A two-dimensional water quality management model, the unsteady/uncertainty water quality model (UUWQM), is developed for three kinds of analysis: hydrodynamic and advection–diffusion analyses by using the Petrov–Galerkin finite element method, and a reliability analysis by using uncertainty techniques. This model is then applied to a 35 km reach of the Nakdong River in Korea. Two-dimensional hydrodynamic and deterministic water quality analyses were performed in this reach. The Monte Carlo simulation (MCS) method was used to decide and verify 14 key input parameters among 80 total input parameters. These key input parameters were incorporated to compute exceedance probabilities and frequency distributions using the mean first-order second-moment (MFOSM) and MCS methods at several locations along this reach of the Nakdong River. From the results of the probable risk for water quality standard, it shows that the outputs from the MFOSM method were similar to those from the MCS method. In practical usage, the MFOSM method is more attractive in terms of its computational simplicity and shorter execution time. Therefore, the UUWQM can be applied efficiently and accurately to estimate the water quality distribution and the risk assessment for the specified water quality in any river.

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