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

Abstract

Analytical solutions of the one-dimensional (1D) advection–dispersion equations, describing the substance transport in streams, are often used because of their simplicity and computational speed. Practical computations, however, clearly show the limits and the inaccuracies of this approach. These are especially visible in cases where the streams deform concentration distribution of the transported substance due to hydraulic and morphological conditions, e.g., by transient storage zones (dead zones), vegetation, and irregularities in the stream hydromorphology. In this paper, a new approach to the simulation of 1D substance transport is presented, adapted, and tested on tracer experiments available in the published research, and carried out in three small streams in Slovakia with dead zones. Evaluation of the proposed methods, based on different probability distributions, confirmed that they approximate the measured concentrations significantly better than those based upon the commonly used Gaussian distribution. Finally, an example of the application of the proposed methods to an iterative (inverse) task is presented.

Impact of roughness changes on contaminant transport in sewers

“…Because of this, we used in our research also alternative formulation of the onedimensional analytic solution of the ADE based on the assumption of asymmetrical substance spreading. This alternative solution is based on the Gumbel statistical distribution and it has the form (Sokáč et al, 2019):…”

Impact of Sediment Layer on Longitudinal Dispersion in Sewer Systems

“…For this reason, an alternative function based on the asymmetrical substance spreading assumption has been used for the 1-D analytic solution of the ADE. This function comes from the Gumbel statistical distribution [32]:…”

“…Even better results and conformity between models and data from real conditions can be obtained using the three parametric Generalised Extreme Value (GEV) distribution model [32]:…”

Advances in Environmental Hydraulics

“…The second review paper [11] deals with the environmental impacts associated with the rapidly growing mariculture industry, while one research paper [12] investigated the flow and concentration patterns downstream an aquaculture cage net panel in parametric flume experiments. Four studies approached the stream and river systems from a variety of perspectives, ranging from the physical modelling of flow with vegetation [13] and the numerical simulation of solute transport in river with dead zones [14], to the laboratory study of flood discharge atomisation [15] and the geomorphic characterisation and classification of a large river [16]. Three contributions are about hyporheic fluxes: two field studies investigated these fluxes at a small river confluence [17] and the effects of such fluxes on the macroinvertebrate community [18], while their relationship with the bioturbation activity of macroinvertebrates was studied in laboratory [19].…”

“…However, natural streams often contain complexities such as transient storage zones (dead zones), vegetation and irregular stream morphology that could interfere with the solute transport processes, causing a strong asymmetry in the shape of the concentration distribution curve over time and invalidating the Gaussian distribution traditionally assumed in classic 1D ADE. To address this issue, Sokáč et al [14] proposed a simple 1D model with alternative asymmetrical statistical distributions, such as Gumbel, log-normal and generalised extreme value (GEV), for solute transport in streams with dead zones. Tests against literature field tracer experiments as well as data collected in three small streams in Slovakia with dead zones suggested that, compared with Gaussian distribution, the alternative formulations overall showed a significantly improved prediction of the dispersion process from an instantaneous source.…”