Advertisement

Data-Based Mechanistic Modelling: Natural Philosophy Revisited?

  • Peter C. Young

Abstract

The Data-Based Mechanistic (DBM) modelling of stochastic, dynamic systems is predominantly an inductive approach that attempts to extract as much mechanistic information as possible from the available time series data, normally in the form of an identifiable linear, or nonlinear, transfer function model that explains the data well. It recognises that, in contrast to most man-made dynamic systems, the nature of many natural systems, particularly at the holistic or macro-level (global climate, river catchment, macro-economy etc.), is still not well understood. ‘Reductionist’ approaches to modelling such systems, often based on the aggregation of hypothetico–deductive models formulated at the micro level, normally results in very large computer simulation models. In contrast to their DBM counterparts, such large models are not normally identifiable from the available data and so rely not only on the validity of the multiple hypotheses on which they are based, but also on how these hypotheses are perceived to combine, in order to produce the aggregate model. This chapter places DBM modelling in the historical context of ‘natural philosophy’; outlines the major stages in its analysis of time series data; and argues that it can help to bridge the gap between complex computer models and simple, ‘dominant mode’, data-based models. This is illustrated by an example which shows how the DBM approach has been used to evaluate models for the transport and dispersion of solutes in river systems.

Keywords

Advection Dispersion Equation Transient Storage Steady State Gain Deductive Model Simulation Model Parameter 
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.

Notes

Acknowledgements

I am extremely grateful to the friends and colleagues I have worked with over the past half century, particularly all of those who have so generously prepared chapters for this book. Thanks also to Chris Martinez and William Wise, for providing the tracer data; and my colleague Keith Beven for his useful comments on the chapter. And, of course, a special thank you to my wife Wendy, who has so selflessly put up with me so well for all this time.

References

  1. 1.
    Beer, T., Young, P.C.: Longitudinal dispersion in natural streams. ASME J. Environ. Eng. 109, 1049–1067 (1983) CrossRefGoogle Scholar
  2. 2.
    von Bertalanffy, K.L.: General System Theory: Foundations, Development, Applications. George Braziller, New York (1968) Google Scholar
  3. 3.
    Beven, K.J.: Prophecy, reality and uncertainty in distributed hydrological modelling. Adv. Water Resour. 16, 41–51 (1993) CrossRefGoogle 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.
    Cohen, I.B.: The first English version of Newton’s hypotheses non fingo. ISIS 53(173), 379–388 (1962) MATHCrossRefGoogle Scholar
  6. 6.
    De Smedt, F.: Analytical solutions for transport of decaying solutes in rivers with transient storage. J. Hydrol. 330, 672–680 (2006) CrossRefGoogle Scholar
  7. 7.
    Green, H.M., Beven, K.J., Buckley, K., Young, P.C.: Pollution incident prediction with uncertainty. In: Beven, K.J., Chatwin, P., Millbank, J. (eds.) Mixing and Transport in the Environment, pp. 113–137. Wiley, Chichester (1994) Google Scholar
  8. 8.
    Konikow, L.F., Bredehoeft, J.D.: Ground water models cannot be validated. Adv. Water Resour. 15, 75–83 (1992) CrossRefGoogle Scholar
  9. 9.
    Kuhn, T.: The Structure of Scientific Revolutions. University of Chicago, Chicago (1962) Google Scholar
  10. 10.
    Martinez, C.J., Wise, W.R.: Analysis of constructed treatment wetland hydraulics with the transient storage model OTIS. Ecol. Eng. 20(3), 211–222 (2003) CrossRefGoogle Scholar
  11. 11.
    Oreskes, N., Shrader-Frechette, K., Belitz, K.: Verification, validation, and confirmation of numerical models in the earth sciences. Science 263, 641–646 (1994) CrossRefGoogle Scholar
  12. 12.
    Parkinson, S., Young, P.C.: Uncertainty and sensitivity in global carbon cycle modelling. Clim. Res. 9, 157–174 (1998) CrossRefGoogle Scholar
  13. 13.
    Popper, K.: The Logic of Scientific Discovery. Hutchinson, London (1959) MATHGoogle Scholar
  14. 14.
    Price, L., Young, P.C., Berckmans, D., Janssens, K., Taylor, J.: Data-based mechanistic modelling and control of mass and energy transfer in agricultural buildings. Annu. Rev. Control 23, 71–82 (1999) Google Scholar
  15. 15.
    Rigaud, S.P.: Historical Essay on the First Publication of Sir Isaac Newton’s Principia. Oxford University Press, Oxford (1838) Google Scholar
  16. 16.
    Romanowicz, R.J., Young, P.C., Beven, K.J.: Data assimilation and adaptive forecasting of water levels in the River Severn catchment. Water Resour. Res. 42, W06407 (2006). doi: 10.1029/2005WR004373 CrossRefGoogle Scholar
  17. 17.
    Runkel, R.L., Chapra, S.C.: An efficient numerical solution of the transient storage equations for solute transport in small streams. Water Resour. Res. 29(1), 211–215 (1993). doi: 10.1029/92WR02217 CrossRefGoogle Scholar
  18. 18.
    Taylor, G.I.: The dispersion of matter in turbulent flow through a pipe. Proc. R. Soc. A 223, 446–468 (1954) CrossRefGoogle Scholar
  19. 19.
    Valentine, E.M., Wood, I.R.: Longitudinal dispersion with dead zones. J. Hydraul. Div. 103(9), 975–990 (1977) Google Scholar
  20. 20.
    Wagener, T., Camacho, L.A., Wheater, H.S.: Dynamic identifiability analysis of the transient storage model for solute transport in rivers. J. Hydroinform. 4, 199–211 (2002) Google Scholar
  21. 21.
    Wallis, S.G., Young, P.C., Beven, K.J.: Experimental investigation of the aggregated dead zone model for longitudinal solute transport in stream channels. Proc. Inst. Civ. Eng. 2. Res. Theory 87, 1–22 (1989) CrossRefGoogle Scholar
  22. 22.
    Young, P.C.: Recursive approaches to time-series analysis. Bull. Inst. Math. Appl. 10, 209–224 (1974) Google Scholar
  23. 23.
    Young, P.C.: A general theory of modeling for badly defined dynamic systems. In: Vansteenkiste, G.C. (ed.) Modeling, Identification and Control in Environmental Systems, pp. 103–135. North Holland, Amsterdam (1978) Google Scholar
  24. 24.
    Young, P.C.: Recursive Estimation and Time-Series Analysis. Springer, Berlin (1984) (new revised and enlarged edition published 2011: see http://www.springer.com/engineering/control/book/978-3-642-21980-1) MATHGoogle Scholar
  25. 25.
    Young, P.C.: Data-based mechanistic modeling of environmental, ecological, economic and engineering systems. Environ. Model. Softw. 13, 105–122 (1998) CrossRefGoogle Scholar
  26. 26.
    Young, P.C.: Data-based mechanistic modelling, generalised sensitivity and dominant mode analysis. Comput. Phys. Commun. 117, 113–129 (1999) CrossRefGoogle Scholar
  27. 27.
    Young, P.C.: Data-based mechanistic modelling and validation of rainfall-flow processes. In: Anderson, M.G., Bates, P.D. (eds.) Model Validation: Perspectives in Hydrological Science, pp. 117–161. Wiley, Chichester (2001) Google Scholar
  28. 28.
    Young, P.C.: Data-based mechanistic modelling of environmental systems. In: Proceedings, IFAC Workshop on Environmental Systems, First Plenary Session Keynote Paper, Yokohama, Japan (2001) Google Scholar
  29. 29.
    Young, P.C.: Advances in real-time flood forecasting. Philos. Trans. R. Soc., Math. Phys. Eng. Sci. 360(9), 1433–1450 (2002) CrossRefGoogle Scholar
  30. 30.
    Young, P.C.: The data-based mechanistic approach to the modelling, forecasting and control of environmental systems. Annu. Rev. Control 30, 169–182 (2006) CrossRefGoogle Scholar
  31. 31.
    Young, P.C.: The refined instrumental variable method: unified estimation of discrete and continuous-time transfer function models. J. Eur. Syst. Autom. 42, 149–179 (2008) Google Scholar
  32. 32.
    Young, P.C.: Gauss, Kalman and advances in recursive parameter estimation. J. Forecast. 30, 104–146 (2010) (special issue celebrating 50 years of the Kalman Filter) CrossRefGoogle Scholar
  33. 33.
    Young, P.C.: Real-time updating in flood forecasting and warning. In: Pender, G.J., Faulkner, H. (eds.) Flood Risk Science and Management, pp. 163–195. Wiley-Blackwell, Oxford (2010) CrossRefGoogle Scholar
  34. 34.
    Young, P.C., Beck, M.B.: The modelling and control of water quality in a river system. Automatica 10, 455–468 (1974) CrossRefGoogle Scholar
  35. 35.
    Young, P.C., Lees, M.J.: The active mixing volume: a new concept in modelling environmental systems. In: Barnett, V., Turkman, K.F. (eds.) Statistics for the Environment, pp. 3–43. Wiley, Chichester (1993) Google Scholar
  36. 36.
    Young, P.C., Price, L., Berckmans, D., Janssens, K.: Recent developments in the modelling of imperfectly mixed airspaces. Comput. Electron. Agric. 26, 239–254 (2000) CrossRefGoogle Scholar
  37. 37.
    Young, P.C., Ratto, M.: A unified approach to environmental systems modeling. Stoch. Environ. Res. Risk Assess. 23, 1037–1057 (2009) CrossRefGoogle Scholar
  38. 38.
    Young, P.C., Ratto, M.: Statistical emulation of large linear dynamic models. Technometrics 53, 29–43 (2011) MathSciNetCrossRefGoogle Scholar
  39. 39.
    Young, P.C., Wallis, S.G.: Solute transport and dispersion in channels. In: Beven, K.J., Kirkby, M.J. (eds.) Channel Network Hydrology, pp. 129–173. Wiley, Chichester (1993) Google Scholar

Copyright information

© Springer-Verlag London Limited 2012

Authors and Affiliations

  1. 1.Centre for Research on Environmental Systems and StatisticsUniversity of LancasterLancasterUK
  2. 2.Fenner School of Environment and SocietyAustralian National UniversityCanberraAustralia

Personalised recommendations