Improving Rainfall Forecasting Efficiency Using Modified Adaptive Neuro-Fuzzy Inference System (MANFIS)

Rainfall is one of the most complicated effective hydrologic processes in runoff prediction and water management. The adaptive neuro-fuzzy inference system (ANFIS) has been widely used for modeling different kinds of nonlinear systems including rainfall forecasting. Adaptive Neuro-Fuzzy Inference Systems (ANFIS) combines the capabilities of Artificial Neural Networks (ANN) and Fuzzy Inference Systems (FIS) to solve different kinds of problems, especially efficient in rainfall prediction. This paper after reconsidering conventional ANFIS architecture brings up a modified ANFlS (MANFlS) structure developed with attention to making ANFIS technique more efficient regarding to Root Mean Square Error (RMSE), Correlation Coefficient (R ²), Root Mean Absolute Error (RMAE), Signal to Noise Ratio (SNR) and computing epoch. The modified ANFIS (MANFIS) architecture is simpler than conventional ANFIS with nearly the same performance for modeling nonlinear systems. In this study, two scenarios were introduced; in the first scenario, monthly rainfall was used solely as an input in different time delays from the time (t) to the time (t-4) to conventional ANFIS, second scenario used the modified ANFIS to improve the rainfall forecasting efficiency. The result showed that the model based Modified ANFIS performed higher rainfall forecasting accuracy; low errors and lower computational complexity (total number of fitting parameters and convergence epochs) compared with the conventional ANFIS model.     

A Wavelet-ANFIS Hybrid Model for Groundwater Level Forecasting for Different Prediction Periods

Artificial neural network (ANN) and Adaptive Neuro-Fuzzy Inference System (ANFIS) have an extensive range of applications in water resources management. Wavelet transformation as a preprocessing approach can improve the ability of a forecasting model by capturing useful information on various resolution levels. The objective of this research is to compare several data-driven models for forecasting groundwater level for different prediction periods. In this study, a number of model structures for Artificial Neural Network (ANN), Adaptive Neuro-Fuzzy Inference System (ANFIS), Wavelet-ANN and Wavelet-ANFIS models have been compared to evaluate their performances to forecast groundwater level with 1, 2, 3 and 4 months ahead under two case studies in two sub-basins. It was demonstrated that wavelet transform can improve accuracy of groundwater level forecasting. It has been also shown that the forecasts made by Wavelet-ANFIS models are more accurate than those by ANN, ANFIS and Wavelet-ANN models. This study confirms that the optimum number of neurons in the hidden layer cannot be always determined by using a specific formula but trial-and-error method. The decomposition level in wavelet transform should be determined according to the periodicity and seasonality of data series. The prediction of these models is more accurate for 1 and 2 months ahead (for example RMSE?=?0.12, E?=?0.93 and R ²?=?0.99 for wavelet-ANFIS model for 1 month ahead) than for 3 and 4 months ahead (for example RMSE?=?2.07, E?=?0.63 and R ²?=?0.91 for wavelet-ANFIS model for 4 months ahead).     

Streamflow Forecasting Using Four Wavelet Transformation Combinations Approaches with Data-Driven Models: A Comparative Study

This study investigates the use of wavelet transformation (WT) as preprocessing tool in data-driven models (DDMs) for forecasting streamflow 7 days ahead. WT used are Continuous wavelet transformation (CWT), discrete wavelet transformation (DWT), and a new proposed combination of CWT and DWT, namely discrete continuous wavelet transformation (DCWT). In addition to these three different WTs, the single DDMs were used also to create four different schematic layouts. The DDMs applied were artificial neural network (ANN), adaptive neuro-fuzzy inference system (ANFIS), and support vector machines (SVM). The lagged rainfall, temperature, and streamflow were incorporated as inputs into the WT-DDMs. It was found that CWT improved the forecasting accuracy of models which only included the rainfall and temperature but not the streamflow. Moreover, DWT improved the performance dramatically for the models with streamflow. Notably, DWT layout outperformed CWT layout in general while CWT layouts resulted in higher improvement to the models with rainfall and temperature only. The proposed DCWT in which CWT applied on the rainfall and temperature variables and DWT applied on the streamflow improved the forecasting ability in several models combinations when ANN was applied. Nevertheless, improvement in the forecasting accuracy was deteriorated in those with SVM while no improvement was observed with ANFIS. ANN outperformed both ANFIS and SVM while ANFIS performed better than SVM.     

Monthly Rainfall Prediction Using Wavelet Neural Network Analysis

Rainfall is one of the most significant parameters in a hydrological model. Several models have been developed to analyze and predict the rainfall forecast. In recent years, wavelet techniques have been widely applied to various water resources research because of their time-frequency representation. In this paper an attempt has been made to find an alternative method for rainfall prediction by combining the wavelet technique with Artificial Neural Network (ANN). The wavelet and ANN models have been applied to monthly rainfall data of Darjeeling rain gauge station. The calibration and validation performance of the models is evaluated with appropriate statistical methods. The results of monthly rainfall series modeling indicate that the performances of wavelet neural network models are more effective than the ANN models.     

Estimation of Monthly Mean Reference Evapotranspiration in Turkey

Monthly mean reference evapotranspiration (ET ₀ ) is estimated using adaptive network based fuzzy inference system (ANFIS) and artificial neural network (ANN) models. Various combinations of long-term average monthly climatic data of wind speed, air temperature, relative humidity, and solar radiation, recorded at stations in Turkey, are used as inputs to the ANFIS and ANN models so as to calculate ET ₀ given by the FAO-56 PM (Penman-Monteith) equation. First, a comparison is made among the estimates provided by the ANFIS and ANN models and those by the empirical methods of Hargreaves and Ritchie. Next, the empirical models are calibrated using the ET ₀ values given by FAO-56 PM, and the estimates by the ANFIS and ANN techniques are compared with those of the calibrated models. Mean square error, mean absolute error, and determination coefficient statistics are used as comparison criteria for evaluation of performances of all the models considered. Based on these evaluations, it is found that the ANFIS and ANN schemes can be employed successfully in modeling the monthly mean ET ₀ , because both approaches yield better estimates than the classical methods, and yet ANFIS being slightly more successful than ANN.     

ANN、ANFIS和AR模型在日径流时间序列预测中的应用比较

水文预测是水文学为经济和社会服务的重要方面。其预报结果不仅能为水库优化调度提供决策支持,而且对水电系统的经济运行、航运以及防洪等方面具有重大意义。自回归模型(AR模型)、人工神经网络(ANN)和自适应神经模糊推理系统(ANFIS)在日径流时间序列中应用广泛。将这三种模型应用于桐子林的日径流时间序列预测中,不仅采用纳什系数(NS系数)、均方根误差(RMSE)和平均相对误差(MARE)为评价指标,对三种模型的综合性能进行了比较。而且,在对三种模型预测结果的平均相对误差的阈值统计基础上,分析了三种模型的预测误差分布。同时,通过研究模型性能指标随预见期的变化过程评价了三种模型不同预见期下的预测能力。结果表明ANFIS相对于ANN和AR模型不仅具有更好的模拟能力、泛化能力,而且在相同的预见期下具有更优的模型性能,可以作为日径流时间序列预测的推荐模型。     

Improving ANFIS Based Model for Long-term Dam Inflow Prediction by Incorporating Monthly Rainfall Forecasts

The necessity of long-term dam inflow forecast has been recognized for many years. Despite numerous studies, the accurate long-term dam inflow prediction is still a challenging task. This paper presents an adaptive neuro-fuzzy inference system (ANFIS) based model and evaluates the applicability of categorical rainfall forecast for improvement of monthly dam inflow prediction. In order to obtain appropriate ANFIS model configuration for dam inflow prediction, several models were trained and tested using various numbers of input variables i.e. monthly observed rainfall, relative humidity, temperature, dam inflow and categorical monthly rainfall forecast. The ANFIS based models were configured and evaluated for six major dams of South Korea i.e. Andong, Chungju, Daecheong, Guesan, Soyang and Sumjin having high, medium and low reservoir capacity. The results showed significant improvement in dam inflow prediction for all the selected dams using the ANFIS based model with categorical rainfall forecast compared to the ANFIS based model with only preceding month’s dam inflow and weather data.     

Improving Flood Forecasting in a Developing Country: A Comparative Study of Stepwise Multiple Linear Regression and Artificial Neural Network

Due to limited data sources, practical situations in most developing countries favor black-box models in real time operations. In a simple and robust approach, this study examines performances of stepwise multiple linear regression (SMLR) and artificial neural network (ANN) models, as tools for multi-step forecasting Chindwin River floods in northern Myanmar. Future river stages are modeled using past water levels and rainfall at the forecasting station as well as at the hydrologically connected upstream station. The developed models are calibrated with flood season data from 1990 to 2007 and validated with data from 2008 to 2011. Model performances are compared for 1- to 5-day ahead forecasts. With a high accuracy, both candidate models performed well for forecasting the full range of flood levels. The ANN models were superior to the SMLR models, particularly in predicting the extreme floods. Correlation analysis was found to be useful for determining the initial input variables. Contribution of upstream data to both models could improve the forecasting performance with higher R ² values and lower errors. Considering the commonly available data in the region as primary predictors, the results would be useful for real time flood forecasting, avoiding the complexity of physical processes.     

Soil Water Simulation and Predication Using Stochastic Models Based on LS-SVM for Red Soil Region of China

The seasonal drought and the low available soil moisture affect the agricultural production in red soil region, China. Therefore, it is necessary to simulate and predict the dynamic changes of soil water in the field. Presently, dynamic model has been applied to obtain the soil water information. While the simulation accuracy of dynamic model depends on many complicated parameters, which are difficult to obtain. In this study, the various nonlinear Stochastic Model of soil water simulation systems and chaotic time series analysis methods of prediction systems had been set up. In the nonlinear Stochastic Model of soil water simulation systems, the daily soil water content simulated by Least squares support vector machine (LS-SVM) with the meteorological factors had more stabilities and advantages in soil water simulation performance over the Back Propagation Artificial Neural Network (BP-ANN) and Adaptive Neuro-Fuzzy Inference System (ANFIS). In chaotic time series analysis method of prediction systems, the various signal preprocessing methods including the appropriate de-noising methods and wavelet decomposition methods were applied to preprocess the original chaotic soil water signal. The results of the prediction systems showed that the appropriate de-noising methods and the tendency of wavelet transformation had less effect on the delay time (τ) and embedding dimension (m). The de-noising methods may ignore the detail information of the soil water signal, while the appropriate wavelet transformation to get smaller Maximum Lyapunov Exponent (λ₁) of the chaotic soil water signal detail and tendency information can improve the predicting capacity.     

A Multivariate ANN-Wavelet Approach for Rainfall–Runoff Modeling

Without a doubt the first step in any water resources management is the rainfall–runoff modeling over the watershed. However considering high stochastic property of the process, many models are being still developed in order to define such a complex phenomenon in the field of hydrologic engineering. Recently Artificial Neural Network (ANN) as a non-linear inter-extrapolator is extensively used by hydrologists for rainfall–runoff modeling as well as other fields of hydrology. In the current research, the wavelet analysis was linked to the ANN concept for modeling Ligvanchai watershed rainfall–runoff process at Tabriz, Iran. For this purpose the main time series of two variables, rainfall and runoff, were decomposed to some multi-frequently time series by wavelet theory, then these time series were imposed as input data to the ANN to predict the runoff discharge 1 day ahead. The obtained results show the proposed model can predict both short and long term runoff discharges because of using multi-scale time series of rainfall and runoff data as the ANN input layer.     

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.     

Subset Modeling Basis ANFIS for Prediction of the Reference Evapotranspiration

The study investigates accuracy of a new modeling scheme, subset adaptive neuro fuzzy inference system (subset ANFIS), in estimating the daily reference evapotranspiration (ET₀). Daily weather data of relative humidity, solar radiation, air temperature, and wind speed from three stations in Central Anatolian Region of Turkey were utilized as input to the applied models. The input data set for modeling the ET₀ was divided to several subsets to calibrate the local data using a local modeling-based ANFIS. The estimates obtained from subset ANFIS models were compared with those of the M5 model tree (M5Tree), ANFIS models and ANN. Mean absolute error (MAE), root mean square error (RMSE), and model efficiency factor criteria were applied for analysis of models. The accuracy of M5Tree (from 15.3% to 32.5% in RMSE, from 14.4% to 24.2% in MAE), ANN (from 24.3% to 65.3% in RMSE, from 34.1% to 47% in MAE) and ANFIS (from 17.4% to 35.4% in RMSE, from 10.8% to 28.3% in MAE) models was significantly increased using subset ANFIS for estimating da ily ET_0.     

Application of Several Data-Driven Techniques for Predicting Groundwater Level

In this study, several data-driven techniques including system identification, time series, and adaptive neuro-fuzzy inference system (ANFIS) models were applied to predict groundwater level for different forecasting period. The results showed that ANFIS models out-perform both time series and system identification models. ANFIS model in which preprocessed data using fuzzy interface system is used as input for artificial neural network (ANN) can cope with non-linear nature of time series so it can perform better than others. It was also demonstrated that all above mentioned approaches could model groundwater level for 1 and 2 months ahead appropriately but for 3 months ahead the performance of the models was not satisfactory.     

Rainfall Pattern Forecasting Using Novel Hybrid Intelligent Model Based ANFIS-FFA

In this study, a new hybrid model integrated adaptive neuro fuzzy inference system with Firefly Optimization algorithm (ANFIS-FFA), is proposed for forecasting monthly rainfall with one-month lead time. The proposed ANFIS-FFA model is compared with standard ANFIS model, achieved using predictor-predictand data from the Pahang river catchment located in the Malaysian Peninsular. To develop the predictive models, a total of fifteen years of data were selected, split into nine years for training and six years for testing the accuracy of the proposed ANFIS-FFA model. To attain optimal models, several input combinations of antecedents’ rainfall data were used as predictor variables with sixteen different model combination considered for rainfall prediction. The performances of ANFIS-FFA models were evaluated using five statistical indices: the coefficient of determination (R ² ), Nash-Sutcliffe efficiency (NSE), Willmott’s Index (WI), root mean square error (RMSE) and mean absolute error (MAE). The results attained show that, the ANFIS-FFA model performed better than the standard ANFIS model, with high values of R ² , NSE and WI and low values of RMSE and MAE. In test phase, the monthly rainfall predictions using ANFIS-FFA yielded R ² , NSE and WI of about 0.999, 0.998 and 0.999, respectively, while the RMSE and MAE values were found to be about 0.272 mm and 0.133 mm, respectively. It was also evident that the performances of the ANFIS-FFA and ANFIS models were very much governed by the input data size where the ANFIS-FFA model resulted in an increase in the value of R ² , NSE and WI from 0.463, 0.207 and 0.548, using only one antecedent month of data as an input (t-1), to almost 0.999, 0.998 and 0.999, respectively, using five antecedent months of predictor data (t-1, t-2, t-3, t-6, t-12, t-24). We ascertain that the ANFIS-FFA is a prudent modelling approach that could be adopted for the simulation of monthly rainfall in the present study region.     

Artificial Neural Network and Support Vector Machine Models for Inflow Prediction of Dam Reservoir (Case Study: Zayandehroud Dam Reservoir)

Inflow prediction of reservoirs is of considerable importance due to its application in water resources management related to downstream water release planning and flood protection. Therefore, in this research, different new input patterns for predicting inflow to Zayandehroud dam reservoir is proposed employing artificial neural network (ANN) and support vector machine (SVM) models. Nine different models with different patterns of input data such as inflow to the dam reservoir considering time duration lags, time index, and monthly rainfall of Ghaleh-Shahrokh station have been proposed to predict the inflow to the dam reservoir. Comparison of the results indicates that the ninth proposed model has the least error for inflow prediction in which the results of SVM model outperform those of ANN model. That is, the least error has been obtained using the ninth SVM (ANN) model with correlation coefficient (R) values of 0.8962 (0.89296), 0.9303 (0.92983) and 0.9622 (0.95333) and root mean squared error (RMSE) values of 47.9346 (48.5441), 42.69093 (43.748) and 23.56193 (28.5125) for training, validation and test data, respectively.

     

Forecasting Daily Streamflow for Basins with Different Physical Characteristics through Data-Driven Methods

Modelling streamflow is essential for activities, such as flood control, drought mitigation, and water resources utilization and management. Artificial neural network (ANN), adaptive neuro-fuzzy inference system (ANFIS), and support vector machines (SVM) are techniques that are frequently used in hydrology to specifically model streamflow. This study compares the accuracy of ANN, ANFIS, and SVM in forecasting the daily streamflow with the traditional approach known as autoregressive (AR) model for basins with different physical characteristics. The accuracies of the models are compared for three basins, that is, 1801, 1805, and 1822, at the Seyhan River Basin in Turkey. The comparison was performed by using coefficient of efficiency, index of agreement, and root-mean-square error. Results indicate that ANN and ANFIS are more accurate than AR and SVM for all the basins. ANN and ANFIS perform similarly, while ANN outperformed ANFIS. Among the models used, the ANN demonstrates the highest performance in forecasting the peak flood values. This study also finds that physical characteristics, such as small area, high slope, and high elevation variation, and streamflow variance deteriorate the accuracy of the methods.     

Utilizing RBF-NN and ANFIS Methods for Multi-Lead ahead Prediction Model of Evaporation from Reservoir

Evaporation as a major meteorological component of the hydrologic cycle plays a key role in water resources studies and climate change. The estimation of evaporation is a complex and unsteady process, so it is difficult to derive an accurate physical-based formula to represent all parameters that effect on estimate evaporation. Artificial intelligence-based methods may provide reliable prediction models for several applications in engineering. In this research have been introduced twelve networks with the RBF-NN and ANFIS methods. These models have applied to prediction daily evaporation at Layang reservoir, located in the southeast part of Malaysia. The used meteorological data set to develop the models for prediction daily evaporation rate from water surface for Layang reservoir includes daily air temperature, solar radiation, pan evaporation, and relative humidity that measured at a case study for fourteen years. The obtained result denote to the superiority of the RBF-NN models on the ANFIS models. A comparison of the model performance between RBF-NN and ANFIS models indicated that RBF-NN method presents the best estimates of daily evaporation rate with the minimum MSE 0.0471 , MAE 0.0032, RE and maximum R² 0.963.     

基于ASWPD-BO-GRU的月径流量预测模型

为提高月径流量预测精度,并针对传统分解集成径流预测模型错误使用未来数据的问题,提出并建立了基于自适应小波包分解（ASWPD）和贝叶斯优化（BO）的门控循环单元（GRU）月径流量预测模型（ASWPD-BO-GRU）。首先,利用ASWPD对原始月径流量时间序列进行分解,在不使用未来数据的前提下得到4个相对规律的分解子序列,以降低预测难度;然后,利用BO优选分解后的子序列对应的GRU模型超参数;最终,对每个子序列进行预测,将预测结果相加重组得出月径流量预测结果。将提出并建立的模型应用于黑河流域莺落峡水文站月径流量预测中,并与GRU、BO-GRU、WPD-BO-GRU模型（基于传统分解思想对原始月径流量时间序列整体进行分解的预测模型）的预测结果进行对比。结果表明：ASWPD-BO-GRU模型的纳什效率系数（NSE）为0.89,在实例应用中预测精度最高,说明ASWPD-BO-GRU模型在正确分解的前提下具有较高的预测精度和更强的泛化能力。     

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.     

Artificial Neural Network (ANN) Based Modeling for Karstic Groundwater Level Simulation

A relatively new method of addressing different hydrological problems is the use of artificial neural networks (ANN). In groundwater management ANNs are usually used to predict the hydraulic head at a well location. ANNs can prove to be very useful because, unlike numerical groundwater models, they are very easy to implement in karstic regions without the need of explicit knowledge of the exact flow conduit geometry and they avoid the creation of extremely complex models in the rare cases when all the necessary information is available. With hydrological parameters like rainfall and temperature, as well as with hydrogeological parameters like pumping rates from nearby wells as input, the ANN applies a black box approach and yields the simulated hydraulic head. During the calibration process the network is trained using a set of available field data and its performance is evaluated with a different set. Available measured data from Edward??s aquifer in Texas, USA are used in this work to train and evaluate the proposed ANN. The Edwards Aquifer is a unique groundwater system and one of the most prolific artesian aquifers in the world. The present work focuses on simulation of hydraulic head change at an observation well in the area. The adopted ANN is a classic fully connected multilayer perceptron, with two hidden layers. All input parameters are directly or indirectly connected to the aquatic equilibrium and the ANN is treated as a sophisticated analogue to empirical models of the past. A correlation analysis of the measured data is used to determine the time lag between the current day and the day used for input of the measured rainfall levels. After the calibration process the testing data were used in order to check the ability of the ANN to interpolate or extrapolate in other regions, not used in the training procedure. The results show that there is a need for exact knowledge of pumping from each well in karstic aquifers as it is difficult to simulate the sudden drops and rises, which in this case can be more than 6 ft (approx. 2 m). That aside, the ANN is still a useful way to simulate karstic aquifers that are difficult to be simulated by numerical groundwater models.