An approximate method for 1-D simulation of pollution transport in streams with dead zones

Abstract

Analytical solutions describing the 1D substance transport in streams have many limitations and factors, which determine their accuracy. One of the very important factors is the presence of the transient storage (dead zones), that deform the concentration distribution of the transported substance. For better adaptation to such real conditions, a simple 1D approximation method is presented in this paper. The proposed approximate method is based on the asymmetric probability distribution (Gumbel’s distribution) and was verified on three streams in southern Slovakia. Tracer experiments on these streams confirmed the presence of dead zones to various extents, depending mainly on the vegetation extent in each stream. Statistical evaluation confirms that the proposed method approximates the measured concentrations significantly better than methods based upon the Gaussian distribution. The results achieved by this novel method are also comparable with the solution of the 1D advection-diffusion equation (ADE), whereas the proposed method is faster and easier to apply and thus suitable for iterative (inverse) tasks.

The Influence of Pool-Riffle Morphological Features on River Mixing

“…This implied that by including pool-riffle expansion ratios in addition to the reach average values, 64% of the variability was explained by Equation (8). The resulting equation was an improvement from previous work that did not include bed complexity, which reported R 2 values of 0.55, 0.25, 0.5, and 0.55 [14,26,29,31]. In addition, 75% of the data were within the acceptable range defined by Seo and Cheong [26], which was higher than the 34%, 47%, and 31% obtained by Antonopoulos et al [65].…”

“…Dispersion in the longitudinal, lateral, and vertical directions accounts for the effects of spatial differences in velocities over the channel cross-section, and consequently its magnitude depends upon the scales of turbulent diffusion and mixing, owing to channel irregularities [6][7][8][9][10]. Prediction of longitudinal mixing is complicated in natural rivers as the channel morphology increases in complexity (e.g., planform curvature, bed irregularity, variable roughness provided by macroforms, substrate, and vegetation) [11][12][13][14][15][16]. Under such circumstances the inertial terms in the hydrodynamic equation become increasingly important for mixing and pollutant transport.…”

Numerical Investigation of Dissolved Oxygen Transportation through a Coupled SWE and Streeter–Phelps Model

“…Although the complete S-P model allows us to discuss the influence of more factors or to study more indicators, such as NBOD, CBOD, and salinity, to establish a more complete water quality evaluation system, and to ensure the simplicity of model research, we only investigate DO as a preliminary indicator of water quality, which also has guiding significance for further establishment of a well-rounded water quality model. Sudden changes in the cross section often appear in natural rivers due to morphological irregularities, such as cavities in sand or gravel beds, side arms, embayment, or obstacles [46]. Some artificial constructions, such as hydropower stations, can also transform the turbulent state of the river, form dead zones, and eventually affect the oxygen concentration distribution.…”

Application of Asymmetrical Statistical Distributions for 1D Simulation of Solute Transport in Streams

“…A partial comparison of the presented methods with the dead zone model was presented in [40], where the GaussD and the GumbelD were compared with the aggregated dead zone (ADZ) model, represented by the OTIS-P model [8]. As referred in this paper, the performance of both methods (GumbelD and ADZ) was comparable, so it can be assumed that it will be similar also in the case of the LogNormD and GEVD methods.…”