Probabilistic Methods for Uncertainty Analysis and Parameter Estimation for Dissolved Oxygen Models

Abstract

Water quality models are essential to the development of least-cost water quality control strategies based on ambient criteria. Such policies are particularly important if financial resources are limited which is currently the case in Central and Eastern European countries. In turn, the derivation of realistic model parameters is a pre-requisite of successful model application. Often, longitudinal water quality profile measurements are performed for the above purpose, but the traditional evaluation of this data encounters significant difficulties due to measurement and other uncertainties. Thus, probabilistic methods are preferred. This paper discusses two of them: the Hornberger‒Spear‒Young procedure using Monte Carlo simulation and a Bayesian approach. Both methods are rather generic, but they are applied here solely for the traditional Streeter‒Phelps model and its extensions. For the purpose of illustration, water quality measurements from the highly polluted Nitra River in Slovakia are employed as a part of a policy oriented study. The BOD decay rate obtained was rather high due to partial biological wastewater treatment and small water depth, but overall, derived parameter values were in harmony with literature findings. Alternative dissolved oxygen models (2‒3 state variables and 2‒5 parameters) could also be calibrated to the data set. Ranges of probability density functions (PDFs) for model parameters were rather broad calling for a well suited formulation of a water quality management model.

A homotopy training algorithm for fully connected neural networks

“…Parameter estimation often requires a tremendous number of model evaluations to obtain the solution information on the parameter space [21,36,37]. However, this large number of model evaluations becomes very difficult and even impossible for large-scale computational models [38,39]. Then, a surrogate model needs to be built in order to approximate the parameter space.…”

Barriers to sustainable water-quality management

“…For example, Li and Chen (1994) proposed a model for simulating organics removal and oxygen consumption by biofilms in an open-channel. Masliev and Somlyody (1994) advanced a probabilistic method for uncertainty analysis and parameter estimation for dissolved oxygen models. Kazmi and Hansen (1997) developed a numerical model for water-quality simulation and applied it to a case-study in the Yamuna River, India.…”

“…For example, Masliev and Somlyody (1994) proposed a probabilistic method for uncertainty analysis and parameter estimation for dissolved-oxygen models, and used the modeling results for further risk assessment. Reckhow (1994) conducted uncertainty analysis for risk assessment and decision-making in a water-resource system, based on a water-quality-simulation model.…”

Global Optimization in Action

“…Incomplete knowledge, inadequate model structure, process decomposition and aggregation, natural variability, observation errors, and differences in the (partly) subjective interpretation of results all contribute to uncertainty in modelling: see, for example, Hornberger and Spear (1981), Gardner, Cale and O'Neill (1982), Somly6dy (1982a,b), Beck and van Straten (1983), Hornberger and Cosby (1985), Beck (1985aBeck ( , 1987a, Cosby, Wright, Hornberger and Galloway (1985), Cosby, Hornberger, Galloway and Wright (1985), Fields and Miller (1988), Loehle (1988), Warwick and Cale (1988), Cooke (1994), Klepper and Hendrix (1994), and Masliev and Somly6dy (1994) on these issues, primarily in the context of environmental systems.…”