Model Parameter Estimation for Particle Transport
Publication: Journal of Environmental Engineering
Volume 117, Issue 5
Abstract
A generic parameter estimation algorithm was developed for the simultaneous extraction of multiple parameters from experimental or field observations. The basis of the method lies in the minimization of the variation between model predictions and observations via the iterative numerical determination of the functional minima of the model with respect to the parameters being determined. A multivariable Newton technique, and derivatives thereof, are used for this purpose. By relying on numerical differentiation in the iterative process, the technique is not limited by the model complexity, solution methodology, or scale of its domain. Model parameters have been estimated successfully for analytical and numerical solutions to dispersive and advective‐dispersive particle transport model equations. The effect of sampling or measurement error and initial parameter estimates on algorithm performance has been evaluated. This approach has been successfully applied to determine data requirements and constraints (quantity, quality, and location) for measurement of hydrodynamic and transport characteristics of dye clouds and aquatic particles in laboratory‐mixed settling columns.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Autenrieth, R. L. (1986). “Sorption and desorption partition characterization of selected organochlorine compounds with phytoplankton,” thesis presented to Clarkson University, at Potsdam, New York, in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
2.
Bard, Y. (1974). Non‐linear parameter estimation. Academic Press, New York, N.Y.
3.
Bonner, J. S., Hunt, C. D., Paul, J. F., and Biermam, V. J. (1986). “Prediction of vertical transport of low level radioactive middlesex soil at a deep ocean disposal site.” Tech. Report EPA 520/1‐86‐016, Environmental Research Laboratory, U.S. Environmental Protection Agency, Narragansett, R.I.
4.
Bonner, J. S., Ernest, A. N., Autenrieth, R. L., and Ducharme, S. L. (in press 1990). “Parameterizing models for contaminated sediment transport.” Transport and transformation of contaminants near the sediment‐water interface. J. V. De‐Pinto, ed., Springer‐Verlag, Berlin, Germany.
5.
Box, G. E. P., and Coutie, G. A. (1956). “Application of digital computers in the exploration of functional relationships.” Proc., Institute of Electrical Engineers, London, England, 103B (Suppl. 1) 100.
6.
Carpenter, B. (1987). “Pcb sediment decontamination: Technical/economical assessment of selected alternative treatments.” Tech. Report EPA/600/S2‐86/112, U.S. Environmental Protection Agency, Washington, D.C.
7.
Chapra, S. C., and Canale, R. P. (1988). Numerical methods for engineers. Second Ed., McGraw‐Hill, New York, N.Y.
8.
Dennis Jr., J., and Schnabel, R. (1983). Numerical methods for unconstrained optimization and non‐linear equations. Prentice Hall, Englewood Cliffs, N.J.
9.
Draper, N., and Smith, H. (1981). Applied regression analysis. John Wiley & Sons, New York, N.Y.
10.
Ducharme, S. L. (1989). “Design and validation of a settling column for particle transport studies,” thesis presented to Texas A&M University, at College Station, Texas, in partial fulfillment of the requirements for the degree of Master of Science.
11.
Elzerman, A., and Coates, J. (1987). “Hydrophobic organic compounds on sediments: Equilibria and kinetics of sorption.” Envir. Sci. Tech., 8(1), 58–63.
12.
Gawthrop, P. J. (1984). “Parameter estimation from noncontiguous data,” Proc., Institute of Electrical Engineers, London, England, 131(6), 261–266.
13.
Hunt, J. R., and Pandya, J. (1984). “Sewage sludge coagulation and settling in seawater.” Envir. Sci. Tech., 18(2), 119–121.
14.
Kunisch, K., and White, L. (1985). The parameter estimation problem for parabolic equations and discontinuous observation operators. SIAM J. Control Optim., 23(6), 900–927.
15.
Lee, D.‐Y., Lick, W., and Kang, S. (1981). “The entrainment and deposition of fine‐grained sediments in Lake Erie.” J. Great Lakes Res., 7(3), 224–233.
16.
Lick, W., and Kang, S. (1987). “Entrainment of sediments and dredged materials in shallow lake waters.” J. Great Lakes Res., 13(4), 619–627.
17.
Lick, W. (1982). “Entrainment, deposition and transport of fine grain sediments in lakes.” Hydrobiologia, 91(1), 31–40.
18.
McCreary, E. R. (1990). “Biodegradation of hazardous wastes using activated sludge microbes,” thesis presented to Texas A&M University, at College Station, Texas, in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
19.
O'Melia, C. R. (1972). “Coagulation and flocculation.” Physico‐chemical processes for water quality control. Wiley Interscience, New York, N.Y.
20.
Rodgers, P. (1983). “Model simulation of pcb dynamics in Lake Michigan.” Physical behavior of PCB's in the Great Lakes, D. Mackay, S. Paterson, S. Eisenich, and M. Simmons, eds., 311–328.
21.
Rorschach, R. C. (1990). “Desorption of hexachlorobiphenol from selected particulate matters,” thesis presented to Texas A&M University, at College Station, Texas, in partial fulfillment of the requirements for the degree of Master of Science.
22.
Russel, W. (1981). “Brownian motion of the small particles suspended in liquids.” Ann. Rev. Fluid Mech., 13, 425–455.
23.
Sanders, S. C. (1990). “Vertical transport and dynamic size distribution of new bedford harbor sediments,” thesis presented to Texas A&M University, at College Station, Texas, in partial fulfillment of the requirements for the degree of Master of Science.
24.
Srinivasan, V., and Aiken, R. C. (1986). “Stage‐wise parameter estimation for stiff differential equations.” AIChE J., 32(2), 195–199.
25.
Stefanski, L. A. (1985). “The effects of measurement error on parameter estimation.” Biometrika, 72(3), 583–592.
Information & Authors
Information
Published In
Journal of Environmental Engineering
Volume 117 • Issue 5 • September 1991
Pages: 573 - 594
Copyright
Copyright © 1991 ASCE.
History
Published online: Sep 1, 1991
Published in print: Sep 1991
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.