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.
The Water Framework Directive requires as an obligatory goal to achieve and to keep "good water quality" status within the defined period (for Slovakia-up to the year 2015). For surface waters, the main criterion is the ecological and chemical status of the water. Mathematical and numerical modelling allows evaluating various situations of contaminants spreading in rivers (from everyday wastewater disposal through fatal accidents and discharges of the toxic substances) without immediate destructive impact to the environment. Determination of longitudinal and transverse dispersion coefficient values, as the main hydrodynamic characteristics of the dispersion, has the highest extent of uncertainty for hydrodynamic models simulating pollutant transport in streams. This paper deals with the determination of dispersion coefficients based on field tracer experiments performed in a small modified stream (basic hydrodynamic parameters during the experiments were: discharge Q = 0.138-0.553 m 3 .s −1 , depth h=0.29-0.48 m, width B=5.2-5.9 m). During the experiments, various conditions and situations were taken into account, e.g., continuous and instantaneous pollution source, as well as various positions of pollution source along the river width, among others. Field measurements were evaluated using three different methods for dispersion coefficient determination: based on statistical evaluation, based on analytical solutions of advection-dispersion equation, and using numerical models. The dimensionless dispersion coefficients values were determined, which can be used for numerical simulation of pollutant transport in similar types of streams.
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 Water Framework Directive (WFD) is a key initiative aimed at improving water quality throughout the EU. The development of the computer technologies enables us to solve the ecological problems in water management practice very efficiently. The mathematical and numerical modelling allows evaluating various situations of contaminants spread in rivers (from everyday wastewater disposal through the fatal discharges of toxic substances) without immediate destructive impact on the environment. The paper deals with 1-dimensional numerical model HEC-RAS and its response on various values of dispersion coefficient. This parameter is one of the most important input data for simulation of pollution spread in streams. There were performed tracer experiments in the Malá Nitra River and results of these measurements are compared with results of numerical simulations. The values of the longitudinal dispersion coefficient were estimated from this comparison. The range of mean values of this coefficient determined on the base of numerical model application was 0.05 – 0.13 m2 s−1, for the other flow condition it was 0.07 – 2.5 m2 s−1 or 0.28 – 0.6 m2 s−1. The next task was carrying out the model sensitivity analysis, which means to evaluate input data influences, especially longitudinal dispersion coefficient, on outputs computed by 1-dimensional simulation model HEC-RAS. According to the results it can be said that the model HEC-RAS responds to longitudinal dispersion coefficient value changes adequately, suitably and proportionately. The application of the model HEC-RAS demonstrated the eligibility for simulation of pollution spread in streams, which means that it is a suitable tool allowing a reasonable support in decision making process connected to river water quality management.
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