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.     

A Comparative Study of Various Hybrid Wavelet Feedforward Neural Network Models for Runoff Forecasting

Considering network topologies and structures of the artificial neural network (ANN) used in the field of hydrology, one can categorize them into two different generic types: feedforward and feedback (recurrent) networks. Different types of feedforward and recurrent ANNs are available, but multilayer perceptron type of feedforward ANN is most commonly used in hydrology for the development of wavelet coupled neural network (WNN) models. This study is conducted to compare performance of the various wavelet based feedforward artificial neural network (ANN) models. The feedforward ANN types used in the study include the multilayer perceptron neural network (MLPNN), generalized feedforward neural network (GFFNN), radial basis function neural network (RBFNN), modular neural network (MNN) and neuro-fuzzy neural network (NFNN) models. The rainfall-runoff data of four catchments located in different hydro-climatic regions of the world is used in the study. The discrete wavelet transformation (DWT) is used in the present study to decompose input rainfall data using db8 wavelet function. A total of 220 models are developed in this study to evaluate the performance of various feedforward neural network models. Performance of the developed WNN models is compared with their counterpart simple models developed without applying wavelet transformation (WT). The results of the study are further compared with - multiple linear regression (MLR) model which suggest that the WNN models outperformed their counterpart simple models. The hybrid wavelet models developed using MLPNN, the GFFNN and the MNN models performed best among the six selected data driven models explored in the study. Moreover, performance of the three best models is found to be similar and thus the hybrid wavelet GFFNN and the MNN models can be considered as an alternative to the most commonly used hybrid WNN models developed using MLPNN. The study further reveals that the wavelet coupled models outperformed their counterpart simple models only with the parsimonious input vector.     

Error Correction Modelling of Wind Speed Through Hydro-Meteorological Parameters and Mesoscale Model: A Hybrid Approach

Accurate estimation of wind speed is essential for many hydrological applications. One way to generate wind velocity is from the fifth generation PENN/NCAR MM5 mesoscale model. However, there is a problem in using wind speed data in hydrological processes due to large errors obtained from the mesoscale model MM5. The theme of this article has been focused on hybridization of MM5 with four mathematical models (two regression models- the multiple linear regression (MLR) and the nonlinear regression (NLR), and two artificial intelligence models – the artificial neural network (ANN) and the support vector machines (SVMs)) in such a way so that the properly modelled schemes reduce the wind speed errors with the information from other MM5 derived hydro-meteorological parameters. The forward selection method was employed as an input variable selection procedure to examine the model generalization errors. The input variables of this statistical analysis include wind speed, temperature, relative humidity, pressure, solar radiation and rainfall from the MM5. The proposed conjunction structure was calibrated and validated at the Brue catchment, Southwest of England. The study results show that relatively simple models like MLR are useful tools for positively altering the wind speed time series obtaining from the MM5 model. The SVM based hybrid scheme could make a better robust modelling framework capable of capturing the non-linear nature than that of the ANN based scheme. Although the proposed hybrid schemes are applied on error correction modelling in this study, there are further scopes for application in a wide range of areas in conjunction with any higher end models.     

陕西省月平均气温空间插值方法研究

为弥补陕西省气象站点数量有限、空间分布不均等问题,对常用空间插值方法进行比较研究,探寻适宜陕西省气温空间插值方法。根据陕西省内外110个气象站点1981-2010年的月平均温度,选用反距离权重法、普通克里金法与多元线性回归法进行空插值,利用实际验证法进行精度评估。结果表明,考虑了经度、纬度和高程的多元线性回归法的插值精度最高,普通克里金法次之,反距离权重法精度最低;多元线性回归分析法对陕西省气温插值最为适宜。     

Effect of Utilization of Discrete Wavelet Components on Flood Forecasting Performance of Wavelet Based ANFIS Models

Wavelet based flood forecasting models are known to perform better than conventional models, yet the effect of the way wavelet components are combined to develop a model on the forecasting performance, is inadequately investigated. To demonstrate this, two types of wavelet- adaptive neuro-fuzzy inference system (WANFIS), i.e. WANFIS-split data model (WANFIS-SD) and WANFIS-modified time series model (WANFIS-MS) are developed to forecast river water levels with 1-day lead time. To develop these models, first the original level time series (OLTS) is decomposed into discrete wavelet components (DWCs) by discrete wavelet transform (DWT) upto three resolution levels. In WANFIS-SD, all wavelet components are used as inputs while WANFIS-MS ignores the noise wavelet components and utilizes only the effective wavelet components. The effectiveness of the developed models are evaluated through application to two Indian rivers, Kamla and Kosi, which vary significantly in their catchment area and flow patterns. The proposed models are found to forecast river water levels accurately. On comparison, the WANFIS-SD is found to perform better than WANFIS-MS for high flood levels.     

A regional suspended load yield estimation model for ungauged watersheds

Developing regional models using physiographic, climatic, and hydrologic variables is an approach to estimating suspended load yield (SLY) in ungauged watersheds. However, using all the variables might reduce the applicability of these models. Therefore, data reduction techniques (DRTs), e.g., principal component analysis (PCA), Gamma test (GT), and stepwise regression (SR), have been used to select the most effective variables. The artificial neural network (ANN) and multiple linear regression (MLR) are also common tools for SLY modeling. We conducted this study (1) to obtain the most effective variables influencing SLY through DRTs including PCA, GT, and SR, and then, to use them as input data for ANN and MLR; and (2) to provide the best SLY models. Accordingly, we used 14 physiographic, climatic, and hydrologic parameters from 42 watersheds in the Hyrcanian forest region (in northern Iran). The most effective variables as determined through DRTs as well as the original data sets were used as the input data for ANN and MLR in order to provide an SLY model. The results indicated that the SLY models provided by ANN performed much better than the MLR models, and the GT-ANN model was the best. The determination of coefficient, relative error, root mean square error, and bias were 99.9%, 26%, 323 t/year, and 6 t/year in the calibration period, and 70%, 43%, 456 t/year, and 407 t/year in the validation period, respectively. Overall, selecting the main factors that influence SLY and using artificial intelligence tools can be useful for water resources managers to quickly determine the behavior of SLY in ungauged watersheds.     

Development of Bio-Inspired- and Wavelet-Based Hybrid Models for Reconnaissance Drought Index Modeling

The present study aimed to model reconnaissance drought index (RDI) time series at three various time scales (i.e., RDI-6, RDI-9, RDI-12). Two weather stations located at Iran, namely Tehran and Dezful, were selected as the case study. First, support vector regression (SVR) was utilized as the standalone modeling technique. Then, hybrid models were implemented via coupling the standalone SVR with two bio-inspired-based techniques including firefly algorithm (FA) and whale optimization algorithm (WOA) as well as wavelet analysis (W). Accordingly, the hybrid SVR-FA, SVR-WOA, and W-SVR models were proposed. It is worth mentioning that six mother wavelets (i.e., Haar, Daubechies (db2, db4), Coifflet, Symlet, and Fejer-Korovkin) were employed in development of the hybrid W-SVR models. The performance of models was assessed through root mean square error (RMSE), mean absolute error (MAE), Willmott index (WI), and Nash-Sutcliffe efficiency (NSE). Generally, the implemented coupled models illustrated better results than the standalone SVR in modeling the RDI time series of studied locations. Besides, the Coifflet mother wavelet was found to be the best-performing wavelet. The most accurate results were achieved for RDI-12 modeling via the W-SVR utilizing db4(2) at Tehran station (RMSE = 0.253, MAE = 0.174, WI= 0.888, NSE = 0.934) and Coifflet(2) at Dezful station (RMSE = 0.301, MAE = 0.166, WI= 0.910, NSE = 0.936). As a result, the hybrid models developed in the current study, specifically W-SVR ones, can be proposed as suitable alternatives to the single SVR.

     

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.     

基于尺度特征融合的随机森林日供水量预测模型

针对日供水量时间序列的非平稳性和耦合特征的复杂性,引入小波分解技术和随机森林回归模型,构建了基于尺度特征融合的随机森林模型(SF-RF).首先,使用离散小波变换将单一尺度的原始时间序列分解为低、高频尺度的特征序列,提取耦合特征的多尺度信息;然后,使用随机森林回归模型拟合不同尺度特征;最后,线性融合各尺度的拟合结果获得总...     

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。     

考虑黏弹性滞后效应的拱坝位移监控组合模型

位移监控模型需要对拱坝变形性态兼具良好的解释和预测能力。水压-滞后-周期性温度-时效四因子HHST(Hydraulic,Hysteretic,Seasonal and Time)模型能够合理地解释锦屏一级拱坝的黏弹性滞后变形性态。为进一步提升该模型的预测精度,使用支持向量机(SVM)建立有限元计算所得拱坝黏弹性滞后位移与其因果因子之间的隐式关系,再将其融入到HHST模型中,进而基于多元线性回归建立拱坝位移的组合监控模型。以锦屏一级拱坝为例,减少输入因子数的组合模型的预测精度明显高于直接以HHST模型中18个因子作为输入的单一模型;SVM对滞后水压位移分量的预测精度明显高于基于约束最小二乘法的线性回归模型,采用2种滞后水压分量所建组合模型对拱坝变形性态具有相近的解释能力,而采用SVM滞后水压分量建立的组合模型可有效地提高拱坝位移的预测精度,多测点均方误差(MSE)平均降低21.67%,决定系数R²整体提高0.07%。     

Multivariable Time Series Forecasting for Urban Water Demand Based on Temporal Convolutional Network Combining Random Forest Feature Selection and Discrete Wavelet Transform

Urban water demand forecasting is crucial to reduce the waste of water resources and environmental protection. However, the non-stationarity and non-linearity of the water demand series under the influence of multivariate makes water demand prediction one of the long-standing challenges. This paper proposes a new hybrid forecasting model for urban water demand forecasting, which includes temporal convolution neural network (TCN), discrete wavelet transform (DWT) and random forest (RF). In order to improve the model’s forecasting abilities, the RF method is used to rank the factors and remove the less important factors. The dimension of raw data is reduced to improve calculating efficiency and accuracy. Then, the original water demand series is decomposed into different characteristic sub-series of multiple variables with better-behavior by DWT to weaken the fluctuation of original series. At the core of the proposed model, TCN is utilized to establish appropriate prediction models. Finally, to test and validate the proposed model, a real-world multivariate dataset from a water plant in Suzhou, China, is used for comparison experiments with the most recent state-of-the-art models. The results show that the mean absolute percentage error (MAPE) of the proposed model is 1.22% which is smaller than the other benchmark models. The proposed model indicates the only 2.2% of the prediction results have a relative error of more than 5%. It shows that the reliable results of the proposed model can be a superior tool for urban water demand forecasting.

     

Enhancing Long-Term Streamflow Forecasting and Predicting using Periodicity Data Component: Application of Artificial Intelligence

Streamflow forecasting and predicting are significant concern for several applications of water resources and management including flood management, determination of river water potentials, environmental flow analysis, and agriculture and hydro-power generation. Forecasting and predicting of monthly streamflows are investigated by using three heuristic regression techniques, least square support vector regression (LSSVR), multivariate adaptive regression splines (MARS) and M5 Model Tree (M5-Tree). Data from four different stations, Besiri and Malabadi located in Turkey, Hit and Baghdad located in Iraq, are used in the analysis. Cross validation method is employed in the applications. In the first stage of the study, the heuristic regression models are compared with each other and multiple linear regression (MLR) in forecasting one month ahead streamflow of each station, individually. In the second stage, the models are evaluated and compared in predicting streamflow of one station using data of nearby station. The research investigated also the influence of the periodicity component (month number of the year) as an external sub-set in modeling long-term streamflow. In both stages, the comparison results indicate that the LSSVR model generally performs superior to the MARS, M5-Tree and MLR models. In addition, it is seen that adding periodicity as input to the models significantly increase their accuracy in forecasting and predicting monthly streamflows in both stages of the study.     

Multiple Random Forests Modelling for Urban Water Consumption Forecasting

The precise forecasting of water consumption is the basis in water resources planning and management. However, predicting water consumption fluctuations is complicated, given their non-stationary and non-linear characteristics. In this paper, a multiple random forests model, integrated wavelet transform and random forests regression (W-RFR), is proposed for the prediction of daily urban water consumption in southwest of China. Raw time series were first decomposed into low- and high-frequency parts with discrete wavelet transformation (DWT). The random forests regression (RFR) method was then used for prediction using each subseries. In the process, the input and output constructions of the RFR model were proposed for each subseries on the basis of the delay times and the embedding dimension of the attractor reconstruction computed by the C-C method, respectively. The forecasting values of each subseries were summarized as the final results. Four performance criteria, i.e., correlation coefficient (R), mean absolute percentage error (MAPE), normalized root mean square error (NRMSE) and threshold static (TS), were used to evaluate the forecasting capacity of the W-RFR. The results indicated that the W-RFR can capture the basic dynamics of the daily urban water consumption. The forecasted performance of the proposed approach was also compared with those of models, i.e., the RFR and forward feed neural network (FFNN) models. The results indicated that among the models, the precision of the predictions of the proposed model was greater, which is attributed to good feature extractions from the multi-scale perspective and favorable feature learning performance using the decision trees.     

Applying Pedo-transfer Functions to Simulate Spatial Heterogeneity of Cinnamon Soil Water Retention Characteristics in Western Liaoning Province

In this study, by measuring soil water retention characteristics and fitting them to van Genuchten Equation, three types of pedo-transfer functions (PTFs) were estimated using linear regression (MLR3) and nonlinear regression (ENR3) based on three textural classifications, and using linear regression (MLR7) based on seven textural classification. And their abilities to quantify soil water retention characteristics and spatial heterogeneity in field scale were evaluated as well. By comparisons between fitted and PTFs-estimated parameters, the parameters from MLR7 and ENR3 were closer to fitted values than ones from MLR3. The results showed that some complex mathematical approaches such as nonlinear regression, and detailed soil classification may obtain more accurate PTFs. The analysis on spatial heterogeneity of retention characteristics using geostatistics indicated that PTFs-estimated parameters’ semivariances were fitted a spherical model. Great autocorrelation range and proportion of structural variance for MLR3 and MLR7 shows linear regression could express suitably the spatial heterogeneity, but detailed soil textual classification didn’t improve structure of variability.     

Monthly rainfall forecasting by a hybrid neural network of discrete wavelet transformation and deep learning

Rainfall forecast is critical to the management and allocation of water resources. Deep learning is used to predict rainfall time series with high temporal and spatial variability. Discrete wavelet transform (DWT), long-short term memory (LSTM) and dilated causal convolutional neural network (DCCNN) is integrated to build a hybrid model (DWT-CLSTM-DCCNN). Two methods of sample construction are used to train DWT-CLSTM-DCCNN and their effects on the model performance are analyzed. LSTM and DCCNN are built as benchmark models. The forecasting performance of DWT-CLSTM-DCCNN on monthly rainfall data from four major cities in China is evaluated. The results of DWT-CLSTM-DCCNN are compared with those of benchmark models in terms of the mean absolute error (MAE), root mean squared error (RMSE) and Nash-Sutcliffe efficiency (NSE) as well as the forecasting curves. The results show that DWT-CLSTM-DCCNN outperforms the benchmark models in model accuracy and peak and mutational rainfall capture.

     

多元线性回归与GM（1，1）模型耦合预测城市用水量

合理预测城市用水量对于城市的发展有着极其重要的意义。本文首先应用多元回归的方法，采取向前选择变量法进行优选，得到相对最优的回归预测模型。然后利用灰色GM（1，1）模型，预测出规划年每个变量的值，代入多元回归模型，这样充分利用了两种模型的优点，预测精度高，结果更为合理可靠。     

Monthly Rainfall Forecasting Using EEMD-SVR Based on Phase-Space Reconstruction

Rainfall links atmospheric and surficial processes and is one of the most important hydrologic variables. We apply support vector regression (SVR), which has a high generalization capability, to construct a rainfall forecasting model. Before construction of the model, a self-adaptive data analysis methodology called ensemble empirical mode decomposition (EEMD) is used to preprocess a rainfall data series. In addition, the phase-space reconstruction method is implemented to design input vectors for the forecasting model. The proposed hybrid model is applied to forecast the monthly rainfall at a weather station in Changchun, China as a case study. To demonstrate the capacity of the proposed hybrid model, a typical three-layer feed-forward artificial neural network model, an auto-regressive integrated moving average model, and a support vector regression model are constructed. Predictive performance of the models is evaluated based on normalized mean squared error (NMSE), mean absolute percent error (MAPE), Nash–Sutcliffe efficiency (NSE), and the coefficient of correlation (CC). Results indicate that the proposed hybrid model has the lowest NMSE and MAPE values of 0.10 and 14.90, respectively, and the highest NSE and CC values of 0.91 and 0.83, respectively, during the validation period. We conclude that the proposed hybrid model is feasible for monthly rainfall forecast and is better than the models currently in common use.     

Short-term River streamflow modeling using Ensemble-based additive learner approach

Accurate streamflow (Q_t) prediction can provide critical information for urban hydrological management strategies such as flood mitigation, long-term water resources management, land use planning and agricultural and irrigation operations. Since the mid-20th century, Artificial Intelligence (AI) models have been used in a wide range of engineering and scientific fields, and their application has increased in the last few years. In this study, the predictive capabilities of the reduced error pruning tree (REPT) model, used both as a standalone model and within five ensemble-approaches, were evaluated to predict streamflow in the Kurkursar basin in Iran. The ensemble-approaches combined the REPT model with the bootstrap aggregation (BA), random committee (RC), random subspace (RS), additive regression (AR) and disjoint aggregating (DA) (i.e. BA-REPT, RC-REPT, RS-REPT, AR-REPT and DA-REPT). The models were developed using 15 years of daily rainfall and streamflow data for the period 23 September 1997 to 22 September 2012. A set of eight different input scenarios was constructed using different combinations of the input variables to find the most effective scenario based on the linear correlation coefficient. A comprehensive suite of graphical (time-variation graph, scatter-plot, violin plot and Taylor diagram) and quantitative metrics (root mean square error (RMSE), mean absolute error (MAE), Nash-Sutcliff efficiency (NSE), Percent of BIAS (PBIAS) and the ratio of RMSE to the standard deviation of observation (RSR)) was applied to evaluate the prediction accuracy of the six models developed. The outcomes indicated that all models performed well but the AR-REPT outperformed all the other models by rendering lower errors and higher precision across a number of statistical measures. The use of the BA, RC, RS, AR and DA models enhanced the performance of the standalone REPT model by about 26.82%, 18.91%, 7.69%, 28.99% and 28.05% respectively.     

包头市市区居民生活用水量预测分析

用水量预测对区域水资源规划、利用和管理提供重要依据.运用灰色关联度分析法分析包头市市区居民生活用水量影响因素的基础上,分别建立多元线性回归模型、灰色GM(1,1)模型及灰色线性组合模型对该地区2009年和2010年的生活用水量进行预测分析,同时比较了三个模型的预测精度.结果表明:城市居民生活用水量与城市用水人口、人均居住面积和水价的关联度较高;2009年和2010年用水量的预测采用组合灰色模型精度最高,相对误差分别为13.6％％和6.5％,均方根相对误差为10.7％.组合预测模型的预测精度明显优于单一模型,使结果更加准确、合理,符合实际情况.