Modelling of stormwater networks and the related object (combined sewer overflows, diversion chambers, retention tanks) is a complex task requiring colleting of data with appropriate time and spatial resolution as well as application of adequate models. Often there is a need to find balance between the costs of conducting measurement (period, resolution) and the uncertainty of the model results. This paper presents an overview of simulation tools for sewerage networks modelling, related objects, as well as low-impact development (LID) systems in relation to the hydrodynamic and statistical models. Consecutive stages of data collection, sources of data uncertainty, limitations resulting from the adopted measurement methodology, as well as their influence on the simulation results and possible decision-making using the developed hydrodynamic or statistical model, are discussed. Attention is drawn to the optimization methods enabling reduction in the uncertainty of statistical models. The methods enabling the analysis of model uncertainty, as well as evaluation of its influence on the calculation results pertaining to stormwater hydrographs, retention tank capacity and combined sewers overflows, are also discussed. This is a very important aspect in terms of optimizing construction works in the sewerage network and designing their appropriate dimensions to achieve the assumed hydraulic effects.

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 m³.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 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.

Experiments focused on pollution transport and dispersion phenomena in conditions of low flow (low water depth and velocities) in sewers with bed sediment and deposits are presented. Such conditions occur very often in sewer pipes during dry weather flows. Experiments were performed in laboratory conditions. To simulate real hydraulic conditions in sewer pipes, sand of fraction 0.6–1.2 mm was placed on the bottom of the pipe. In total, we performed 23 experiments with 4 different thicknesses of sand sediment layers. The first scenario is without sediment, the second is with sediment filling 3.4% of the pipe diameter (sediment layer thickness = 8.5 mm), the third scenario represents sediment filling 10% of the pipe diameter (sediment layer thickness = 25 mm) and sediment fills 14% of the pipe diameter (sediment layer thickness = 35 mm) in the last scenario. For each thickness of the sediment layer, a set of tracer experiments with different flow rates was performed. The discharge ranges were from (0.14–2.5)·10⁻³ m³·s⁻¹, corresponding to the range of Reynolds number 500–18,000. Results show that in the hydraulic conditions of a circular sewer pipe with the occurrence of sediment and deposits, the value of the longitudinal dispersion coefficient D_x decreases almost linearly with decrease of the flow rate (also with Reynolds number) to a certain limit (inflexion point), which is individual for each particular sediment thickness. Below this limit the value of the dispersion coefficient starts to rise again, together with increasing asymmetricity of the concentration distribution in time, caused by transient (dead) storage zones.

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.