Modeling dimensionless longitudinal dispersion coefficient in natural streams using artificial intelligence methods

Learning the Longitudinal Dispersion (LD) mechanism in natural channel is vitally important to be able to control water pollution and to prevent different stratification in flow that crucial for water resources conservation for both human and aquatic life. Many related studies can be found in the existing literature. However, almost all studies aim to investigate the mechanism of the LD in natural channels or to model dimensional LD coefficient. The main goal of this work is to develop three models based on different artificial neural network techniques to predict dimensionless (not dimensional) LD coefficients in natural channels. Another goal of this study is to present a large and critical assessment on the existing studies made on both dimensional and dimensionless LD. The data sets obtained from the literature concerning more than 30 rivers at different times in the United States of America, include the depth, the width, and the mean cross-sectional velocity of the flow, shear velocity, and dimensionless longitudinal dispersion coefficient. The results have been compared with the data at hand, a fuzzy based model, and seven conventional equations proposed in literature by using statistical magnitudes, error modes, and contour map method. It is observed that the feed forward neural network yields the best reliable results.

[1]  Yun‐Sheng Yu,et al.  LONGITUDINAL DISPERSION IN RWERS: A DEAD‐ZONE MODEL SOLUTION , 1989 .

[2]  A. Sooky.  Longitudinal Dispersion in Open Channels , 1969 .

[3]  Z. Fuat Toprak,et al.  Longitudinal Dispersion Coefficient Modeling in Natural Channels using Fuzzy Logic , 2007 .

[4]  D. Broomhead,et al.  Radial Basis Functions, Multi-Variable Functional Interpolation and Adaptive Networks , 1988 .

[5]  Hamid Mehdizadeh,et al.  A framework development for predicting the longitudinal dispersion coefficient in natural streams using an artificial neural network , 2011 .

[6]  Roger A Falconer,et al.  Longitudinal dispersion coefficients in natural channels. , 2002, Water research.

[7]  Indrajeet Chaubey,et al.  Comparison of artificial neural network models for hydrologic predictions at multiple gauging stations in an agricultural watershed , 2008 .

[8]  Zekai Sen,et al.  Comment on "Longitudinal dispersion coefficients in natural channels". , 2004, Water research.

[9]  George V. Sabol,et al.  Empirical data on longitudinal dispersion in rivers , 1974 .

[10]  Qiang Zhang.  Transient Behavior of Mixing Induced by a Random Velocity Field , 1995 .

[11]  Thomas N. Keefer,et al.  Simple Method for Predicting Dispersion in Streams , 1974 .

[12]  Mohammad Bagher Menhaj,et al.  Training feedforward networks with the Marquardt algorithm , 1994, IEEE Trans. Neural Networks.

[13]  H. A. Basha,et al.  Analytical Model of Two-Dimensional Dispersion in Laterally Nonuniform Axial Velocity Distributions , 1997 .

[14]  Ozgur Kisi,et al.  Streamflow Forecasting Using Different Artificial Neural Network Algorithms , 2007 .

[15]  Rajeev Ranjan Sahay,et al.  Prediction of longitudinal dispersion coefficients in natural rivers using artificial neural network , 2011 .

[16]  Mohammad Mehdi Ebadzadeh,et al.  An expert system for predicting longitudinal dispersion coefficient in natural streams by using ANFIS , 2009, Expert Syst. Appl..

[17]  O. Kisi,et al.  Pan Evaporation Modeling Using Neural Computing Approach for Different Climatic Zones , 2012, Water Resources Management.

[18]  Mohammad Sohrab,et al.  Empirical Relations for Longitudinal Dispersion in Streams , 2000 .

[19]  K. S. Davar,et al.  LONGITUDINAL DISPERSION FOR FLOW OVER ROUGH BEDS , 1976 .

[20]  Shang-Liang Chen,et al.  Orthogonal least squares learning algorithm for radial basis function networks , 1991, IEEE Trans. Neural Networks.

[21]  Il Won Seo,et al.  Estimation of the Longitudinal Dispersion Coefficient using the Velocity Profile in Natural Streams , 2004 .

[22]  Hugo B. Fischer,et al.  The Mechanics of Dispersion in Natural Streams , 1967 .

[23]  K. Chau,et al.  Neural network and genetic programming for modelling coastal algal blooms , 2006 .

[24]  Özgür Kişi,et al.  Multi-layer perceptrons with Levenberg-Marquardt training algorithm for suspended sediment concentration prediction and estimation / Prévision et estimation de la concentration en matières en suspension avec des perceptrons multi-couches et l’algorithme d’apprentissage de Levenberg-Marquardt , 2004 .

[25]  Harvey E. Jobson,et al.  Predicting Travel Time and Dispersion in Rivers and Streams , 1997 .

[26]  Antonello Provenzale,et al.  Parameterization of dispersion in two-dimensional turbulence , 2001, Journal of Fluid Mechanics.

[27]  Soon Heung Chang,et al.  Radial basis function networks applied to DNBR calculation in digital core protection systems , 2003 .

[28]  Il Won Seo,et al.  Predicting Longitudinal Dispersion Coefficient in Natural Streams , 1998 .

[29]  Antonis D. Koussis,et al.  HYDRAULIC ESTIMATION OF DISPERSION COEFFICIENT FOR STREAMS , 1998 .

[30]  O. Ks.  Multi-layer perceptrons with Levenberg-Marquardt training algorithm for suspended sediment concentration prediction and estimation , 2004 .

[31]  W. Chen,et al.  Intelligent Manipulation and Calibration of Parameters for Hydrological Models , 2006 .

[32]  Chun-tian Cheng,et al.  FUZZY ITERATION METHODOLOGY FOR RESERVOIR FLOOD CONTROL OPERATION 1 , 2001 .

[33]  I. Guymer,et al.  Closure of "Longitudinal Dispersion in Sinuous Channel with Changes in Shape" , 1998 .

[34]  Lefteri H. Tsoukalas,et al.  Fuzzy and neural approaches in engineering , 1997 .

[35]  W. W. Sayre.  Dispersion of mass in open-channel flow , 1967 .

[36]  Rajandrea Sethi,et al.  Artificial neural network simulation of hourly groundwater levels in a coastal aquifer system of the Venice lagoon , 2012, Eng. Appl. Artif. Intell..

[37]  Shoji Fukuoka,et al.  Longitudinal Dispersion in Sinuous Channels , 1973 .

[38]  G. Taylor.  Dispersion of soluble matter in solvent flowing slowly through a tube , 1953, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[39]  Vijay P. Singh,et al.  Longitudinal dispersion coefficient in single-channel streams , 2002 .

[40]  Hikmet Kerem Cigizoglu,et al.  Predicting longitudinal dispersion coefficient in natural streams by artificial intelligence methods , 2008 .

[41]  S. Adarsh,et al.  Prediction of Longitudinal Dispersion Coefficient in Natural Channels Using Soft Computing Techniques , 2010 .

[42]  Adrian E. Scheidegger,et al.  Statistical Hydrodynamics in Porous Media , 1954 .

[43]  Abbas Afshar,et al.  Multi objective calibration of large scaled water quality model using a hybrid particle swarm optimization and neural network algorithm , 2012, KSCE Journal of Civil Engineering.

[44]  Hugo B. Fischer,et al.  Discussion of Simple Method for Predicting Dispersion in Streams by Raul S. McQuivey and Thomas N. Keefer , 1975 .

[45]  J. W. Elder.  The dispersion of marked fluid in turbulent shear flow , 1959, Journal of Fluid Mechanics.

[46]  Yan Li,et al.  Comparison of Several Flood Forecasting Models in Yangtze River , 2005 .

[47]  Yung-Chi Chang,et al.  Lateral Mixing in Meandering Channels , 1984 .

[48]  Stream Velocity Profiles and Longitudinal Dispersion , 1997 .

[49]  Geoffrey Ingram Taylor,et al.  The dispersion of matter in turbulent flow through a pipe , 1954, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[50]  Mahmut Firat,et al.  Evaluation of Artificial Neural Network Techniques for Municipal Water Consumption Modeling , 2009 .

[51]  T. Day,et al.  Longitudinal dispersion in natural channels , 1975 .

[52]  Jacek Makinia,et al.  Evaluation of empirical formulae for estimation of the longitudinal dispersion in activated sludge reactors. , 2005, Water research.

[53]  E. Anderson,et al.  Estimating longitudinal dispersion in rivers using Acoustic Doppler Current Profilers , 2010 .

[54]  Shu Guang Li,et al.  Stochastic Theory for Irregular Stream Modeling. II: Solute Transport , 1997 .

[55]  M. K. Bansal.  Dispersion in Natural Streams , 1971 .

[56]  David A. Benson,et al.  Subordinated advection‐dispersion equation for contaminant transport , 2001 .

[57]  Y. Sheng,et al.  Estimation of water quality model parameters , 2010 .

[58]  Uwe Jaekel,et al.  Renormalization group analysis of macrodispersion in a directed random flow , 1997 .

[59]  Peter Schlosser,et al.  Determination of longitudinal dispersion coefficient and net advection in the tidal hudson river with a large-scale, high resolution SF6 tracer release experiment. , 2002, Environmental Science and Technology.

[60]  Simon Haykin,et al.  Neural Networks: A Comprehensive Foundation , 1998 .

[61]  I. Willis,et al.  Subglacial drainage system structure and morphology of Brewster Glacier, New Zealand , 2009 .

[62]  Hugo B. Fischer,et al.  Measurement of mixing characteristics of the Missouri River between Sioux City, Iowa, and Plattsmouth, Nebraska , 1970 .

[63]  V. Singh,et al.  Analytical water quality model for biochemical oxygen demand simulation in River Gomti of Ganga Basin, India , 2008 .

[64]  Donald F. Specht,et al.  A general regression neural network , 1991, IEEE Trans. Neural Networks.

[65]  Henry Liu.  Predicting Dispersion Coefficient of Streams , 1977 .

[66]  Longitudinal Dispersion Coefficients in Estuary , 1992 .

[67]  Keith Beven,et al.  Discharge‐dependent pollutant dispersion in rivers: Estimation of aggregated dead zone parameters with surrogate data , 2006 .

[68]  Gokmen Tayfur,et al.  Fuzzy, ANN, and regression models to predict longitudinal dispersion coefficient in natural streams , 2006 .

[69]  David Williams,et al.  Modelling of floating seed dispersal in a fluvial environment , 2009 .

[70]  K. W. Chau,et al.  River stage prediction based on a distributed support vector regression , 2008 .

[71]  A 2‐D numerical simulation study on longitudinal solute transport and longitudinal dispersion coefficient , 2011 .

[72]  W. W. Sayre,et al.  A LABORATORY INVESTIGATION OF OPEN CHANNEL DISPERSION PROCESSES FOR DISSOLVED, SUSPENDED, AND FLOATING DISPERSANTS , 1968 .

[73]  A. Facchi,et al.  On the relative role of hydrodynamic dispersion for river water quality , 2001 .

[74]  Jui-Sheng Chen,et al.  Development of an artificial neural network model for determination of longitudinal and transverse dispersivities in a convergent flow tracer test , 2010 .

[75]  Ozgur Kisi,et al.  Suspended sediment estimation using neuro-fuzzy and neural network approaches/Estimation des matières en suspension par des approches neurofloues et à base de réseau de neurones , 2005 .

[76]  P. Vervier,et al.  Hydromorphological control of phosphorus in a large free‐flowing gravel bed river: the Garonne River (France) , 2001 .

[77]  The dispersion of matter in turbulent shear flow , 1971 .

[78]  Peter A. Krenkel,et al.  Longitudinal Mixing in Natural Streams , 1967 .

[79]  P. Chatwin.  Presentation of Longitudinal Dispersion Data , 1980 .

[80]  D. Benson,et al.  Application of a fractional advection‐dispersion equation , 2000 .

[81]  Manoj K. Jha,et al.  A DEM‐based parallel computing hydrodynamic and transport model , 2012 .

[82]  Adam P. Piotrowski,et al.  Are Artificial Neural Network Techniques Relevant for the Estimation of Longitudinal Dispersion Coefficient in Rivers , 2005 .

[83]  H. Fischer.  Mixing in Inland and Coastal Waters , 1979 .

[84]  Gwo-Fong Lin,et al.  An RBF network with a two-step learning algorithm for developing a reservoir inflow forecasting model , 2011 .

[85]  H. Fischer.  The effect of bends on dispersion in streams , 1969 .

[86]  R. G. Godfrey,et al.  Stream dispersion at selected sites , 1970 .

[87]  Jaroslaw J. Napiorkowski,et al.  Are artificial neural network techniques relevant for the estimation of longitudinal dispersion coefficient in rivers? / Les techniques de réseaux de neurones artificiels sont-elles pertinentes pour estimer le coefficient de dispersion longitudinale en rivières? , 2005 .

[88]  John Yearsley,et al.  A semi‐Lagrangian water temperature model for advection‐dominated river systems , 2009 .

[89]  Adam P. Piotrowski,et al.  Flash-flood forecasting by means of neural networks and nearest neighbour approach – a comparative study , 2006 .

[90]  Majid Dehghani,et al.  Predicting the Longitudinal Dispersion Coefficient Using Support Vector Machine and Adaptive Neuro-Fuzzy Inference System Techniques , 2009 .

[91]  K. Kwiatkowski,et al.  Response to the slug injection of a tracer—a large-scale experiment in a natural river / Réponse à l'injection impulsionnelle d'un traceur—expérience à grande échelle en rivière naturelle , 2008 .

[92]  D. D. Silva,et al.  Development and validation of an equation to estimate longitudinal dispersion coefficient in medium-sized rivers. , 2010 .

[93]  Hikmet Kerem Cigizoglu,et al.  Application of Generalized Regression Neural Networks to Intermittent Flow Forecasting and Estimation , 2005 .

[94]  H. B. Fisher,et al.  Dispersion Predictions in Natural Streams , 1968 .

[95]  Hikmet Kerem Cigizoglu,et al.  Suspended sediment load simulation by two artificial neural network methods using hydrometeorological data , 2007, Environ. Model. Softw..

[96]  S. Naib,et al.  Oblique and vertical jet dispersion in channels , 1997 .

[97]  Vijay P. Singh,et al.  Longitudinal dispersion coefficient in straight rivers , 2001 .

[98]  M. Franca,et al.  Impacts of sand transport on flow variables and dissolved oxygen in gravel‐bed streams suitable for salmonid spawning , 2010 .