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

Sokáč Sokáč,Gualtieri Gualtieri,Velísková Velísková

doi:10.3390/w11102145

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.

Highlights

Solute transport in streams and rivers is strongly related to river characteristics, such as mean flow velocity, velocity distribution, secondary currents, and turbulence features
The evaluation of the results from the approximation methods is based on comparison of the normalized root mean square error (NRMSE), which is the standard root mean square error (RMSE) divided by the maximal difference of measured values [39]
If the NRMSE for the Gaussian distribution (GaussD) method will be regarded as 100%, values less than 100% demonstrate that the approximation method was more accurate than the GaussD method, whereas values over 100%

Summary

Introduction

Solute transport in streams and rivers is strongly related to river characteristics, such as mean flow velocity, velocity distribution, secondary currents, and turbulence features. These parameters are mainly determined by the river morphology and the discharge conditions. In rivers, which are regulated by man-made constructions such as spur dikes, groins, stabilized bed, and so on, the morphological diversity is often less pronounced, and flow velocities are more homogeneous. Some of these morphological irregularities, such as small cavities existing in sand or gravel beds, side arms and embayments, bigger obstacles, bank vegetation, and uprooted trees, can produce recirculating flows, which occur on different scales on the riverbanks and the riverbed

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