A mathematical process, developed in Maple environment, has been successful in decreasing the error of measurement results and in the precise calculation of the moments of corrected tracer functions. It was proved that with this process, the measured tracer results of horizontal subsurface flow constructed wetlands filled with coarse gravel (HSFCW-C) can be fitted more accurately than with the conventionally used distribution functions (Gaussian, Lognormal, Fick (Inverse Gaussian) and Gamma). This statement is true only for the planted HSFCW-Cs. The analysis of unplanted HSFCW-Cs needs more research. The result of the analysis shows that the conventional solutions (completely stirred series tank reactor (CSTR) model and convection-dispersion transport (CDT) model) cannot describe these types of transport processes with sufficient accuracy. These outcomes can help in developing better process descriptions of very difficult transport processes in HSFCW-Cs. Furthermore, a new mathematical process can be developed for the calculation of real hydraulic residence time (HRT) and dispersion coefficient values. The presented method can be generalized to other kinds of hydraulic environments.

We have created a divided convective-dispersive transport (D-CDT) model that can be used to provide an accurate simulation of conservative transport processes in planted horizontal sub-surface flow constructed wetlands filled with coarse gravel (HSFCW-C). This model makes a fitted response curve from the sum of two independent CDT curves, which show the contributions of the main and side streams. The analytical solutions of both CDT curves are inverse Gaussian distribution functions. We used Fréchet distribution to provide a fast optimization mathematical procedure. As a result of our detailed analysis, we concluded that the most important role in the fast upward part of the tracer response curve is played by the main stream, with high porous velocity and dispersion. This gives the first inverse Gaussian distribution function. The side stream shows slower transport processes in the micro-porous system, and this shows the impact of back-mixing and dead zones, too. The significance of this new model is that it can simulate transport processes in this kind of systems more accurately than the conventionally used convective-dispersive transport (CDT) model. The calculated velocity and dispersion coefficients with the D-CDT model gave differences of 24-54% (of velocity) and 22-308% (of dispersion coeff.) from the conventional CDT model, and were closer to actual hydraulic behaviour.

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We studied water loss performance in a model plant, the Tufted sedge (Carex elata All.), which is an active water balance component of subsurface flow constructed wetlands. Due to active regulation of transpiration, the volume and dynamics of water loss in these constructed wetlands are difficult to plan without preliminary and targeted measurements and calculations with regard to the specific plant component. We estimated transpiration values in the laboratory based on daytime transpiration ranges for spring, summer and autumn, and examined the transpiration effect of the hydraulic load. During spring, water loss via transpiration can reach 83% of the hydraulic load on certain days. During summer, this value can increase to 100% of the hydraulic load, which means that the daytime transpiration can significantly affect effluent concentration. Air humidity proved to be the most critical environmental factor for water loss resulting from transpiration, therefore a water discharge plan designed in such a way as to be able to also adjust soil moisture is the key to optimal water circulation at the system level.

This paper offers a novel application of our model worked out in Maple environment to help understand the very complex transport processes in horizontal subsurface flow constructed wetland with coarse gravel (HSFCW-C). We made tracer measurements: Inside a constructed wetland, we had 9 sample points, and samples were taken from each point at two depths. Our model is a divided convective-dispersive transport (D-CDT) model which makes a fitted response curve from the sum of two separate CDT curves showing the contributions of the main and side streams. Analytical solutions of CDT curves are inverse Gaussian distribution functions. This model was fitted onto inner points of the measurements to demonstrate that the model gives better fitting to the inner points than the commonly used convective-dispersive transport model. The importance of this new application of the model is that it can resemble transport processes in these constructed wetlands more precisely than the regularly used convective-dispersive transport (CDT) model. The model allows for calculations of velocity and dispersion coefficients. The results showed that this model gave differences of 4–99% (of velocity) and 2–474% (of dispersion coefficient) compared with the CDT model and values were closer to actual hydraulic behavior. The results also demonstrated the main flow path in the system.