Identification in nonlinear, distributed parameter water quality models

Abstract

Systematic and efficient numerical algorithms are developed and applied to the identification of unknown functional parameters in nonlinear estuarine water quality models based on input‐output measurements. As an illustration of the methodology the longitudinal dispersion coefficient is identified from an intratidal, time‐varying, variable area, salinity intrusion model by using both simulated data and actual data from the Delaware River estuary. A comparison among three proposed algorithms through extensive simulation research shows that Marquardt's algorithm emerged as the most efficient one. Effects of noise content and the number of data measurement locations on parameter sensitivity are investigated. Actual monitored salinity data for 3 days in September 1965 are tested in the saline portion of the Delaware River estuary. The spatial variation of the longitudinal dispersion coefficient for this period is estimated. The results obtained indicate that the methodology is generally applicable and it represents a different and supplementary alternative to the methods based on analytical predictions and empirical correlations.

A Review of Surface Water Quality Models

“…The one-dimensional model was updated to a two-dimensional one which was applied to water quality simulation of lakes and gulfs [37, 38]. Nonlinear system models were developed during the period from 1970 to 1975 [39]. These models included the N and P cycling system, phytoplankton and zooplankton system and focused on the relationships between biological growing rate and nutrients, sunlight and temperature, and phytoplankton and the growing rate of zooplankton [35, 37, 39].…”

“…Nonlinear system models were developed during the period from 1970 to 1975 [39]. These models included the N and P cycling system, phytoplankton and zooplankton system and focused on the relationships between biological growing rate and nutrients, sunlight and temperature, and phytoplankton and the growing rate of zooplankton [35, 37, 39]. The finite difference method and finite element method were applied to these water quality models due to the previous nonlinear relationships and they were simulated using one- or two-dimensional models.…”

Numerical techniques for estimating best‐distributed Manning's Roughness Coefficients for open estuarial river systems

“…Another crucial factor in implementing inverse problems is the proper choice of the minimization algorithm. A recent overview of parameter identification in distributed systems is The survey failed to reveal a single formal application of inverse problem methodology to estuarial systems except for the previous work by Yih and Davidson [1975] and an earlier one by Baltzer and Lai [1968]. Up to the present the situation appears to be that there were also no available or practical least squares procedures that were really suitable for the general nonlinear-distributed parameter system, for which the analytical derivative and/or analytical solution is unavailable.…”

Automatic Calibration of Water Quality and Hydrodynamic Model (CE-QUAL-W2)

“…The sum-of-least-squares approach as an objective function was employed in the most of the model calibration studies using optimization (Yih and Davidson, 1975;Wood et al, 1990;Little and Williams, 1992;Mulligan and Brown, 1998;Van Griensven and Bauwens, 2001). Minimizing the error between the observed and simulated state variables is the general objective in all of these studies, although they applied different methods to find the best solution for the objective function such as Kalman filters, Nelder mead algorithm, etc.…”