10.2190/JCHN-0KRK-4JQN-EDMW JCHN0KRK4JQNEDMW 2 Nonlinear Least Squares Techniques for System Identification in Water Quality 23 37 20020509 20020509 20020509 20020509 JCHN0KRK4JQNEDMW.pdf http://baywood.metapress.com/link.asp?target=contribution&id=JCHN0KRK4JQNEDMW 1 J.-G. Beliveau G. Mattingly Department of Civil Engineering, Columbia University Department of Civil and Geological Engineering, Princeton University In natural surface waters such as rivers and lakes, the supply of dissolved oxygen (DO) and the oxygen demand (BOD) axe measurable quantities which determine the water's quality. Using specific water quality modeling systems and records of these measurable quantities, the important parameters governing the system response can be found. Once these parameters are determined, meaningful sets of controls may be imposed to keep water quality at or above acceptable standards. Many models have been proposed to represent the experimental observations. Most of these are variations of the classical Streeter-Phelps equation for the oxygen-sag relationship in rivers. The model which is considered in the present effort is due to Camp, and considers such effects (and the respective parameters) as sedimentation, (k₃); photosynthesis (A); runoff (R); reaeration rate (k₂); and the deoxygenation rate (k₁). The method of nonlinear least squares combined with eigenvalue perturbations and parametric differentiation is used for parameter estimation for cases with both BOD and DO data and for DO data only. Both numerically generated test cases and actual laboratory experiments are considered in this "inverse" procedure. J. S. Shastry, L. T. Fan, and L. E. Erickson, Nonlinear parameter estimation in water quality modeling, <i>Jnl. of the Environmental Engr.</i>, Div. ASCE, June 1973. R. W. Cleary and D. D. Adrian, New analytical solutions for dye diffusion equations, <i>Jnl. Environmental Engr.</i>, Div. ASCE, June 1973. T. R. Camp, <i>Water and Its Impurities</i>, Reinhold Publishing Corporation, New York, 1963. W. E. Dobbins, BOD and oxygen relationships in streams, <i>Jnl. Sanitary Engr.</i>, Division ASCE, 90, 1964. J. W. Clark and W. Veissman, Jr., <i>Water Supply and Pollution Control</i>, International Textbook Company, Scranton, Pa., 1965. E. S. Lee and I. Hwang, Stream quality modeling by quasilinearization, <i>Jnl. Water Pollution Control Federation</i>, Feb. 1971. E. S. Lee and I. Hwang, Dynamic modeling of stream quality by invariant imbedding, <i>Water Resources Bulletin</i>, Feb. 1971. J.-G. Beliveau, <i>Suspension Bridge Aero elasticity: Nonlinear Least Squares Techniques for System Identification</i>, Ph.D. Thesis, Dept. of Civil and Geological Engineering, Princeton University, Sept. 1973. M. Coantic and A. Favre, Air Sea Interactions: Research Program and Facilities at I. M. S. T., Eighth Symposium on Naval Hydrodynamics, ACR 179, ONR 1970.