Mathematical expression of discharge capacity of compound open channels using MARS technique

In this paper, analytical methods, artificial neural network (ANN) and multivariate adaptive regression splines (MARS) techniques were utilised to estimate the discharge capacity of compound open channels (COC). To this end, related datasets were collected from literature. The results showed that the divided channel method with a coefficient of determination (R ²) value of 0.76 and root mean square error (RMSE) value of 0.162 has the best performance, among the various analytical methods tested. The performance of applied soft computing models with R ²=0.97 and RMSE = 0.03 was found to be more accurate than analytical approaches. Comparison of MARS with the ANN model, in terms of developed discrepancy ratio (DDR) index, showed that the accuracy of MARS model was better than that of MLP model. Reviewing the structure of the derived MARS model showed that the longitudinal slope of the channel (S), relative flow depth (H _r ) and relative area (A _r ) have a high impact on modelling and forecasting the discharge capacity of COCs.     

Suspended sediment load prediction of river systems: GEP approach

This study presents gene expression programming (GEP), an extension of genetic programming, as an alternative approach to modeling the suspended sediment load relationship for the three Malaysian rivers. In this study, adaptive neuro-fuzzy inference system (ANFIS), regression model, and GEP approaches were developed to predict suspended load in three Malaysian rivers: Muda River, Langat River, and Kurau River [ANFIS (R ²?=?0.93, root mean square error (RMSE)?=?3.19, and average error (AE)?=?1.12) and regression model (R ²?=?0.63, RMSE?=?13.96, and AE?=?12.69)]. Additionally, the explicit formulations of the developed GEP models are presented (R ²?=?0.88, RMSE?=?5.19, and AE?=?6.5). The performance of the GEP model was found to be acceptable compare to ANFIS and better than the conventional models.     

A comparative study of shallow groundwater level simulation with WA–ANN and ITS model in a coastal island of south China

Accurate and reliable prediction of shallow groundwater level is a critical component in water resources management. Two nonlinear models, WA–ANN method based on discrete wavelet transform (WA) and artificial neural network (ANN) and integrated time series (ITS) model, were developed to predict groundwater level fluctuations of a shallow coastal aquifer (Fujian Province, China). The two models were testified with the monitored groundwater level from 2000 to 2011. Two representative wells are selected with different locations within the study area. The error criteria were estimated using the coefficient of determination (R ²), Nash–Sutcliffe model efficiency coefficient (E), and root-mean-square error (RMSE). The best model was determined based on the RMSE of prediction using independent test data set. The WA–ANN models were found to provide more accurate monthly average groundwater level forecasts compared to the ITS models. The results of the study indicate the potential of WA–ANN models in forecasting groundwater levels. It is recommended that additional studies explore this proposed method, which can be used in turn to facilitate the development and implementation of more effective and sustainable groundwater management strategies.     

Predicting longitudinal dispersion coefficient using ANN with metaheuristic training algorithms

A reliable prediction of dispersion coefficient can provide valuable information for environmental scientists and river engineers as well. The main objective of this study is to apply intelligence techniques for predicting longitudinal dispersion coefficient in rivers. In this regard, artificial neural network (ANN) models were developed. Four different metaheuristic algorithms including genetic algorithm (GA), imperialist competitive algorithm (ICA), bee algorithm (BA) and cuckoo search (CS) algorithm were employed to train the ANN models. The results obtained through the optimization algorithms were compared with the Levenberg–Marquardt (LM) algorithm (conventional algorithm for training ANN). Overall, a relatively high correlation between measured and predicted values of dispersion coefficient was observed when the ANN models trained with the optimization algorithms. This study demonstrates that the metaheuristic algorithms can be successfully applied to make an improvement on the performance of the conventional ANN models. Also, the CS, ICA and BA algorithms remarkably outperform the GA and LM algorithms to train the ANN model. The results show superiority of the performance of the proposed model over the previous equations in terms of DR, R ² and RMSE.     

Application of “panel-data” modeling to predict groundwater levels in the Neishaboor Plain, Iran

The aim of this research was to predict groundwater levels in the Neishaboor plain, Iran, using a ??panel-data?? model. Panel-data analysis endows regression analysis with both spatial and temporal dimensions. The spatial dimension pertains to a set of cross-sectional units of observation. The temporal dimension pertains to periodic observations of a set of variables characterizing these cross-sectional units over a particular time span. Firstly, the available observation wells in the Neishaboor plain were clustered according to their fluctuation behavior using the ??Ward?? method, which resulted in six areal zones. Then, for each cluster, an observation well was selected as its representative, and for each zone, values of monthly precipitation and temperature, as independent variables, were estimated by the inverse-distance method. Finally, the performance of different panel-data regression models such as fixed-effects and random-effects models were investigated. The results showed that the two-way fixed-effects model was superior. The performance indicators for this model (R ²?=?0.97, RMSE?=?0.05?m and ME?=?0.81?m) reveal the effectiveness of the method. In addition, the results were compared with the results of an artificial-neural-network (ANN) model, which demonstrated the superiority of the panel-data model over the ANN model.     

Predicting saturated hydraulic conductivity using particle swarm optimization and genetic algorithm

Soil saturated hydraulic conductivity (K_s) is considered as soil basic hydraulic property, and its precision estimation is a key element in modeling water flow and solute transport processes both in the saturated and vadose zones. Although some predictive methods (e.g., pedotransfer functions, PTFs) have been proposed to indirectly predict K_s, the accuracy of these methods still needs to be improved. In this study, some easily available soil properties (e.g., particle size distribution, organic carbon, calcium carbonate content, electrical conductivity, and soil bulk density) are employed as input variables to predict K_s using a fuzzy inference system (FIS) trained by two different optimization techniques: particle swarm optimization (PSO) and genetic algorithm (GA). To verify the derived FIS, 113 soil samples were taken, and their required physical properties were measured (113 sample points?×?7 factors?=?791 input data). The initial FIS is compared with two methods: FIS trained by PSO (PSO-FIS) and FIS trained by GA (GA-FIS). Based on experimental results, all three methods are compared according to some evaluation criteria including correlation coefficient (r), modeling efficiency (EF), coefficient of determination (CD), root mean square error (RMSE), and maximum error (ME) statistics. The results showed that the PSO-FIS model achieved a higher level of modeling efficiency and coefficient of determination (R²) in comparison with the initial FIS and the GA-FIS model. EF and R² values obtained by the developed PSO-FIS model were 0.69 and 0.72, whereas they were 0.63 and 0.54 for the GA-FIS model. Moreover, the results of ME and RMSE indices showed that the PSO-FIS model can estimate soil saturated hydraulic conductivity more accurate than the GA-FIS model with ME?=?10.4 versus 11.5 and RMSE?=?5.2 versus 5.5 for PSO-FIS and GA-FIS, respectively.     

Artificial neural network study of observed pattern of scour depth around bridge piers

An artificial neural networks (ANN) model is developed to study the observed pattern of local scour at bridge piers using an FHWA (Federal Highway Administration) data set composed of 380 measurements at 56 bridges in 13 states. Various ANN estimates of observed pier scour depth on different choices of input variables are examined. Reducing the number of variables from 14 to 9 has negligible effect on the coefficient of determination, R², (0.73 vs. 0.72). Further sensitivity analysis indicates that pier scour depth can be estimated using only four variables: pier shape and skew, flow depth and velocity with a coefficient of determination of 0.81, suggesting that inclusion of some variables actually diminishes the quality of ANN predictions of short term observed pattern of scour. The ANN estimates indicate that flow depth and flow velocity make up 66% of the coefficient of determination.     

Monthly reservoir inflow forecasting using a new hybrid SARIMA genetic programming approach

Forecasting reservoir inflow is one of the most important components of water resources and hydroelectric systems operation management. Seasonal autoregressive integrated moving average (SARIMA) models have been frequently used for predicting river flow. SARIMA models are linear and do not consider the random component of statistical data. To overcome this shortcoming, monthly inflow is predicted in this study based on a combination of seasonal autoregressive integrated moving average (SARIMA) and gene expression programming (GEP) models, which is a new hybrid method (SARIMA–GEP). To this end, a four-step process is employed. First, the monthly inflow datasets are pre-processed. Second, the datasets are modelled linearly with SARIMA and in the third stage, the non-linearity of residual series caused by linear modelling is evaluated. After confirming the non-linearity, the residuals are modelled in the fourth step using a gene expression programming (GEP) method. The proposed hybrid model is employed to predict the monthly inflow to the Jamishan Dam in west Iran. Thirty years’ worth of site measurements of monthly reservoir dam inflow with extreme seasonal variations are used. The results of this hybrid model (SARIMA–GEP) are compared with SARIMA, GEP, artificial neural network (ANN) and SARIMA–ANN models. The results indicate that the SARIMA–GEP model (R ²=78.8, VAF =78.8, RMSE =0.89, MAPE =43.4, CRM =0.053) outperforms SARIMA and GEP and SARIMA–ANN (R ²=68.3, VAF =66.4, RMSE =1.12, MAPE =56.6, CRM =0.032) displays better performance than the SARIMA and ANN models. A comparison of the two hybrid models indicates the superiority of SARIMA–GEP over the SARIMA–ANN model.     

Assessment of a conceptual hydrological model and artificial neural networks for daily outflows forecasting

Artificial neural networks (ANNs) are used by hydrologists and engineers to forecast flows at the outlet of a watershed. They are employed in particular where hydrological data are limited. Despite these developments, practitioners still prefer conventional hydrological models. This study applied the standard conceptual HEC-HMS’s soil moisture accounting (SMA) algorithm and the multi layer perceptron (MLP) for forecasting daily outflows at the outlet of Khosrow Shirin watershed in Iran. The MLP [optimized with the scaled conjugate gradient] used the logistic and tangent sigmoid activation functions resulting into 12 ANNs. The R ² and RMSE values for the best trained MPLs using the tangent and logistic sigmoid transfer function were 0.87, 1.875 m³ s^?1 and 0.81, 2.297 m³ s^?1, respectively. The results showed that MLPs optimized with the tangent sigmoid predicted peak flows and annual flood volumes more accurately than the HEC-HMS model with the SMA algorithm, with R ² and RMSE values equal to 0.87, 0.84 and 1.875 and 2.1 m³ s^?1, respectively. Also, an MLP is easier to develop due to using a simple trial and error procedure. Practitioners of hydrologic modeling and flood flow forecasting may consider this study as an example of the capability of the ANN for real world flow forecasting.     

An application of artificial intelligence for rainfall-runoff modeling

This study proposes an application of two techniques of artificial intelligence (AI) for rainfall-runoff modeling: the artificial neural networks (ANN) and the evolutionary computation (EC). Two different ANN techniques, the feed forward back propagation (FFBP) and generalized regression neural network (GRNN) methods are compared with one EC method, Gene Expression Programming (GEP) which is a new evolutionary algorithm that evolves computer programs. The daily hydrometeorological data of three rainfall stations and one streamflow station for Juniata River Basin in Pennsylvania state of USA are taken into consideration in the model development. Statistical parameters such as average, standard deviation, coefficient of variation, skewness, minimum and maximum values, as well as criteria such as mean square error (MSE) and determination coefficient (R ²) are used to measure the performance of the models. The results indicate that the proposed genetic programming (GP) formulation performs quite well compared to results obtained by ANNs and is quite practical for use. It is concluded from the results that GEP can be proposed as an alternative to ANN models.     

Determination and prediction of standardized precipitation index (SPI) using TRMM data in arid ecosystems

Drought over a period threatens the water resources, agriculture, and socioeconomic activities. Therefore, it is crucial for decision makers to have a realistic anticipation of drought events to mitigate its impacts. Hence, this research aims at using the standardized precipitation index (SPI) to predict drought through time series analysis techniques. These adopted techniques are autoregressive integrating moving average (ARIMA) and feed-forward backpropagation neural network (FBNN) with different activation functions (sigmoid, bipolar sigmoid, and hyperbolic tangent). After that, the adequacy of these two techniques in predicting the drought conditions has been examined under arid ecosystems. The monthly precipitation data used in calculating the SPI time series (SPI 3, 6, 12, and 24 timescales) have been obtained from the tropical rainfall measuring mission (TRMM). The prediction of SPI was carried out and compared over six lead times from 1 to 6 using the model performance statistics (coefficient of correlation (R), mean absolute error (MAE), and root mean square error (RMSE)). The overall results prove an excellent performance of both predicting models for anticipating the drought conditions concerning model accuracy measures. Despite this, the FBNN models remain somewhat better than ARIMA models with R?≥?0.7865, MAE?≤?1.0637, and RMSE?≤?1.2466. Additionally, the FBNN based on hyperbolic tangent activation function demonstrated the best similarity between actual and predicted for SPI 24 by 98.44%. Eventually, all the activation function of FBNN models has good results respecting the SPI prediction with a small degree of variation among timescales. Therefore, any of these activation functions can be used equally even if the sigmoid and bipolar sigmoid functions are manifesting less adjusted R² and higher errors (MAE and RMSE). In conclusion, the FBNN can be considered a promising technique for predicting the SPI as a drought monitoring index under arid ecosystems.     

雨水口堵塞程度对其泄流能力影响的试验研究

雨水口是下泄地表径流的关键设施,一旦堵塞将导致市政排水系统的泄流能力无法充分发挥,这是引发城市洪涝灾害的主要原因之一。为定量分析雨水口堵塞对其泄流能力的影响,本研究分别考虑进水篦及连接管不同堵塞程度的情况,开展了较大来流水深下的概化水槽试验,共计进行了608组试验。试验结果表明:①进水篦及连接管堵塞均会显著影响雨水口的泄流能力,且后者对雨水口泄流能力的影响更大。②利用试验数据率定了各堵塞情况下水流以堰流或管嘴流形式从雨水口下泄时的流量系数;基于量纲分析及回归分析,给出了各堵塞情况下雨水口泄流能力的幂函数表达式,并利用试验数据对参数进行了率定,率定效果优于堰流或管嘴流公式。③通过与未堵塞情况进行比较,基于幂指数均值假定及非线性拟合方法,建立堵塞系数与堵塞程度之间的经验关系,并最终提出了一个可以分别考虑进水篦与连接管堵塞影响的雨水口泄流能力公式;该公式可以考虑雨水口堰流及管嘴流等不同泄流形式,能够反映进水篦、连接管不同堵塞程度的影响,适用于来流水深较大的情况。     

区域气候模式水平分辨率对黄淮海流域当代气候模拟的影响

区域气候模式是进行流域尺度气候变化研究的重要工具,其中水平分辨率对流域模拟结果的影响亟待评估。本文使用区域气候模式RegCM4,在ERA-Interim再分析资料驱动下,进行2种水平分辨率（50 km和25 km）1990-2010年东亚区域的长时间连续积分模拟。通过与观测资料的对比,评估RegCM4对黄淮海流域的模拟性能,同时分析水平分辨率对模拟结果的影响。结果表明:① 2组模拟均可以较好地再现黄淮海流域冬季、夏季平均气温和降水的空间分布,以及气温和降水的年循环变化;对极端气候事件指数的分布模拟效果也较好,且对与气温有关的极端气候事件指数模拟效果优于与降水有关的极端气候事件指数。②与观测相比,也存在一定的偏差,如模拟的冬季气温存在冷偏差,夏季气温存在暖偏差,冬季、夏季降水在大部分地区偏多等。③ 2组模拟对比来看,对冬季、夏季平均气温的量级和空间分布,25 km模拟与观测更加接近;对冬季、夏季平均降水,50 km模拟与观测的空间相关系数分别为0.86和0.44,较25 km模拟有较大提高;对极端事件,2组模拟差别不大。模拟结果可为后续此版本模式在黄淮海流域气候变化研究中的应用提供参考。     

Comparison of FFNN and ANFIS models for estimating groundwater level

Prediction of water level is an important task for groundwater planning and management when the water balance consistently tends toward negative values. In Maheshwaram watershed situated in the Ranga Reddy District of Andhra Pradesh, groundwater is overexploited, and groundwater resources management requires complete understanding of the dynamic nature of groundwater flow. Yet, the dynamic nature of groundwater flow is continually changing in response to human and climatic stresses, and the groundwater system is too intricate, involving many nonlinear and uncertain factors. Artificial neural network (ANN) models are introduced into groundwater science as a powerful, flexible, statistical modeling technique to address complex pattern recognition problems. This study presents the comparison of two methods, i.e., feed-forward neural network (FFNN) trained with Levenberg–Marquardt (LM) algorithm compared with a fuzzy logic adaptive network-based fuzzy inference system (ANFIS) model for better accuracy of the estimation of the groundwater levels of the Maheshwaram watershed. The statistical indices used in the analysis were the root mean square error (RMSE), regression coefficient (R ²) and error variation (EV).The results show that FFNN-LM and ANFIS models provide better accuracy (RMSE = 4.45 and 4.94, respectively, R ² is 93% for both models) for estimating groundwater levels well in advance for the above location.     

An expert system based on hybrid ICA-ANN technique to estimate macerals contents of Indian coals

Coal, as an initial source of energy, requires a detailed investigation in terms of ultimate analysis, proximate analysis, and its biological constituents (macerals). The rank and calorific value of each type of coal are managed by the mentioned properties. In contrast to ultimate and proximate analyses, determining the macerals in coal requires sophisticated microscopic instrumentation and expertise. This study emphasizes the estimation of the concentration of macerals of Indian coals based on a hybrid imperialism competitive algorithm (ICA)–artificial neural network (ANN). Here, ICA is utilized to adjust the weight and bias of ANNs for enhancing their performance capacity. For comparison purposes, a pre-developed ANN model is also proposed. Checking the performance prediction of the developed models is performed through several performance indices, i.e., coefficient of determination (R ²), root mean square error and variance account for. The obtained results revealed higher accuracy of the proposed hybrid ICA-ANN model in estimating macerals contents of Indian coals compared to the pre-developed ANN technique. Results of the developed ANN model based on R ² values of training datasets were obtained as 0.961, 0.955, and 0.961 for predicting vitrinite, liptinite, and inertinite, respectively, whereas these values were achieved as 0.948, 0.947, and 0.957, respectively, for testing datasets. Similarly, R ² values of 0.988, 0.983, and 0.991 for training datasets and 0.989, 0.982, and 0.985 for testing datasets were obtained from developed ICA-ANN model.     

Application of neural networks to predict net present value in mining projects

Net present value (NPV) is the most popular economic indicator in evaluation of the investment projects. For the mining projects, this criterion is calculated under uncertainty associated with the relevant parameters of say commodity price, discount rate, etc. Accurate prediction of the NPV is a quite difficult process. This paper mainly deals with the development of a new model to predict NPV using artificial neural network (ANN) in the Zarshuran gold mine, Iran. Gold price (as the main product), silver price (as the byproduct), and discount rate were considered as input parameters for the ANN model. To reach an optimum architecture, different types of networks were examined on the basis of a trial and error mechanism. A neural network with architecture 3-15-10-1 and root mean square error of 0.092 is found to be optimum. Prediction capability of the proposed model was examined through computing determination coefficient (R ²?=?0.987) between predicted and real NPVs. Absolute error of US$0.1 million and relative error of 1.4 % also confirmed powerfulness of the developed ANN model. According to sensitivity analysis, it was observed that the gold price is the most effective and discount rate is the least effective parameter on the NPV.     

Flow estimations for the Sohu Stream using artificial neural networks

In this study, daily rainfall–runoff relationships for Sohu Stream were modelled using an artificial neural network (ANN) method by including the feed-forward back-propagation method. The ANN part was divided into two stages. During the first stage, current flows were estimated by using previously measured flow data. The best network architecture was found to utilise two neurons in the input layer (the delayed flows from the first and second days), two hidden layers, and one output layer (the current flow). The coefficient of determination (R ²) in this architecture was 81.4%. During the second stage, the current flows were estimated by using a combination of previously measured values for precipitation, temperature, and flows. The best architecture consisted of an input layer of 2 days of delayed precipitation, 3 days of delayed flows, and temperature of the current. The R ² in this architecture was calculated to be 85.5%. The results of the second stage best reflected the real-world situation because they accounted for more input variables. In all models, the variables with the highest R ² ranked as the previous flow (81.4%), previous precipitation (21.7%), and temperature.     

Breach erosion of earthfill dams (BEED) model

A computer model has been developed for simulation of breach erosion of earthfill dams (BEED). The model incorporates the processes of surface erosion and slope sloughing to simulate breach enlargement. Depletion of reservoir water is approximated by a volume continuity equation while broad-crested weir hydraulics is utilized to describe flow over and through the breach. Due to the implicit form of these equations, an iterative solution is proposed with convergence achieved within only a few iterations. The BEED model is written in both FORTRAN 77 and BASIC computer languages. Testing of the model using historical data of the failures of Teton and Huaccoto dams showed that timing, shape, and magnitude of the predicted outflow hydrograph were adequately simulated by this model. The same is true for the dimensions of the terminal breach. A sensitivity analysis indicated that internal friction angle and the relation for surface erosion were the major factors affecting the model results.     

Prediction of river flow using hybrid neuro-fuzzy models

The complex nature of hydrological phenomena, like rainfall and river flow, causes some limitations for some admired soft computing models in order to predict the phenomenon. Evolutionary algorithms (EA) are novel methods that used to cover the weaknesses of the classic training algorithms, such as trapping in local optima, poor performance in networks with large parameters, over-fitting, and etc. In this study, some evolutionary algorithms, including genetic algorithm (GA), ant colony optimization for continuous domain (ACO_R), and particle swarm optimization (PSO), have been used to train adaptive neuro-fuzzy inference system (ANFIS) in order to predict river flow. For this purpose, classic and hybrid ANFIS models were trained using river flow data obtained from upstream stations to predict 1-, 3-, 5-, and 7-day ahead river flow of downstream station. The best inputs were selected using correlation coefficient and a sensitivity analysis test (cosine amplitude). The results showed that PSO improved the performance of classic ANFIS in all the periods such that the averages of coefficient of determination, R², root mean square error, RMSE (m³/s), mean absolute relative error, MARE, and Nash-Sutcliffe efficiency coefficient (NSE) were improved up to 0.19, 0.30, 43.8, and 0.13%, respectively. Classic ANFIS was only capable to predict river flow in 1-day ahead while EA improved this ability to 5-day ahead. Cosine amplitude method was recognized as an appropriate sensitivity analysis method in order to select the best inputs.     

Application of neural network and MODIS 250m imagery for estimating suspended sediments concentration in Hangzhou Bay,China

Suspended sediments concentration (SSC) in surface water derived from bottom sediment resuspension or discharge of sediment-laden rivers is an important indication of coastal water quality and changes rapidly in high-energy coastal area. Since artificial neural networks (ANN) had been proven successful in modeling a variety of geophysical transfer functions, an ANN model to simulate the relationship between surface water SSC and satellite-received radiances was employed. In situ SSC measurements from the Hangzhou Bay and the Moderate-resolution Imaging Spectroradiometer (MODIS) 250 m daily products were adopted in this study. Significant correlations were observed between in situ measurements and band 1–2 reflectance values of MODIS images, respectively. Results indicated that application of ANN model with one hidden layer appeared to yield superior simulation performance (r ² = 0.98; n = 25) compared with regression analysis method. The RMSE for the ANN model was less than 10%, whereas the RMSE for the regression analysis was more than 25%. Results also showed that different tidal situations affect the model simulation results to some extent. The SSC of surface water in Hangzhou Bay is high and changes rapidly due to tidal flood and ebb during a tidal cycle. The combined utilization of Terra and Aqua MODIS data can capture the tidal cycle induced dynamic of surface water SSC. This study demonstrated that MODIS 250 m daily products and ANN model are useful for monitoring surface SSC dynamic within high-energy coastal water environments.