model. The results proved the accuracy of the proposed hybrid model in estimating the daily streamflow of the study area, where the value of R² was 0.92 in the training period and 0.88 in the validation period of the model.

     

Impact of Normalization and Input on ARMAX-ANN Model Performance in Suspended Sediment Load Prediction

The suspended sediment load in rivers is an important parameter in watershed planning and management. Since daily suspended sediment time series contain linear and nonlinear components, existing prediction models are associated with limitations. Therefore, this study introduces a new hybrid model comprising two commonly used stochastic and nonlinear models. The sediment load is first modeled by an autoregressive-moving average with exogenous terms (ARMAX) model. Subsequently, the ARMAX residuals are modeled with an artificial neural network (ANN). For this purpose, discharge (Q) and sediment (S) are considered as model input parameters. Three modeling scenarios are defined to investigate the impact of data normalization on the hybrid model. The exponential and Box-Cox transformation methods are combined into a new data normalization method called mixed transformation. The performance of these methods is then compared. In addition, the impact of the type and number of input combinations on ARMAX-ANN model accuracy is evaluated. To this end, 12 input combinations and 1331 ARMAX and ANN models are verified. The ARMAX model inputs include S, Q and the white noise disturbance term (e), while the ANN model inputs include the ARMAX model results and residuals. Moreover, the hybrid model’s accuracy is compared with the ARMAX and ANN models.