A one-dimensional two-zone mathematical model, comprising a pair of advection-dispersion equations coupled by a mass exchange term, is proposed to study longitudinal dispersion in channels with sequences of pools and riffles. An implicit finite-difference numerical scheme is employed, and its effectiveness is assessed with reference to known analytical solutions. Moreover, sets of longitudinal dispersion experiments were performed on various simple geometries of sequences of pools and riffles developed in a laboratory flume. The results were compared with corresponding numerical solutions to calibrate the two-zone model. and Pro studium podélné disperze v korytech s opakující se soustavou tůní a prahů byl navržen jednorozměrný dvouzónový matematický model. Model zahrnuje dvojici rovnic pro advektivní disperzi doplněných výrazem pro přenos hmoty. Byl použit implicitní model konečných diferencí a jeho vhodnost ověřena porovnáním se známým analytickým řešením. Navíc, v laboratorním žlabu byla provedena série měření podélné disperze pro různé jednoduché geometrie koryta se střídajícími se tůněmi a prahy. Pro kalibraci dvouzónového modelu byly výsledky měření porovnány s odpovídajícími matematickými řešeními.
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.