The quantification of prediction uncertainty associated with water quality models using Monte Carlo Simulation

[摘要] ENGLISH ABSTRACT: Water Quality Models are mathematical representations of ecological systems and they play a major role in the planning and management of water resources and aquatic environments. Important decisions concerning capital investment and environmental consequences often rely on the results of Water Quality Models and it is therefore very important that decision makers are aware and understand the uncertainty associated with these models. The focus of this study was on the use of Monte Carlo Simulation for the quantification of prediction uncertainty associated with Water Quality Models.Two types of uncertainty exist: Epistemic Uncertainty and Aleatory Uncertainty. Epistemic uncertainty is a result of a lack of knowledge and aleatory uncertainty is due to the natural variability of an environmental system. It is very important to distinguish between these two types of uncertainty because the analysis of a model's uncertainty depends on it. Three different configurations of Monte Carlo Simulation in the analysis of uncertainty were discussed and illustrated: Single Phase Monte Carlo Simulation (SPMCS), Two Phase Monte Carlo Simulation (TPMCS) and Parameter Monte Carlo Simulation (PMCS). Each configuration of Monte Carlo Simulation has its own objective in the analysis of a model's uncertainty and depends on the distinction between the types of uncertainty.As an experiment, a hypothetical river was modelled using the Streeter-Phelps model and synthetic data was generated for the system. The generation of the synthetic data allowed for the experiment to be performed under controlled conditions. The modelling protocol followed in the experiment included two uncertainty analyses. All three types of Monte Carlo Simulations were used in these uncertainty analyses to quantify the model's prediction uncertainty in fulfilment of their different objectives.The first uncertainty analysis, known as the preliminary uncertainty analysis, was performed to take stock of the model's situation concerning uncertainty before any effort was made to reduce the model's prediction uncertainty. The idea behind the preliminary uncertainty analysis was that it would help in further modelling decisions with regards to calibration and parameter estimation experiments. Parameter uncertainty was reduced by the calibration of the model. Once parameter uncertainty was reduced, the second uncertainty analysis, known as the confirmatory uncertainty analysis, was performed to confirm that the uncertainty associated with the model was indeed reduced. The two uncertainty analyses were conducted in exactly the same way.In conclusion to the experiment, it was illustrated how the quantification of the model's prediction uncertainty aided in the calculation of a Total Maximum Daily Load (TMDL). The Margin of Safety (MOS) included in the TMDL could be determined based on scientific information provided by the uncertainty analysis. The total MOS assigned to the TMDL was -35% of the mean load allocation for the point source. For the sake of simplicity load allocations from non-point sources were disregarded.

[发布机构] Stellenbosch University