Transport and Dispersion in Large Rivers: Application of the Aggregated Dead Zone Model

  • Sarka D. Blazkova
  • Keith J. Beven
  • Paul J. Smith


The Aggregated Dead Zone (ADZ) model developed by Peter Young and Tom Beer is here applied to the analysis of tracer data from larger rivers. The model provides excellent fits to the observed concentrations, with a dispersive fraction parameter that varies relatively little with discharge. It is also shown how the information on transport and dispersion at different discharges can be augmented by pollution incident and continuously logged water quality data. The model can then be applied to predict the downstream dispersion of pollutants at any arbitrary discharge, taking account of the uncertainty in estimating the ADZ model parameters. Further work remains to be done on relating the parameters of the model to the physical and hydraulic characteristics of river reaches and in gathering data on the gain factor for different pollutants.


Large River Tracer Experiment Surrogate Data Hyporheic Zone Tracer Data 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



KB first met Peter Young when he was passing through the University of Virginia on his way back to England to take up the post of Head of Environmental Sciences at Lancaster University in 1981, our talk soon turned to the analysis of tracing experiments. We wrote a grant proposal to start the joint work on the ADZ model when KB also returned to the UK at the Institute of Hydrology, before joining Peter at Lancaster in 1985.

BfG Koblenz, Elbe River Board, TGM WRI and Lancaster University performed the tracer experiments.The surrogate data has been collected by the Elbe River Board. SB has been supported by a grant of Ministry of Environment of the Czech Republic SP/2e7/229/07. Information about tracing experiments on the River Rhine were supplied by A. van Mazijk.


  1. 1.
    Beer, T., Young, P.C.: Longitudinal dispersion in natural streams. J. Environ. Eng. 109, 1049–1067 (1983) CrossRefGoogle Scholar
  2. 2.
    Bencala, K.E., Walters, R.A.: Simulation of solute transport in a mountain pool-and-riffle stream: a transient storage model. Water Resour. Res. 19, 718–724 (1983) CrossRefGoogle Scholar
  3. 3.
    Beven, K.J., Buckley, K.M., Young, P.C.: ADZ-analysis manual part I. CRES Technical Report TR/90, Lancaster University (1991) Google Scholar
  4. 4.
    Beven, K.J., Young, P.C.: An aggregated mixing zone model of solute transport through porous media. J. Contam. Hydrol. 3, 129–143 (1988) CrossRefGoogle Scholar
  5. 5.
    Buckley, K.M., Beven, K.J.: ADZ-protect manual. CRES Technical Report TR/92, Lancaster University, UK (1991) Google Scholar
  6. 6.
    Buckley, K.M., Beven, K.J., Young, P.C., Benner, S.: ADZ-analysis manual part II. CRES Technical Report TR/91, Lancaster University, UK (1991) Google Scholar
  7. 7.
    Costa, J.R., Young, P., French, P.: Aggregated dead zone (ADZ) interactive water-quality model for the Ave River. Water Sci. Technol. 19, 1213–1224 (1987) Google Scholar
  8. 8.
    Day, T.: Longitudinal dispersion in natural channels. Water Resour. Res. 11, 909–918 (1975) CrossRefGoogle Scholar
  9. 9.
    Fischer, H.R., List, E.J., Koh, R.C.Y., Imberger, J., Brooks, N.H.: Mixing in Inland and Coastal Waters. Academic Press, New York (1979) Google Scholar
  10. 10.
    Godfrey, R.G., Frederick, B.J.: Stream dispersion at selected sites. USGS Prof. Paper 433-K, Washington, DC (1970) Google Scholar
  11. 11.
    Green, H.M., Beven, K.J.: Prediction of times of travel for a pollution incident on the River Eden in March 1993. Report for the North West Region, National Rivers Authority, CRES Technical Report TR/99, Lancaster University (1993) Google Scholar
  12. 12.
    Graf, J.B.: Measured and predicted velocity and longitudinal dispersion at steady and unsteady flow, Colorado River, Glen Canyon Dam to Lake Mead. Water Resour. Bull. 31(2), 265–281 (1995) Google Scholar
  13. 13.
    Green, H.M., Beven, K.J., Buckley, K., Young, P.C.: Pollution incident prediction with uncertainty. In: Beven, K.J., Chatwin, P.C., Millbank, J.H. (eds.) Mixing and Transport in the Environment, pp. 113–140. Wiley, New York (1994) Google Scholar
  14. 14.
    Green, H.M.: Unpublished PhD thesis, Lancaster University, UK (1997) Google Scholar
  15. 15.
    Guymer, I.: A national database of travel time. Dispersion and Methodologies for the Protection of River Abstractions, Environment Agency R & D Technical Report P346, ISBN 1 85705 821 6 (2002) Google Scholar
  16. 16.
    Guymer, I., O’Brien, R.T.: Longitudinal dispersion due to surcharged manhole. J. Hydraul. Eng. 126, 137–149 (2000) CrossRefGoogle Scholar
  17. 17.
    Guymer, I., O’Brien, R., Harrison, C.: Representation of solute transport and mixing within a surcharged benched manhole using an aggregated dead zone (ADZ) technique. Water Sci. Technol. 34, 95–101 (1996) CrossRefGoogle Scholar
  18. 18.
    Guymer, I., O’Brien, R.T.: The effects of surcharged manholes on the travel time and dispersion of solutes in sewer systems. Water Sci. Technol. 31, 51–59 (1995) Google Scholar
  19. 19.
    Hojati, M., Bector, C.R., Smimou, K.: A simple method for computation of fuzzy linear regression. Eur. J. Oper. Res. 166, 172–184 (2005). doi: 10.1016/j.ejor.2004.01.039 MathSciNetMATHCrossRefGoogle Scholar
  20. 20.
    Höttges, J., Wallis, S.G., Guymer, I.: Das ATZ-Modell zur Vorhersage des Schadstofftransports in Flüssen’. Wasserwirtschart, pp. 494–497 (October 1992) (in German) Google Scholar
  21. 21.
    Konieczki, A.D., Graf, J.B., Carpenter, M.C.: Streamflow and sediment data collected to determine the effects of a controlled flood in March and April 1996 on the Colorado River between Lees Ferry and Diamond Creek, Arizona: U.S. Geological Survey Open—File Report 97–224, 55 p. (1997) Google Scholar
  22. 22.
    Lees, M.J., Camacho, L.A., Whitehead, P.: Extension of the QUASAR river water quality model to include dead zone mixing. Hydrol. Earth Syst. Sci. 2, 353–365 (1998) CrossRefGoogle Scholar
  23. 23.
    Lees, M., Camacho, L.A., Chapra, S.: On the relationship of transient storage and aggregated dead zone models of longitudinal solute transport in streams. Water Resour. Res. 36, 213–224 (2000). doi: 10.1029/1999WR900265 CrossRefGoogle Scholar
  24. 24.
    Nordin, C.F., Sabol, G.L.: Empirical data on longitudinal dispersion in rivers. In: USGS Water Resource Investigation, Lakewood, Colorado, pp. 20–74 (1974) Google Scholar
  25. 25.
    Nordin, C.F., Troutman, D.M.: Longitudinal dispersion in rivers: the persistence of skewness in observed data. Water Resour. Res. 16, 123–128 (1980) CrossRefGoogle Scholar
  26. 26.
    Osuch, M., Romanowicz, R., Wallis, S.G.: Uncertainty in the relationship between flow and parameters in models of pollutant transport. Paper presented at 28th International School of Hydraulics, Krag, Poland, 23–26 September and published in Monographic, Volume E-10(406), Institute of Geophysics, Polish Academy of Sciences, pp. 127–138 (2008) Google Scholar
  27. 27.
    Reynolds, C.S., Carling, P.A., Beven, K.J.: Flow in river channels: new insights into hydraulic retention. Arch. Hydrobiol. 121, 171–179 (1991) Google Scholar
  28. 28.
    Richardson, K., Carling, P.A.: The hydraulics of a straight bedrock channel: insights from solute dispersion studies. Geomorphology 82, 98–125 (2006). doi: 10.1016/j.geomorph.2005.09.022 CrossRefGoogle Scholar
  29. 29.
    Romanowicz, R.J., Osuch, M., Wallis, S.: Modelling of pollutant transport in rivers under unsteady flow. In: Proceedings of IAHR European Division Conference, Edinburgh, UK, May 2010 (2010). Paper FPIIb Google Scholar
  30. 30.
    Rutherford, J.C.: River Mixing. Wiley, Chichester (1994) Google Scholar
  31. 31.
    Smith, P.J., Beven, K.J., Tawn, J., Blazkova, S., Merta, L.: Discharge dependent pollutant dispersion in rivers: estimation of ADZ parameters with surrogate data. Water Resour. Res. 42, W04412 (2006). doi: 10.1029/2005WR004008 CrossRefGoogle Scholar
  32. 32.
    Spreafico, M., van Mazijk, A.: Alarmmodell Rhein ein modell für die operationelle Vorhersage des Transportes von Schadstoffen im Rhein. Bericht Nr. I-12, Kommission für die Hydrologie des Rheins, Lelystad (1993) Google Scholar
  33. 33.
    Thackston, E.L., Schnelle, K.B.: Predicting effects of dead zones on stream mixing. J. Sanit. Eng. Div. ASCE 96, 319–331 (1970) Google Scholar
  34. 34.
    Valentine, E.M., Wood, I.R.: Longitudinal dispersion with dead zones. J. Hydraul. Eng. Div. ASCE 103, 975–990 (1977) Google Scholar
  35. 35.
    van Mazijk, A., Veling, E.J.M.: Tracer experiments in the Rhine Basin: evaluation of the skewness of observed concentration distributions. J. Hydrol. 307, 60–78 (2005) CrossRefGoogle Scholar
  36. 36.
    Wallis, S.G., Young, P.C., Beven, K.J.: Experimental investigation of the aggregated dead zone model for longitudinal solute transport in stream channels. In: Proceedings of the Institution of Civil Engineers, Part 2, vol. 87, March, pp. 1–22 (1989) Google Scholar
  37. 37.
    Wallis, S.G.: Aggregated mixing zone modelling of solute transport in rivers. In: Proceedings of the Fourth National Hydrology Symposium, Cardiff, 13–16 September, pp. 5.9–5.13 (1993) Google Scholar
  38. 38.
    Wallis, S.G., Clarke, R.F.: Hydrological modelling of solute transport in the river Rhine. In: Proceedings of the 5th National BHS Hydrology Symposium, Edinburgh, 4–7 September, pp. 9.31–9.36 (1995) Google Scholar
  39. 39.
    Whitehead, P.G., Williams, R.J., Hornberger, G.M.: On the identification of pollutant or tracer sources using dispersion theory. J. Hydrol. 84, 273–286 (1986) CrossRefGoogle Scholar
  40. 40.
    Young, P.C.: Parallel processes in hydrology and water quality: a unified time-series approach. J. Inst. Water Eng. Manag. 6, 598–612 (1992) CrossRefGoogle Scholar
  41. 41.
    Young, P.C.: Recursive Estimation and Time-Series Analysis. Springer, Berlin (1984) MATHGoogle Scholar
  42. 42.
    Young, W.F., Wallis, S.G.: The aggregated dead zone (ADZ) model for dispersion in rivers. In: Int. Conf. on River Quality Modelling in the Inland Natural Environment (Bournemouth) (1986). BHRA Paper LI 421-433 Google Scholar
  43. 43.
    Young, P.C., Wallis, S.G.: Solute transport and dispersion in channels. In: Beven, K.J., Kirkby, M.J. (eds.) Channel Network Hydrology, pp. 129–174. Wiley, Chichester (1993) Google Scholar
  44. 44.
    Young, P.C., Lees, M.J.: The active mixing volume: a new concept in modelling environmental systems. In: Barnett, V., Turkman, K. (eds.) Statistics for the Environment, pp. 3–34. Wiley, Chichester (1993) Google Scholar

Copyright information

© Springer-Verlag London Limited 2012

Authors and Affiliations

  • Sarka D. Blazkova
    • 1
  • Keith J. Beven
    • 2
  • Paul J. Smith
    • 2
  1. 1.T G Marsaryk Water Resource InstitutePragueCzech Republic
  2. 2.Lancaster Environment CentreLancaster UniversityLancasterUK

Personalised recommendations