Improvement of the Two-Dimensional Routing Procedure for Observing Dispersion Coefficients in Open-Channel Flow

Abstract

The dispersion coefficients are crucial in understanding the spreading of pollutant clouds in river flows, particularly in the context of the depth-averaged two-dimensional (2D) advection–dispersion equation (ADE). Traditionally, the 2D stream-tube routing procedure (2D STRP) has been the predominant method for determining both the longitudinal and transverse dispersion coefficients of the 2D ADE under transient concentration conditions. This study aims to quantitatively analyze and address the limitations of the 2D STRP using hypothetically generated data. The findings of these evaluations revealed that the existing 2D STRP failed to accurately reproduce reliable results when the tracer clouds reached wall boundaries. This limitation prompted the development of the 2D STRP-i, which effectively resolves this drawback. The newly developed routing-based observation method, 2D STRP-i, enables the reliable estimation of dispersion coefficients, considering the effect of the wall boundary. The results indicated that the existing 2D STRP yielded 2D dispersion coefficients with relative errors ranging from 40% to 200%, while 2D STRP-i consistently yielded relative errors of 3% to 5% on average. When applied to tracer test data obtained through remote sensing, the 2D STRP-i demonstrated its ability to accurately observe temporal concentration distributions, even when wall boundaries have a significant impact on contaminant transport.