Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Hostname: page-component-745bb68f8f-mzp66 Total loading time: 0 Render date: 2025-01-22T03:44:44.584Z Has data issue: false hasContentIssue false

9 - Real-time flow forecasting

Published online by Cambridge University Press:  15 December 2009

By
P. C. Young
Edited by
Howard Wheater ,
Soroosh Sorooshian  and
K. D. Sharma
P. C. Young
Affiliation:
Lancaster University, UK
Howard Wheater
Affiliation:
Imperial College of Science, Technology and Medicine, London
Soroosh Sorooshian
Affiliation:
University of California, Irvine
K. D. Sharma
Affiliation:
National Institute of Hydrology, India
Get access

Summary

INTRODUCTION

The primary objective of this chapter is to describe recent research on the design of real-time, adaptive forecasting procedures for the prediction of flow (discharge) or river level (stage) in river systems and to illustrate this with a case study based on data from a semi-arid river catchment in Western Australia. In particular, the aim is to produce an on-line, real-time approach to flow forecasting that is inherently stochastic and so able to predict not only the likely level of future flow, but also the uncertainty associated with this prediction. In this manner, the probability of a flood occurring in the near future can be quantified and this additional information can then be used as a basis for decision-making, operational management, and risk assessment in relation to the flooding of flood-prone locations.

The methodology described in subsequent sections of the chapter can be applied to the forecasting of either river flow or level. For simplicity, however, “flow” will be used here as a generic term to mean either of these two measures. Also, “flow” will be taken to mean the total flow in the river, not just the “run-off” component of total flow. In this context, the approach to forecasting described here is model-based, i.e., depending on the nature of the catchment and the forecasting objectives, the flow forecasts are based on an appropriate combination of stochastic, dynamic models for the relationships between: (i) rainfall and flow, and (ii) flow at various locations along the river, i.e. “flow routing” models.

Type
Chapter
Information
Hydrological Modelling in Arid and Semi-Arid Areas , pp. 113 - 138
Publisher: Cambridge University Press
Print publication year: 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abbot, M. B., Bathurst, J. C., Cunge, J. A., O'Connell, P. E., and Rasmussen, J. (1986). An introduction to the European Hydrological System – Système Hydrologique Européen, SHE. J. Hydrol., 87, 45–59.CrossRefGoogle Scholar
Ahsan, M. and O'Connor, K. M. (1993). A simple non-linear rainfall-runoff model with a variable gain factor. J. Hydrol., 155, 151–83.CrossRefGoogle Scholar
Akaike, H. (1974). A new look at statistical model identification. IEEE Trans. Auto. Control, AC 19, 716–23.CrossRefGoogle Scholar
Anderson, M. G. and Burt, T. P. (eds.) (1985). Hydrological Forecasting. Chichester: Wiley.Google Scholar
Bacon, F. (1620). Novum Organum: see for example Montague, Basil (ed. and trans.) (1854), The Works, 3 vols. Philadelphia: Parry & MacMillan, 343–71.Google Scholar
Beck, M. B. (1983). Uncertainty, system identification and the prediction of water quality. In Uncertainty and Forecasting of Water Quality, ed. Beck, M. B. and Straten, G.. Berlin: Springer-Verlag, 3–68.CrossRefGoogle Scholar
Beck, M. B. and Young, P. C. (1975). A dynamic model for BOD-DO relationships in a non-tidal stream, Water Res., 9, 769–76.CrossRefGoogle Scholar
Beven, K. J. (2000). Uniqueness of place and process representations in hydrological modelling, Hydrol. Earth Sys. Sci., 4, 203–13.CrossRefGoogle Scholar
Beven, K. J. (2001). Rainfall-Runoff Modelling: The Primer. Chichester: Wiley.Google Scholar
Beven, K. J. and Binley, A. M. (1992). The future of distributed models: model calibration and uncertainty prediction, Hydrol. Proc., 6, 279–98.CrossRefGoogle Scholar
Beven, K. J. and Kirkby, M. J. (1979). A physically based variable contributing area model of basin hydrology. Hydrol. Sci. J., 24, 43–69.CrossRefGoogle Scholar
Beven, K. J., Romanowicz, R., and Hankin, B. (2000). Mapping the probability of flood inundation (even in real time). In Flood Forecasting: What Does Current Research Offer the Practitioner? ed. Lees, M. J. and Walsh, P., 56–63. BHS Occasional paper No. 12. London: produced by the Centre for Ecology and Hydrology on behalf of the British Hydrological Society.Google Scholar
Beven, K. J. and Young, P. C. (2003). Comment on “Bayesian recursive parameter estimation for hydrologic models” by M. Thiemann et al., Water Resour. Res., 39(5), 1116.Google Scholar
Billings, S. A. and Voon, W. S. F. (1986). Correlation based model validity tests for non-linear models, Int. J. Contr., 44, 235–44.CrossRefGoogle Scholar
Box, G. E. P. and Jenkins, G. M (1970). Time-Series Analysis, Forecasting and Control. San Francisco: Holden-Day.Google Scholar
Brath, A. and Rosso, R. (1993). Adaptive calibration of a conceptual model for flash flood forecasting. Water Resour. Res., 29, 2561–72.CrossRefGoogle Scholar
Bryson, A. E. and Ho, Y.- C. (1969). Applied Optimal Control. Massachusetts: Blaisdell Publishing.Google Scholar
Cluckie, I. D. (1993). Real-time flood forecasting using weather radar. In Concise Encyclopedia of Environmental Systems, ed. Young, P. C.. Oxford: Pergamon Press, 291–8.Google Scholar
Crawford, N. H. and Linsley, R. K. (1966). Digital simulation in hydrology: the Stanford Watershed Model IV, Tech. Report no. 39, Stanford University, California.
Davis, H. T. and Jones, R. H. (1968). Estimation of the innovations variance of a stationary time series, J. Am. Stat. Assoc., 63, 141–9.Google Scholar
Dooge, J. C. I. (1959). A general theory of the unit hydrograph. J. Geophys. Res., 64. 241–56.CrossRefGoogle Scholar
Dooge, J. C. I. (1986). Theory of flood routing. In River Flow Modelling and Forecasting, ed. Kraijenhoff, D. A. and Moll, J. R.. Dordrecht: D. Reidel, 39–65.CrossRefGoogle Scholar
Dooge, J. C. I. and O'Kane, J. P. (2003). Deterministic Methods in Systems Hydrology. Lisse: Balkema.Google Scholar
Franks, S., Beven, K. J., Quinn, P. F., and Wright, I. (1997). On the sensitivity of soil–vegetation–atmosphere transfer (SVAT) schemes: equifinality and the problem of robust calibration. Agric. Forest Meteorol., 86, 63–75.CrossRefGoogle Scholar
Greenfield, B. J. (1984). The Thames Water Catchment Model, Internal Report, Technology Development Division, Thames Water, UK.
Harvey, A. C. (1989). Forecasting, Structural Time Series Models and the Kalman Filter. Cambridge: Cambridge University Press.Google Scholar
Hasselmann, K. (1998). Climate-change research after Kyoto. Nature, 390, 225–6.CrossRefGoogle Scholar
Hasselmann, K., Hasselmann, S., Giering, R., Ocana, V., and Storch, H. (1997). Sensitivity study of optimal emission paths using a simplified structural integrated assessment (SIAM). Clim. Change, 37, 345–86.CrossRefGoogle Scholar
Hornberger, G. M., Beven, K. J., Cosby, B. J., and Sappington, D. E. (1985). Shenandoah watershed study: calibration of a topography-based variable contributing area hydrological model for a small forested catchment. Water Resour. Res., 21, 1841–50.CrossRefGoogle Scholar
Hu, J., Kumamaru, K., and Hirasawa, K. (2001). A quasi-ARMAX approach to modelling nonlinear systems. Int. J. Cont., 74, 1754–66.CrossRefGoogle Scholar
Jakeman, A. J. and Hornberger, G. M. (1993). How much complexity is warranted in a rainfall-runoff model?Water Resour. Res., 29, 2637–49.CrossRefGoogle Scholar
Jakeman, A. J., Littlewood, I.G., and Whitehead, P. G. (1990). Computation of the instantaneous unit hydrograph and identifiable component flows with application to two small upland catchments, J. Hydrol., 117, 275–90.CrossRefGoogle Scholar
Jakeman, A. J. and Young, P. C. (1979). Refined instrumental variable methods of recursive time-series analysis. Part II: multivariable systems. Int. J. Contr., 29, 621–44.CrossRefGoogle Scholar
Jang, J.-S. R., Sun, C.-T., and Mizutani, E. (1997). Neuro-Fuzzy and Soft Computing. Upper Daddle River, NJ: Prentice Hall.Google Scholar
Jothityangkoon, C., Sivapalan, M., and Farmer, D. L. (2001). Process controls of water balance variability in a large semi-arid catchment: downward approach to hydrological model development. J. Hydrol., 254, 174–98.CrossRefGoogle Scholar
Kalman, R. E. (1960). A new approach to linear filtering and prediction problems. ASME Trans., J. Basic Eng., 82-D, 35–45.CrossRefGoogle Scholar
Kirkby, M. J. (1976). Hydrograph modelling strategies. In Processes in Physical and Human Geography, ed. Peel, R. J., Chisholm, M., and Haggett, P.. London: Academic Press, 69–90.Google Scholar
Klemes, V. (1983). Conceptualisation and scale in hydrology, J. Hydrol., 65, 1–23.CrossRefGoogle Scholar
Konikow, L. F. and Bredehoeft, J. D. (1992). Groundwater models cannot be validated. Adv. Water Resour., 15, 75–83.CrossRefGoogle Scholar
Kraijenhoff, D. A. and Moll, J. R. (1986). River Flow Modelling and Forecasting. Dordrecht: D. Reidel.CrossRefGoogle Scholar
Kuhn, T. (1962). The Structure of Scientific Revolutions. Chicago: University of Chicago.Google Scholar
Lawton, J. (2001). Understanding and prediction in ecology, Institute of Environmental and Natural Sciences, Lancaster University, Distinguished Scientist Lecture.
Lees, M. J. (2000a). Advances in transfer function based flood forecasting. In Flood Forecasting: What Does Current Research Offer the Practitioner? ed. Lees, M. J. and Walsh, P.. BHS Occasional paper No. 12. London: produced by the Centre for Ecology and Hydrology on behalf of the British Hydrological Society, 41–55.Google Scholar
Lees, M. J. (2000b). Data-based mechanistic modelling and forecasting of hydrological systems. J. Hydroinfo., 2, 15–34CrossRefGoogle Scholar
Lees, M., Young, P. C., Beven, K. J., Ferguson, S., and Burns, J. (1994). An adaptive flood warning system for the River Nith at Dumfries. In River Flood Hydraulics, ed. White, W. R. and Watts, J.. Wallingford: Institute of Hydrology, 65–75.Google Scholar
Meijer, H. (1941). Simplified flood routing. Civ. Eng., 11, 306–7.Google Scholar
Moore, R. J. and Jones, D. A. (1978). An adaptive finite difference approach to real-time channel flow routing. In Modeling, Identification and Control in Environmental Systems, ed. Vansteenkiste, G. C.. Amsterdam: North Holland, 153–70.Google Scholar
Moradkhani, H., Sorooshian, S., Gupta, H. V., and Houser, P. R. (2005). Dual stateparameter estimation of hydrological models using ensemble Kalman Filter. Adv. Water Resour., 28, 135–47.CrossRefGoogle Scholar
Nash, J. E. (1959). Systematic determination of unit hydrograph parameters. J. Geophys. Res., 64, 111–15.CrossRefGoogle Scholar
Nash, J. E. and Sutcliffe, J. V. (1970). River flow forecasting through conceptual models: discussion of principles. J. Hydrol., 10, 282–90.CrossRefGoogle Scholar
Natale, L. and Todini, E. (1976). A stable estimator for linear models. 2: Real world hydrologic applications. Water Resour. Res., 12, 672–6.CrossRefGoogle Scholar
Oreskes, N., Shrader-Frechette, K., and Belitz, K. (1994). Verification, validation, and confirmation of numerical models in the earth sciences. Science, 263, 641–6.CrossRefGoogle ScholarPubMed
Parkinson, S. D. and Young, P. C. (1998). Uncertainty and sensitivity in global carbon cycle modelling. Clim. Res., 9, 157–74.CrossRefGoogle Scholar
Popper, K. (1959). The Logic of Scientific Discovery. London: Hutchinson.Google Scholar
Ratto, M., Young, P. C., Romanowicz, R., Pappenberger, F., Saltelli, A., and Pagano, A. (2007). Uncertainty, sensitivity analysis and the role of data based mechanistic modelling in hydrology. Hydrology and Earth System Sciences (HESS), European Geophysical Union, 11, 1249–66 (www.hydrol-earth-syst-sci.net/11/1249/2007/).CrossRefGoogle Scholar
Romanowicz R. J., Beven, K. J., and Tawn, J. A. (1994). Evaluation of predictive uncertainty in non-linear hydrological models using a Bayesian Approach. In Statistics for the Environment (2), Water Related Issues, ed. Barnett, V. and Turkman, F.. Chichester: Wiley, 297–318.Google Scholar
Romanowicz, R., Young, P. C., and Beven, K. J. (2004). Data assimilation in the identification of flood inundation models: derivation of on-line, multi-step predictions of flows. In Hydrology: Science & Practice for the 21st Century, ed. Webb, B., Vol. 1. London: British Hydrological Society, 348–53.Google Scholar
Romanowicz, R. J., Young, P. C., and Beven, K. J. (2006). Data assimilation and adaptive forecasting of water levels in the River Severn catchment. Water Resour. Res., 42 (doi10.1029/2005WR004373).CrossRefGoogle Scholar
Saltelli, A., Chan, K., and Scott, E. M. (2000). Sensitivity Analysis. Chichester: Wiley.Google Scholar
Schwarzenbach, J. and Gill, K. F. (1979). Systems Modelling and Control. London: Edward Arnold.Google Scholar
Schweppe, F. (1965). Evaluation of likelihood functions for Gaussian signals. IEEE Trans. Info. Theory, 11, 61–70.CrossRefGoogle Scholar
Shackley, S., Young, P. C., Parkinson, S. D., and Wynne, B. (1998). Uncertainty, complexity and concepts of good science in climate change modelling: are GCMs the best tools?Clim. Change, 38, 159–205.CrossRefGoogle Scholar
Shaw, E. M. (1994). Hydrology in Practice, 3rd edn. London: Chapman & Hall.Google Scholar
Silvert, W. (1993). Top-down modelling in ecology. In Concise Encyclopedia of Environmental Systems, ed. Young, P. C.. Oxford: Pergamon Press, 60.Google Scholar
Singh, V. P. (ed.) (1995). Computer Models of Watershed Hydrology. Colorado: Water Resources Publications.Google Scholar
Sivapalan, M. and Young, P. C. (2005). Downward approach to hydrological model development. In Encyclopedia of Hydrological Sciences, ed. Anderson, M. G., Vol. 3, part II. Hoboken, NJ: Wiley, 2081–98.CrossRefGoogle Scholar
Sorooshian, S (1985). Development of rainfall-runoff models. Appl. Math. Comp., 17, 279–98.CrossRefGoogle Scholar
Thiemann, M., Trosset, M., Gupta, H., and Sorooshian, S. (2001). Bayesian recursive parameter estimation for hydrologic models. Water Resour. Res., 37, 2521–35.CrossRefGoogle Scholar
Todini, E. (1996). The ARNO rainfall-runoff model. J. Hydrol., 175, 339–82.
Tokar, A. S. and Johnson, P. A. (1999). Rainfall-runoff modeling using artificial neural networks. ASCE J. Hydrol. Eng., 4, 232–9.CrossRefGoogle Scholar
Wallis, S. G., Young, P. C., and Beven, K. J. (1989). Experimental investigation of the aggregated dead zone (ADZ) model for longitudinal solute transport in stream channels, Proc. Inst. Civ. Engrs: Part 2, 87, 1–22.Google Scholar
Wheater, H. S., Jakeman, A. J., and Beven. K. J. (1993). Progress and directions in rainfall-run-off modelling. In Modelling Change in Environmental Systems, ed. Jakeman, A. J., Beck, M. B., and McAleer, M. J., Chichester: Wiley, 101–32.Google Scholar
Whitehead, P. G. and Young, P. C. (1975). A dynamic-stochastic model for water quality in part of the Bedford–Ouse River system. In Computer Simulation of Water Resources Systems, ed. Vansteenkiste, G. C.. Amsterdam: North Holland, 417–38.Google Scholar
Whitehead, P. G., Young, P. C., and Hornberger, G. H. (1976). A systems model of stream flow and water quality in the Bedford–Ouse river. Part l: stream flow modeling, Water Res., 13, 1155–69.CrossRefGoogle Scholar
Wood, E. F. and O'Connell, P. E. (1985). Real-time forecasting. In Hydrological Forecasting, ed. Anderson, M. G. and Burt, T. P.. Chichester: Wiley, 505–58.Google Scholar
Ye, W., Jakeman, A. J., and Young, P. C. (1998). Identification of improved rainfall-runoff models for an ephemeral low yielding Australian catchment, Environ. Mod. Software, 13, 59–74.CrossRefGoogle Scholar
Young, P. C. (1974). Recursive approaches to time-series analysis. Bull. Inst. Maths Appl., 10, 209–24.Google Scholar
Young, P. C. (1978). A general theory of modeling for badly defined dynamic systems. In Modeling, Identification and Control in Environmental Systems, ed. Vansteenkiste, G. C.. Amsterdam: North Holland, 103–35.Google Scholar
Young, P. C. (1983). The validity and credibility of models for badly defined systems. In Uncertainty and Forecasting of Water Quality, ed. Beck, M. B. and Straten, G.. Berlin: Springer-Verlag, 69–100.CrossRefGoogle Scholar
Young, P. C. (1984). Recursive Estimation and Time-Series Analysis. Berlin: Springer-Verlag.CrossRefGoogle Scholar
Young, P. C. (1985). The instrumental variable method: a practical approach to identification and system parameter estimation. In Identification and System Parameter Estimation, ed. Barker, H. A. and Young, P. C.. Oxford: Pergamon Press, 1–16.Google Scholar
Young, P. C. (1986). Time-series methods and recursive estimation in hydrological systems analysis. In River Flow Modelling and Forecasting, ed. Kraijenhoff, D. A. and Moll, J. R.. Dordrecht: D. Reidel, 129–80.CrossRefGoogle Scholar
Young, P. C. (1989). Recursive estimation, forecasting and adaptive control. In Control and Dynamic Systems: Advances in Theory and Applications, Vol. 30, ed. Leondes, C. T.. San Diego: Academic Press, 119–66.Google Scholar
Young, P. C. (1992). Parallel processes in hydrology and water quality: a unified time series approach. Jnl. Inst. Water and Env. Man., 6, 598–612.CrossRefGoogle Scholar
Young, P. C. (1993). Time variable and state dependent modelling of nonstationary and non-linear time series. In Developments in Time Series Analysis, ed. Rao, T. Subba. London: Chapman & Hall, 374–413.CrossRefGoogle Scholar
Young, P. C. (1998a). Data-based mechanistic modelling of engineering systems. J. Vibr. Contr., 4, 5–28.CrossRefGoogle Scholar
Young, P. C. (1998b). Data-based mechanistic modelling of environmental, ecological, economic and engineering systems. Environ. Mod. Software, 13, 105–22.CrossRefGoogle Scholar
Young, P. C. (1999a). Data-based mechanistic modelling, generalised sensitivity and dominant mode analysis. Comp. Phys. Comm., 117, 113–29.CrossRefGoogle Scholar
Young, P. C. (1999b). Non-stationary time series analysis and forecasting. Prog. Environ. Sci., 1, 3–48.Google Scholar
Young, P. C. (2000). Stochastic, dynamic modelling and signal processing: time variable and state dependent parameter estimation. In Non-stationary and Non-linear Signal Processing, ed. Fitzgerald, W. J., Walden, A., Smith, R., and Young, P. C.. Cambridge: Cambridge University Press, 74–114.Google Scholar
Young, P. C. (2001a). The identification and estimation of non-linear stochastic systems. In Non-linear Dynamics and Statistics, ed. Mees, A. I.. Boston: Birkhauser, 127–66.CrossRefGoogle Scholar
Young, P. C. (2001b). Data-based mechanistic modelling and validation of rainfall-flow processes. In Model Validation: Perspectives in Hydrological Science, ed. Anderson, M. G. and Bates, P. D.. Chichester: Wiley, 117–61.Google Scholar
Young, P. C. (2001c). Comment on “A quasi-ARMAX approach to the modelling of nonlinear systems” by J. Hu et al., Int. J. Contr., 74, 1767–71.CrossRefGoogle Scholar
Young, P. C. (2002). Advances in real-time flood forecasting. Phil. Trans. R. Soc. Lond., 360, 1433–50.CrossRefGoogle ScholarPubMed
Young, P. C. (2003). Top-down and data-based mechanistic modelling of rainfall-flow dynamics at the catchment scale, Hydrol. Proc., 17, 2195–217.CrossRefGoogle Scholar
Young, P. C. (2004). Identification and estimation of continuous-time hydrological models from discrete-time data. In Hydrology: Science & Practice for the 21st Century, Vol. 1, ed. Webb, B.. London: British Hydrological Society, 406–13.Google Scholar
Young, P. C. (2005). Rainfall-runoff modeling: transfer function models. In Encyclopedia of Hydrological Sciences, Vol. 3, Part II, ed. Anderson, M. G.. Hoboken, NJ: Wiley, 1985–2000.CrossRefGoogle Scholar
Young, P. C. and Beven, K. J. (1994). Data-based mechanistic modelling and the rainfall-flow nonlinearity, Environmet., 5, 335–63.CrossRefGoogle Scholar
Young, P. C. and Garnier, H. (2006). Identification and estimation of continuous-time rainfall-flow models. In Proc. 14th International Federation on Automatic Control (IFAC) Symposium on System Identification SYSID06, Newcastle, NSW, Australia, Oxford: Pergamon, 1276–81.CrossRef
Young, P. C. and Jakeman, A. J. (1979). Refined instrumental variable methods of recursive time-series analysis. Part I: single input, single output systems. Int. J. Contr., 29, 1–30.CrossRefGoogle Scholar
Young, P. C. and Jakeman, A. J. (1980). Refined instrumental variable methods of recursive time-series analysis. Part III: extensions. Int. J. Contr., 31, 741–64.CrossRefGoogle Scholar
Young, P. C. and Lees, M. J. (1993). The active mixing volume: a new concept in modelling environmental systems. In Statistics for the Environment, ed. Barnett, V. and Turkman, K. F.. Chichester: Wiley, 3–43.Google Scholar
Young, P. C. and Minchin, P. (1991). Environmetric time-series analysis: modelling natural systems from experimental time-series data. Int. Jnl. Biol. Macromol., 13, 190–201.CrossRefGoogle ScholarPubMed
Young, P. C. and Parkinson, S. D. (2002). Simplicity out of complexity. In Environmental Foresight and Models, ed. Beck, M. B.. Amsterdam: Elsevier, 251–301.Google Scholar
Young, P. C. and Pedregal, D. (1998). Data-based mechanistic modelling. In System Dynamics in Economic and Financial Models, ed. Heij, C. and Schumacher, H.. Chichester: Wiley, 169–213.Google Scholar
Young, P. C. and Pedregal, D. (1999a). Macro-economic relativity: government spending, private investment and unemployment in the USA 1948–1998. Struct. Changes Econ. Dynam., 10, 359–80.CrossRefGoogle Scholar
Young, P. C. and Pedregal, D. (1999b). Recursive and en-bloc approaches to signal extraction. J. App. Stats., 26, 103–28.CrossRefGoogle Scholar
Young, P. C. and Tomlin, C. M. (2000). Data-based mechanistic modelling and adaptive flow forecasting. In Flood Forecasting: What Does Current Research Offer the Practitioner?, ed. Lees, M. J. and Walsh, P.. BHS Occasional paper No. 12 London: produced by the Centre for Ecology and Hydrology on behalf of the British Hydrological Society.Google Scholar
Young, P. C. and Wallis, S. G. (1985). Recursive estimation: a unified approach to the identification, estimation and forecasting of hydrological systems. Appl. Math. Compu., 17, 299–334.Google Scholar
Young, P. C., Chotai, A., and Beven, K. J. (2004). Data-based mechanistic modelling and the simplification of environmental systems. In Environmental Modelling: Finding Simplicity in Complexity, ed. Wainright, J. and Mulligan, M.. Chichester: Wiley, 371–388.Google Scholar
Young, P. C., Jakeman, A. J., and Post, D. A. (1997a). Recent advances in data-based modelling and analysis of hydrological systems. Water Sci. Tech., 36, 99–116.CrossRefGoogle Scholar
Young, P. C., McKenna, P., and Bruun, J. (2001). Identification of non-linear stochastic systems by state dependent parameter estimation. Int. J. Contr., 74, 1837–57.CrossRefGoogle Scholar
Young, P. C., Parkinson, S. D., and Lees, M. (1996). Simplicity out of complexity in environmental systems: Occam's Razor revisited. J. Appl. Stat., 23, 165–210.CrossRefGoogle Scholar
Young, P. C., Schreider, S. Y., and Jakeman, A. J. (1997b). A streamflow forecasting algorithm and results for the Upper Murray Basin. In Proc. MODSIM 97 Congress on Modelling and Simulation, Hobart, Tasmania, ed. A. D McDonald and M. McAleer. Canberra: The Modelling and Simulation Society of Australia, Inc.Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×