Estimation of water quality model parameters

Abstract

A modified Gauss-Newton method was utilized to estimate water quality model parameters, which is important in the modeling of water quality transport process. This method served the unknown parameters of three engineering problems exceptionally well. We applied this method to obtain a set of water quality parameters by solving the kinetic equations for dissolved and particulate water quality species during episodic events in the Indian River Lagoon, FL. The method was successful in producing water quality model parameters, and the relative errors between measurements and model predictions are below 46.4% and 39.4% for all dissolved and particulate water quality state variables, respectively. In this study we evaluated a good capability of suggested parameter estimation method by comparing a couple of water quality model simulations: (1) water quality model simulation using model parameters produced by the modified Gauss-Newton method and (2) water quality model simulation employing model parameters obtained by the trial-and-error method. The average relative error and ROC score between observed data and water quality model results using model parameters calculated by the modified Gauss-Newton method are 58.3% and 0.565, respectively. In the case of water quality model simulation using model parameters obtained by the trial-and-error method, the average relative error and ROC score are 60.5% and 0.555, respectively. This suggests that the modified Gauss-Newton method efficiently yields water quality model parameters resulting in better or similar model prediction errors when compared to the trial-and-error method.

A Fusion Water Quality Soft-Sensing Method Based on WASP Model and Its Application in Water Eutrophication Evaluation

“…The fuzzy comprehensive evaluation result ( ) of the monitoring station in Taihu Lake is obtained by using (22). According to (23), the water eutrophication level based on measured values, simulated values of trial-and -error method, simulated values of nonlinear least squares, and simulated values of UKF is evaluated, and results are shown in Figure 5.…”

“…However, WASP also has a limitation. That is, some model parameters vary among different water areas, and their values are always determined by trial-and-error method [23]. This is insufficient for accurately modeling the water quality variation of a specific water area.…”

Application of one‐step method to parameter estimation in ODE models

“…To check the limits of applicability of the one-step method, our emphasis is on examples with small and moderate sample sizes. Domselaar and Hemker (1975) 0.45 × 10 −5 0.27 × 10 −3 Esposito and Floudas (2000) 0.4593 × 10 −5 0.28285 × 10 −3 Kim and Sheng (2010) 0.46 × 10 −5 0.28 × 10 −3 Tjoa and Biegler (1991) 0.4604 × 10 −5 0.2847 × 10 −3 Varah (1982) 0.46 × 10 −5 0.27 × 10 −3…”

“…Based on the experimental data from Table 39 in Bodenstein (1922), parameters of Equation 20 were estimated via different methods in Bellman et al (1967); Van Domselaar and Hemker (1975), see pp. 18-19; Esposito and Floudas (2000), Section 7.4; Kim and Sheng (2010); Section 3.1; Tjoa and Biegler (1991), Problem 6 on p. 381; and Varah (1982), see pp. 37-38.…”

“…‡ This time, we did not estimate the initial condition and considered ‡ Note that in Table 39 in Bodenstein (1922) and in Table I in Bellman et al (1967), the observation 48.8 corresponding to the time instance t = 19 appears to contain a typo: We tentatively corrected it to 38.8. The same correction was applied in Table 24 in Esposito and Floudas (2000) and in Table 1 in Kim and Sheng (2010). The parameters were estimated using the real data from Bellman et al (1967).…”