4,029
Views
65
CrossRef citations to date
0
Altmetric
Original Articles

Modelling stage—discharge relationships affected by hysteresis using the Jones formula and nonlinear regression

Modélisation des relations hauteur—débit affectées par de l'hystérésis en utilisant la formule de Jones et la régression non-linéaire

Pages 365-388 | Received 10 Mar 2005, Accepted 01 Mar 2006, Published online: 19 Jan 2010

REFERENCES

  • Akaike , H. 1974 . A new look at the statistical model identification. . IEEE Trans. Automatic Control , 19 : 716 – 723 .
  • Azmon , B. 1992 . Manning coefficient of roughness—a case study along Soreq stream. . J. Hydrol. , 132 : 361 – 377 .
  • Bhattacharya , B. and Solomatine , D. P. 2005 . Neural network and M5 model trees in modelling water level—discharge relationship. . Neurocomputing , 63 : 381 – 396 .
  • Boyer , M. C. 1964 . “ Streamflow measurement. ” . In Handbook of Applied Hydrology Edited by: Chow , V. T. New York, USA : McGraw-Hill .
  • Carter , R. W. and Anderson , I. E. 1963 . Accuracy of a current meter measurement. . J. Hydraul. Div. ASCE , 89 : 105 – 115 .
  • Chen , C. L. 1991 . Unified theory on power laws for flow resistance. . J. Hydraul. Engng ASCE , 117 : 371 – 389 .
  • Cheney , W. and Kincaid , D. 1999 . Numerical Mathematics and Computing, , fourth edn Pacific Grove, California, USA : Brooks/Cole Publishing Company .
  • Chow , V. T. 1959 . Open-Channel Hydraulics New York, USA : McGraw-Hill .
  • Corbett , D. M. 1943 . “ Stream-gaging procedure—a manual describing methods and practices of the Geological Survey. ” . In US Geol. Survey Water Supply Paper 888.
  • Day , T. J. 1975 . On the precision of salt dilution gauging. . Water Resour. Res. , 31 : 293 – 306 .
  • De Boor , C. A. 2001 . A Practical Guide to Splines, , revised edn New York, USA : Springer Verlag .
  • Demidenko , E. 2000 . Is this the least square estimate? . Biometrika , 87 : 437 – 452 .
  • Dennis , J. E. and Moré , J. J. 1977 . Quasi-Newton methods, motivation and theory. . SIAM Review , 19 : 46 – 89 .
  • Di Silvio , G. 1969 . Flood wave modifications along prismatic channels. . J. Hydraul. Div. ASCE , 95 : 1589 – 1614 .
  • Efron , B. and Tibshirani , R. J. 1993 . An Introduction to the Bootstrap New York, USA : Chapman & Hall .
  • Faye , R. E. and Cherry , R. N. 1980 . “ Channel and dynamic flow characteristics of the Chattahoochee River, Buford Dam to Georgia Highway 141. ” . In US Geol. Survey Water Supply Paper 2063
  • Fenton , J. D. and Keller , R. J. 2001 . The calculation of streamflow from measurements of stage , Technical Report 01/6 Melbourne, Australia : Cooperative Research Centre for Catchment Hydrology .
  • Ferrick , M. G. 1984 . Modeling rapidly varied flow in tailwaters. . Water Resour. Res. , 20 : 271 – 289 .
  • Ferrick , M. G. 1985 . Analysis of river wave types. . Water Resour. Res. , 21 : 209 – 220 .
  • Fread , D. L. 1975 . Computation of stage—discharge relationships affected by unsteady flow. . Water Resour. Bull. , 11 : 213 – 218 .
  • Gawne , K. D. and Simonovic , S. P. 1994 . A computer-based system for modelling the stage—discharge relationship in steady state conditions. . Hydrol. Sci. J. , 39 ( 5 ) : 487 – 506 .
  • Golub , G. H. and Pereyra , V. 2003 . Separable nonlinear least squares: the variable projection method and its applications. . Inverse Problems , 19 : 1 – 26 .
  • Hall , M. R. , Hall , W. E. and Pierce , C. D. 1914 . “ Daily discharge of rivers of variable slope. ” . In US Geol. Survey Water Supply Paper 345-E
  • Henderson , F. M. 1963 . Flood waves in prismatic channels. . J. Hydraul. Div. ASCE , 89 : 39 – 67 .
  • Henderson , F. M. 1966 . Open Channel Flow New York, USA : Macmillan .
  • Herschy , R. W. 1995 . Streamflow Measurement, , second edn London, UK : E & FN Spon .
  • Herschy , R. W. 1999 . “ Uncertainties in hydrometric measurements ” . In Hydrometry: Principles and Practice, , second edn Edited by: Herschy , R. W. Chichester, UK : John Wiley & Sons .
  • Horton , R. E. 1945 . Erosional development of streams and their drainage basins. . Geol. Soc. Am. Bull. , 56 : 275 – 370 .
  • ISO . 1998 . ISO 1100/2: Determination of the Stage—Discharge Relation Geneva, Switzerland : ISO . (International Standards Organisation)
  • ISO . 2001 . ISO 9123: Stage—Fall—Discharge Relationships Geneva, Switzerland : ISO . (International Standards Organisation)
  • Jain , S. K. and Chalisgaonkar , D. 2000 . Setting up stage—discharge using ANN. . J. Hydrol. Engng ASCE , 5 : 428 – 433 .
  • Jarrett , R. F. 1984 . Hydraulics of high-gradient streams. . J. Hydraul. Div. ASCE , 110 : 1519 – 1539 .
  • Johnson , P. A. 1996 . Uncertainty of hydraulic parameters. . J. Hydraul. Engng ASCE , 122 : 112 – 114 .
  • Jones , B. E. 1916 . “ A method of correcting river discharge for a changing stage. ” . In US Geol. Survey Water Supply Paper 375-E
  • Kennedy , R. W. 1984 . “ Discharge ratings at gaging stations. ” . In Techniques of Water-Resources Investigations, Book 3, Chapter 10 Reston, Virginia, USA : US Geol. Survey .
  • Kirkpatrick , S. , Gelatt , C. D. and Vecchi , M. P. 1983 . Optimization by simulated annealing. . Science , 220 : 671 – 680 .
  • Kleitz , M. 1877 . Note sur la théorie du mouvement non permanent des liquides et sur l'application à la propagation des crues des rivières. . Annales des Ponts et Chaussees , 5 : 133 – 196 .
  • Koloseus , H. J. and Davidian , J. 1966 . “ Free-surface instability correlations, and roughness-concentration effects on flow over hydrodynamically rough surfaces. ” . In US Geol. Survey Water Supply Paper 1592-C
  • Lange , K. 1999 . Numerical Analysis for Statisticians New York, USA : Statistics and Computing. Springer Verlag .
  • Lighthill , M. J. and Whitham , G. B. 1955 . On kinematic waves, 1: long waves in rivers. . Proc. Roy. Soc. London , 229 : 281 – 316 . Ser. A
  • Mäkeläinen , T. , Schmidt , K. and Styan , G. P. H. 1981 . On the existence and uniqueness of the maximum likelihood estimate of a vector-valued parameter in fixed-sample space. . Ann. Statist. , 9 : 758 – 767 .
  • Mander , R. J. 1978 . “ Aspects of unsteady flow and variable backwater ” . In Hydrometry: Principles and Practice, , first edn Edited by: Herschy , R. W. Chichester, UK : John Wiley & Sons .
  • Moyeed , R. A. and Clarke , R. T. 2005 . The use of Bayesian methods for fitting rating curves, with case studies. . Adv. Water Resour. , 28 : 807 – 818 .
  • Murphy , E. C. 1906 . Destructive floods in the United States in 1905 , US Geol. Survey Water Supply and Irrigation Paper 162. Series M, General Hydrographic Investigations no. 17 Washington, USA
  • Neely , B. L. and Bingham , R. H. 1986 . Investigation of the need for discharge adjustments for unsteady flow at selected gaging stations on streams in Tennessee. Water-Resources Investigations Report 84–4144, US Geol Lakewood, Colorado, USA : Survey .
  • Orme , C. D. and Ruud , P. A. 2002 . On the uniqueness of the maximum likelihood estimator. . Economic Lett. , 75 : 209 – 217 .
  • Pawitan , Y. 2001 . In All Likelihood: Statistical Modelling and Inference Using Likelihood Oxford, UK : Oxford University Press .
  • Perumal , M. and Ranga Raju , K. G. 1999 . Approximate convection—diffusion equations. . J. Hydrol. Engng ASCE , 4 : 160 – 164 .
  • Perumal , M. , Shrestha , K. B. and Chaube , U. C. 2004 . Reproducing hysteresis in rating curves. . J. Hydraul. Engng ASCE , 130 : 870 – 878 .
  • Petersen-Øverleir , A. 2004 . Accounting for heteroscedasticity in rating curve estimates. . J. Hydrol. , 292 : 173 – 181 .
  • Petersen-Øverleir , A. and Reitan , T. 2005 . Objective segmentation in compound rating curves. . J. Hydrol. , 311 : 188 – 201 .
  • Ponce , V. M. 1991 . New perspective on the Vedernikov number. . Water Resour. Res. , 27 : 1777 – 1779 .
  • Ponce , V. M. , Li , R. M. and Simons , D. B. 1978 . Applicability of kinematic and diffusion models. . J. Hydraul. Div. ASCE , 104 : 353 – 363 .
  • Rantz , S. E. 1982 . Measurement and computation of streamflow, vol. 2. Computation of discharge. US Geol. Survey Water Supply Paper 2175, US Geol Virginia, USA : Survey, Reston .
  • Reitan , T. and Petersen-Øverleir , A. 2005 . Estimating the discharge rating curve by nonlinear regression—the frequentist approach , Statistical Research Report, Preprint 2 Norway : University of Oslo .
  • Seber , G. A. F. and Wild , C. J. 1989 . Nonlinear Regression New York, USA : John Wiley & Sons .
  • Seddon , J. A. 1900 . River hydraulics. . Trans. ASCE , 43 : 179 – 229 .
  • Singh , V. P. 2001 . Kinematic wave modelling in water resources: a historical perspective. . Hydrol. Processes , 15 : 671 – 706 .
  • Strelkoff , T. S. and Clemmens , A. J. 2000 . Approximating wetted perimeters in power-law cross-sections. . J. Irrig. Drain. Engng Div. ASCE , 126 : 98 – 109 .
  • Sudheer , K. P. and Jain , S. K. 2003 . Radical basis function neural network for modelling rating curves. . J. Hydrol. Engng ASCE , 8 : 161 – 164 .
  • Tang , X. , Knight , D. W. and Samuels , P. G. 2001 . Wave speed—discharge relationships from cross-section survey. . Proc. Instn Civil Engrs, Water & Maritime Engng , 148 : 81 – 96 .
  • Tarekul Islam , G. M. and Chowdhury , J. U. 2003 . Hydraulic characteristics of the Jamuna River gauging station, Bangladesh. . Proc. Instn Civil Engrs, Water & Maritime Engng , 156 : 219 – 224 .
  • Tawfik , M. , Ibrahim , A. and Fahmy , H. 1997 . Hysteresis sensitive neural network for modelling rating curves. . J. Comput. in Civil Engng , 11 : 206 – 211 .
  • Van Laarhoven , P. J. M. and Aarts , E. H. L. 1987 . Simulated Annealing: Theory and Applications Dordrecht, The Netherlands : D. Reidel .
  • Van Loan , C. F. 2000 . Introduction to Scientific Computing. New Jersey, USA : Prentice Hall, Upper Saddle River .
  • Venetis , C. 1970 . A note on the estimation of the parameters in logarithmic stage—discharge relationships with estimation of their error. . Bull. IASH , 15 : 105 – 111 .
  • Weinmann , P. E. and Laurenson , E. M. 1979 . Approximate flood routing methods: a review. . J. Hydraul. Div. ASCE , 105 : 1521 – 1535 .
  • Woolhiser , D. A. and Liggett , J. A. 1967 . Unsteady one-dimensional flow over a plane: the rising hydrograph. . Water Resour. Res. , 3 : 753 – 771 .
  • Zarzer , E. A. 1987 . Some considerations concerning the optimal calculation of stage—discharge functions. . Mathematical Methods and Operation Research (ZOR) , 31 : 193 – 212 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.