Analytical Solution of the Advection-Dispersion Equation Using Asymmetrical Pollution Distribution

Solution of the pollution spreading in rivers is an engineering task, which could be solved by very different ways. For the simulation of the hydrodynamic dispersion in river (pollution spreading) can be 1D, as well 2D or 3D approach used. 2D (eventually 3D) approach requires much more data – physical proportions and model boundaries, velocities and dispersion parameters for two (or three) dimensions. Such data are not always available and it can be very difficult, time and money consuming task to collect necessary data. Because of this, simple analytical solution, derived for simplified initial and boundary conditions, are very often used in the practice. These analytical solutions, describing the 1D substance transport in streams, have of course many limitations and factors, which determine their accuracy. One of the very important factors is the assumption, that the pollution cloud (in case of an instantaneous pollution injection) is spreading downstream and upstream symmetrically. But in reality, almost in all streams are present the transient storage areas (dead zones), deforming the concentration distribution of the transported substance (pollution). 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 field experiments in Slovakia. Tracer experiments confirmed the presence of dead zones in various extents, depending mainly on the vegetation occurrence and extent in stream. Statistical evaluation confirms that the proposed method approximates the measured concentrations significantly better than methods based upon the symmetrical Gaussian distribution.