Skip to main content

Uncertainty, System Identification, and the Prediction of Water Quality

  • Chapter
Uncertainty and Forecasting of Water Quality

Abstract

There would be little disagreement among water quality modelers with the opinion of Orlob (1983a) that virtually all the significant developments since the (now) classical work of Streeter and Phelps (1925) have occurred within the past two decades. During the 1960s and early 1970s there was a very substantial investment in model-building associated with water quality management projects, particularly in the United States. The main legacy of this initial investment is a well-established interest in the development of progressively larger and more complex simulation models. “Large” is admittedly a rather imprecise description of a model, although a glance at some of the recent literature on water quality modeling will give some impression of the intended meaning (for example, Russell, 1975; Patten, 1975, 1976; Jørgensen and Harleman, 1978; Scavia and Robertson, 1979). There is no doubt that the immense scope for complex system simulation created by the advent of electronic computers has fostered the rapid growth of “large” water quality models.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Adachi, N. and Ikeda, S. (1978). Stability Analysis of Eutrophication Models. RM-78-53. International Institute for Applied Systems Analysis, Laxenburg, Austria.

    Google Scholar 

  • Akaike, H. (1974). A new look at statistical model identification. IEEE Transactions on Automatic Control, 19:716–722.

    Article  Google Scholar 

  • Andrews, J.F. (1977). Dynamics and control of wastewater treatment plants. In J.H. Sherrard (Editor), Fundamental Research Needs for Water and Wastewater Treatment Systems. Proceedings of the NSF/AEEP Conference, Arlington, Virginia, December, pp. 83–92.

    Google Scholar 

  • Andrews, J.F. and Stenstrom, M.K. (1978). Dynamic models and control strategies for wastewater treatment plants — an overview. In Y. Sawaragi and H. Akashi (Editors), Environmental Systems Planning, Design, and Control, Volume 2. Pergamon, Oxford, pp. 443–452.

    Google Scholar 

  • Argentesi, F. and Olivi, L. (1976). Statistical sensitivity analyses of a simulation model for the biomass–nutrient dynamics in aquatic ecosystems. In the Proceedings of the Summer Computer Simulation Conference, 4th. Simulation Councils, La Jolla, California, pp. 389–393.

    Google Scholar 

  • Åström, K.J. and Eykhoff, P. (1971). System identification — a survey. Automatica, 7:123–162.

    Article  Google Scholar 

  • Atherton, R.W., Schainker, R.B., and Ducot, E.R. (1975). On the statistical sensitivity analysis of models for chemical kinetics. AIChE Journal, 21(3) : 441–448.

    Article  CAS  Google Scholar 

  • Battista, J.R. (1977). The holistic paradigm and general system theory. General Systems, XXII: 65–71.

    Google Scholar 

  • Beck, M.B. (1978a). A Comparative Case Study of Dynamic Models for DO–BOD–Algae Interaction in a Freshwater River. RR-78-19. International Institute for Applied Systems Analysis, Laxenburg, Austria.

    Google Scholar 

  • Beck, M.B. (1978b). Random signal analysis in an environmental sciences problem. Applied Mathematical Modeling, 2(1):23–29.

    Article  Google Scholar 

  • Beck, M.B. (1979a). Model structure identification from experimental data. In E. Halfon (Editor), Theoretical Systems Ecology. Academic Press, New York, pp. 259–289.

    Google Scholar 

  • Beck, M.B. (1979b). System Identification, Estimation and Forecasting of Water Quality — Part 1: Theory. WP-79-31. International Institute for Applied Systems Analysis, Laxenburg, Austria.

    Google Scholar 

  • Beck, M.B. (1979c). On-line Estimation of Nitrification Dynamics. PP-79-3. International Institute for Applied Systems Analysis, Laxenburg, Austria.

    Google Scholar 

  • Beck, M.B. (1980). Applications of system identification and parameter estimation in water quality modelling. In the Proceedings of the Oxford Symposium on Hydrological Forecasting, IAHS– AIHS Publication No. 129, pp. 123–131.

    Google Scholar 

  • Beck, M.B. (1981). Hard or soft environmental systems? Ecological Modelling, 11:233–251.

    Article  Google Scholar 

  • Beck, M.B. (1982). The Propagation of Errors and Uncertainty in Forecasting Water Quality, Part II: Some Simple Examples and Case Studies. Working Paper. International Institute for Applied Systems Analysis, Laxenburg, Austria. (Forthcoming.)

    Google Scholar 

  • Beck, M.B. and Young, P.C. (1975). A dynamic model for DO–BOD relationships in a non-tidal stream. Water Research, 9:769–776.

    Article  Google Scholar 

  • Beck, M.B. and Young, P.C. (1976). Systematic identification of DO–BOD model structure. Journal of the Environmental Engineering Division, American Society of Civil Engineers, 102 (EE5): 902–927.

    Google Scholar 

  • Beck, M.B., Latten, A., and Tong, R.M. (1978). Modelling and Operational Control of the Activated Sludge Process of Wastewater Treatment. PP-78-10. International Institute for Applied Systems Analysis, Laxenburg, Austria.

    Google Scholar 

  • Beck, M.B., Halfon, E., and van Straten, G. (1979). The Propagation of Errors and Uncertainty in Forecasting Water Quality, Part I: Method. WP-79-100. International Institute for Applied Systems Analysis, Laxenburg, Austria.

    Google Scholar 

  • Bedford-Ouse Study (1979). Final Report. Anglian Water Authority, Huntingdon, UK.

    Google Scholar 

  • Bierman,V.J., Dolan,D.M., Stoermer, E.F., Gannon, J.E., and Smith, V.E. (1980). The Development and Calibration of a Spatially Simplified Multi-Class Phytoplankton Model for Saginaw Bay, Lake Huron. Contribution No. 33. Great Lakes Environmental Planning Study, US Environmental Protection Agency, Grosse Ile, Michigan.

    Google Scholar 

  • Box, G.E.P. and Jenkins, G.M. (1970). Time-Series Analysis, Forecasting and Control. Holden-Day, San Francisco,California.

    Google Scholar 

  • Burns, J.R. (1975). Error analysis of nonlinear simulations: applications to world dynamics. IEEE Transactions on Systems, Man, and Cybernetics, 5(3) : 331–340.

    Google Scholar 

  • Canale, R.P., DePalma, L.M., and Powers, W.F. (1980). Sampling Strategies for Water Quality in the Great Lakes. Report No. EPA-600/3-80-55. US Environmental Protection Agency, Environmental Research Laboratory, Duluth, Minnesota.

    Google Scholar 

  • Chan, C.W., Harris, C.J., and Wellstead, P.E. (1974). An order-testing criterion for mixed autoregressive moving average processes. International Journal of Control, 20:817–834.

    Article  Google Scholar 

  • Cobelli, C., Lepschy, A., and Romanin-Jacur, G. (1979). Structural identifiability of linear compartmental models of ecosystems. In E. Halfon (Editor), Theoretical Systems Ecology. Academic Press, New York, pp. 237–258.

    Google Scholar 

  • Di Toro, D.M.. and van Straten, G. (1979). Uncertainty in the Parameters and Predictions of Phytoplankton Models. WP-79-27. International Institute for Applied Systems Analysis, Laxenburg, Austria.

    Google Scholar 

  • Dobbins, W.E. (1964). BOD and oxygen relationships in streams. Journal of the Sanitary Engineering Division, American Society of Civil Engineers, 90:53–78.

    Google Scholar 

  • Eberhardt, L.L. (1977). Applied systems ecology: models, data, and statistical methods. In G.S. Innis (Editor), New Directions in the Analysis of Ecological Systems. Simulation Council Proceedings Series, 5(1): 43–55.

    Google Scholar 

  • Eykhoff, P. (1974). System Identification — Parameter and State Estimation. Wiley, Chichester.

    Google Scholar 

  • Fedra, K., van Straten, G., and Beck, M.B. (1981). Uncertainty and arbitrariness in ecosystems modeling: a lake modeling example. Ecological Modelling, 13:87–110.

    Article  Google Scholar 

  • Fleming, G. (1979). Total river basin assessment of sediment–erosion–transport–deposition processes by mathematical model. In Pilot Zones for Water Quality Management. Proceedings of a Seminar, Institute for Water Management, Budapest, pp. 262–280.

    Google Scholar 

  • Gardner, R.H., O’Neill, R.V., Mankin, J.B., and Carney, J.H. (1980a). A Comparison of Sensitivity Analysis and Error Analysis Based on a Stream Ecosystem Model. Technical Report. Environmental Sciences Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee.

    Google Scholar 

  • Gardner, R.H., O’Neill, R.V., Mankin, J.B., and Kumar, D. (1980b). Comparative error analysis of six predator–prey models. Ecology, 61(2) : 323–332.

    Article  Google Scholar 

  • Goh, B.S. (1979). Robust stability concepts for ecosystems models. In E. Halfon (Editor), Theoretical Systems Ecology. Academic Press, New York, pp. 467–487.

    Google Scholar 

  • Gustavsson, I. (1975). Survey of applications of identification in chemical and physical processes. Automatica, 11:3–24.

    Article  Google Scholar 

  • Halfon, E. (1979a). The effects of data variability in the development and validation of ecosystems models. In B.P. Zeigler, M.S. Elzas, G.J. Klir, and T.I. Ören (Editors), Methodology in Systems Modelling and Simulation. North-Holland, Amsterdam, pp. 335–343.

    Google Scholar 

  • Halfon, E. (1979b). On the parameter structure of a large-scale ecological model. In G.P. Patil and M.L. Rosenzweig (Editors), Contemporary Quantitative Ecology and Related Econometrics. International Cooperative Publishing House, Fairland, Maryland, pp. 279–293.

    Google Scholar 

  • Holling, C.S. (Editor) (1978). Adaptive Environmental Assessment and Management. Wiley, Chichester.

    Google Scholar 

  • Hornberger, G.M. (1980). Uncertainty in dissolved oxygen prediction due to variability in algal photosynthesis. Water Research, 14:355–361.

    Article  CAS  Google Scholar 

  • Hornberger, G.M. and Spear, R.C. (1980). Eutrophication in Peel Inlet — I. Problem-defining behavior and a mathematical model for the phosphorus scenario. Water Research, 14:29–42.

    Article  CAS  Google Scholar 

  • Hornberger, G.M. and Spear, R.C. (1981). An approach to the preliminary analysis of environmental systems. Journal of Environmental Management, 12(1) : 7–18.

    Google Scholar 

  • International Association of Hydrological Sciences (1978). Modelling the Water Quality of the Hydrological Cycle. Proceedings of the Baden Symposium. IAHS–AIHS Publication No. 125.

    Google Scholar 

  • International Association of Hydrological Sciences (1980). Hydrological Forecasting. Proceedings of the Oxford Symposium. IAHS–AIHS Publication No. 129.

    Google Scholar 

  • Isermann, R. (Editor) (1980). Identification and System Parameter Estimation. Proceedings of the IF AC Symposium, 5 th. Pergamon, Oxford.

    Google Scholar 

  • Jakeman, A.J. and Young, P.C. (1980). Towards optimal modeling of translocation data from tracer studies. Proceedings of the Biennial Conference of the Simulation Society of Australia, 4th, pp. 248–253.

    Google Scholar 

  • Jazwinski, A.H. (1970). Stochastic Processes and Filtering Theory. Academic Press, New York.

    Google Scholar 

  • Jørgensen, S.E. and Harleman, D.R.F. (1978). Hydrophysical and Ecological Modeling of Deep Lakes and Reservoirs. CP-78-7. International Institute for Applied Systems Analysis, Laxenburg, Austria.

    Google Scholar 

  • Kahlig, P. (1979). One-dimensional transient model for short-term prediction of downstream pollution in rivers. Water Research, 13:1311–1316.

    Article  CAS  Google Scholar 

  • Kempf, J. and van Straten, G. (1980). Applications of Catastrophe Theory to Water Quality Modelling. CP-80-12. International Institute for Applied Systems Analysis, Laxenburg, Austria.

    Google Scholar 

  • Kossen, N.W.F. (1979). Mathematical modelling of fermentation processes: scope and limitations. In A.T. Bull, D.C. Ellwood, and C. Ratledge (Editors), Microbial Technology: Current State, Future Prospects. Cambridge University Press, Cambridge, pp. 327–357.

    Google Scholar 

  • Lack, T.J. and Lund, J.W.G. (1974). Observations and experiments on the phytoplankton of Blelham Tarn, English Lake District. Freshwater Biology, 4:399–415.

    Article  Google Scholar 

  • Leonov, A. (1980). Mathematical Modeling of Phosphorus Transformation in the Lake Balaton Ecosystem. WP-80-149. International Institute for Applied Systems Analysis, Laxenburg, Austria.

    Google Scholar 

  • Lewandowska, A. (1981). Structural Properties and Frequency Response Analysis of Simplified Water Quality Models: the Case of Time-Invariant Coefficients. WP-81-116. International Institute for Applied Systems Analysis, Laxenburg, Austria.

    Google Scholar 

  • Lewandowski, A. (1981). Issues in Model Validation. WP-81-32. International Institute for Applied Systems Analysis, Laxenburg, Austria.

    Google Scholar 

  • Ljung, L. (1979). Asymptotic behavior of the extended Kaiman filter as a parameter estimator for linear systems. IEEE Transactions on Automatic Control, 24:36–50.

    Article  Google Scholar 

  • Maciejowski, J.M. (1979). Model discrimination using an algorithmic information criterion. Automatica, 15:579–593.

    Article  Google Scholar 

  • Maciejowski, J.M. (1980). A Least-Genericity Principle for Model Selection. Report No. 91. Control Theory Centre, University of Warwick, Coventry.

    Google Scholar 

  • Magee, B. (1973). Popper. Fontana, London.

    Google Scholar 

  • Mankin, J.B., O’Neill, R.V., Shugart, H.H., and Rust, B.W. (1977). The importance of validation in ecosystem analysis. In G.S. Innis (Editor), New Directions in the Analysis of Ecological Systems. Simulation Council Proceedings Series, 5(1) : 63–72.

    Google Scholar 

  • Marsili-Libelli, S. (1980). The role of microprocessors in water quality management: problems and prospects. In M.B. Beck (Editor), Real-Time Water Quality Management. CP-80-38. International Institute for Applied Systems Analysis, Laxenburg, Austria, pp. 162–183.

    Google Scholar 

  • McLaughlin, D.B. (1983). Statistical analysis of uncertainty propagation and model accuracy. In M.B. Beck and G. van Straten (Editors), Uncertainty and Forecasting of Water Quality. This volume, pp. 305–319.

    Google Scholar 

  • Olsson, G. (1980). Estimation and identification problems in wastewater treatment. In E.F. Wood (Editor), Real-Time Forecasting/Control of Water Resource Systems. Pergamon, Oxford, pp. 93–108.

    Google Scholar 

  • O’Neill, R.V. and Gardner, R.H. (1979). Sources of uncertainty in ecological models. In B.P. Zeigler, M.S. Elzas, G.J. Klir, and T.I. Ören (Editors), Methodology in Systems Modelling and Simulation. North-Holland, Amsterdam, pp. 447–463.

    Google Scholar 

  • Orlob, G.T. (1983a). Introduction. In G.T. Orlob (Editor), Mathematical Modeling of Water Quality: Streams, Lakes, and Reservoirs. Wiley, Chichester, pp. 1–10.

    Google Scholar 

  • Orlob, G.T. (1983b). Future directions. In G.T. Orlob (Editor), Mathematical Modeling of Water Quality: Streams, Lakes, and Reservoirs. Wiley, Chichester, pp. 503–509.

    Google Scholar 

  • Park, R.A., Scavia, D., and Clesceri, N.L. (1975). CLEANER: the Lake George model. In C.S. Russell (Editor), Ecological Modelling in a Resource Management Framework. Working Paper QE-1. Resources for the Future, Washington, D.C., pp. 49–81.

    Google Scholar 

  • Patten, B.C. (Editor) (1975). Systems Analysis and Simulation in Ecology, Volume III. Academic Press, New York, p. 622.

    Google Scholar 

  • Patten, B.C. (1976). Systems Analysis and Simulation in Ecology, Volume IV. Academic Press, New York, p. 608.

    Google Scholar 

  • Popper, K.R. (1959). The Logic of Scientific Discovery. Hutchinson, London.

    Google Scholar 

  • Reckhow, K.H. (1979). The use of a simple model and uncertainty analysis in lake management. Water Resources Bulletin, 15:601–611.

    Google Scholar 

  • Russell, C.S. (Editor) (1975). Ecological Modeling in a Resource Management Framework. Working Paper QE-1. Resources for the Future, Washington, D.C.

    Google Scholar 

  • Scavia, D. and Robertson, A. (Editors) (1979). Perspectives on Lake Ecosystem Modeling. Ann Arbor Science Publishers, Ann Arbor, Michigan.

    Google Scholar 

  • Scavia, D., Powers, W.F., Canale, R.P., and Moody, J.L. (1981). Comparison of first-order error analysis and Monte Carlo simulation in time-dependent lake eutrophication models. Water Resources Research, 17(4): 1051–1069.

    Article  Google Scholar 

  • Shastry, J.S., Fan, L.T., and Erickson, L.E. (1973). Non-linear parameter estimation in water quality modeling. Journal of the Environmental Engineering Division, American Society of Civil Engineers, 99(EE3):315–331.

    Google Scholar 

  • Siljak, D.D. (1979). Structure and stability of model ecosystems. In E. Halfon (Editor), Theoretical Systems Ecology. Academic Press, New York, pp. 151–181.

    Google Scholar 

  • Söderström, T. (1977). On model structure testing in system identification. International Journal of Control, 26:1–18.

    Article  Google Scholar 

  • Söderström, T., Ljung, L., and Gustavsson, I. (1974). On the Accuracy of Identification and the Design of Identification Experiments. Report 7428. Department of Automatic Control, Lund Institute of Technology, Lund, Sweden.

    Google Scholar 

  • Somlyody, L. (1977). Dispersion measurement on the Danube. Water Research, 11:411–417.

    Article  Google Scholar 

  • Somlyody, L. (1981). Water Quality Modelling: A Comparison of Transport-Oriented and Biochemistry-Oriented Approaches. WP-81-117. International Institute for Applied Systems Analysis, Laxenburg, Austria.

    Google Scholar 

  • Spear, R.C. and Hornberger, G.M. (1980). Eutrophication in Peel Inlet — II. Identification of critical uncertainties via generalized sensitivity analysis. Water Research, 14:43–49.

    Article  CAS  Google Scholar 

  • Streeter, H.W. and Phelps, E.B. (1925). A Study of the Pollution and Natural Purification of the Ohio River. Bulletin No. 146. US Public Health Service, Washington, D.C.

    Google Scholar 

  • Thé, G. (1978). Parameter identification in a model for the conductivity of a river based on noisy measurements at two locations. In G.C. Vansteenkiste (Editor), Modeling, Identification and Control in Environmental Systems. North-Holland, Amsterdam, pp. 823–830.

    Google Scholar 

  • Thomann, R.V., Winfield, R.P., and Segna, J.J. (1979). Verification Analysis of Lake Ontario and Rochester Embayment Three-Dimensional Eutrophication Models. Report EPA-600/3-79-094. US Environmental Protection Agency, Environmental Research Laboratory, Duluth, Minnesota.

    Google Scholar 

  • Tong, R.M., Beck, M.B., and Latten, A. (1980). Fuzzy control of the activated sludge wastewater treatment process. Automatica, 16:659–701.

    Article  Google Scholar 

  • Ulanowicz, R.E. (1979). Prediction, chaos, and ecological perspective. In E. Halfon (Editor), Theoretical Systems Ecology. Academic Press, New York, pp. 107–117.

    Google Scholar 

  • Unbehauen, H. and Göhring, B. (1974). Tests for determining model-order in parameter estimation. Automatica, 10:233–244.

    Article  Google Scholar 

  • van den Boom, A.J.M. and van den Enden, A.W.M. (1974). The determination of the orders of process and noise dynamics. Automatica, 10:245–256.

    Article  Google Scholar 

  • van Straten, G. (1980). Analysis of Model and Parameter Uncertainty in Simple Phytoplankton Models for Laka Balaton. WP-80-139. International Institute for Applied Systems Analysis, Laxenburg, Austria.

    Google Scholar 

  • van Straten, G. (1983). Ḿaximum likelihood estimation of parameters and uncertainty in phytoplankton models. In M.B. Beck and G. van Straten (Editors), Uncertainty and Forecasting of Water Quality. This volume, pp. 157–171.

    Google Scholar 

  • van Straten, G. and Golbach, G. (1982). Frequency-Domain and Time-Domain Analysis of Dispersion in the River Rhine. (In preparation.)

    Google Scholar 

  • van Straten, G. and Somlyódy, L. (1980). Lake Balaton Eutrophication Study: Present Status and Future Program. WP-80-187. International Institute for Applied Systems Analysis, Laxenburg, Austria.

    Google Scholar 

  • van Straten, G., Jolankai, G., and Herodek, S. (1979). Review and Evaluation of Research on the Eutrophication of Lake Balaton — A Background Report for Modeling. CP-79-13. International Institute for Applied Systems Analysis, Laxenburg, Austria.

    Google Scholar 

  • Vansteenkiste, G.C. (Editor) (1975). Computer Simulation of Water Resources Systems. North-Holland, Amsterdam, p. 686.

    Google Scholar 

  • Vansteenkiste, G.C. (Editor) (1978). Modeling, Identification and Control in Environmental Systems. North-Holland, Amsterdam, p. 1028.

    Google Scholar 

  • Wellstead, P.E. (1976). Model order testing using an auxiliary system. Proceedings of the Institution of Electrical Engineers, 123:1373–1379.

    Article  Google Scholar 

  • Wellstead, P.E. (1978). An instrumental product moment test for model order estimation. Automatica, 14:89–91.

    Article  Google Scholar 

  • White, K.E., Lee, P.J., and Belcher, A.S.B. (1980). Time-of-travel and its significance. In M.J. Stiff (Editor), River Pollution Control. Ellis Horwood, Chichester, pp. 275–288.

    Google Scholar 

  • Whitehead, P.G. (1979). Application of recursive estimation techniques to time-variable hydrological systems. Journal of Hydrology, 40:1–16.

    Article  Google Scholar 

  • Whitehead, P.G. (1983). Modeling and forecasting of water quality in non-tidal rivers: the Bedford-Ouse study. In M.B. Beck and G. van Straten (Editors), Uncertainty and Forecasting of Water Quality. This volume, pp. 321–337.

    Google Scholar 

  • Whitehead, P.G. and Young, P.C. (1979). Water quality in river systems: Monte Carlo analysis. Water Resources Research, 15(2):451–459.

    Article  Google Scholar 

  • Whitehead, P.G., Young, P.C., and Hornberger, G.M. (1979). A systems model of flow and water quality in the Bedford-Ouse River, Part I: streamflow modelling. Water Research, 13:1155–1169.

    Article  Google Scholar 

  • Woodside, C.M. (1971). Estimation of the order of linear systems. Automatica, 7:727–733.

    Article  Google Scholar 

  • Young, P.C. (1974). A recursive approach to time-series analysis. Journal of the Institute of Mathematics and its Applications, 10:209–224.

    Google Scholar 

  • Young, P.C. (1978). General theory of modeling for badly defined systems. In G.C. Vansteenkiste (Editor), Modeling, Identification and Control in Environmental Systems. North-Holland, Amsterdam, pp. 103–135.

    Google Scholar 

  • Young, P.C. (1979). Self-adaptive Kaiman filter. Electronics Letters, 15(2):358–360.

    Article  Google Scholar 

  • Young, P.C. (1983). The validity and credibility of models for badly defined systems. In M.B. Beck and G. van Straten (Editors), Uncertainty and Forecasting of Water Quality. This volume, pp. 69–98.

    Google Scholar 

  • Young, P.C., Jakeman, A.J., and McMurtrie, R.E. (1980). An instrumental variable method for model order identification. Automatica, 16:281–294.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1983 International Institute for Applied Systems Analysis, Laxenburg/Austria

About this chapter

Cite this chapter

Beck, M.B. (1983). Uncertainty, System Identification, and the Prediction of Water Quality. In: Beck, M.B., van Straten, G. (eds) Uncertainty and Forecasting of Water Quality. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-82054-0_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-82054-0_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-82056-4

  • Online ISBN: 978-3-642-82054-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics