**5. Conclusions**

In this paper, the Lagrangian particle-tracking trajectory model RePLaT-Chaos is introduced and is shown to be applicable for the study of the main features of atmospheric pollutant spreading, which are also discussed in detail. Due to its user-friendly graphical user interface, RePLaT-Chaos is a suitable tool for anyone who is interested in studying the characteristics of the atmospheric spreading of pollutants. Users can design their own "volcano eruptions" changing the location, altitude, extent of the pollutant clouds, as well as the number of the tracked particles and their density and diameter. It can be easily observed how these parameters alter the spreading, and other interesting questions can also be studied, e.g.:


By means of RePLaT-Chaos, it can be easily shown that the spreading of volcanic ash and other atmospheric pollutants is peculiar, because it is an example of what is called a chaotic process. One can reveal that the basic difference between the dispersion of a dye droplet on clothes and the spreading of volcanic ash in the atmosphere is that the former grows slowly in a compact shape, while the latter becomes rapidly distorted into a filament, the length of which increases quickly in time. Furthermore, users can become acquainted with the basic concepts of chaos on their own. They experience the rapid divergence of nearby trajectories, the particles' irregular motion in the atmosphere, and the above-mentioned quick development of pollutant clouds into a filamentary, tortuous and complicated but ye<sup>t</sup> organized shape with many foldings and meanders.

Users can easily assign two quantities to their spreading events to characterize the chaotic behavior. One of them is the stretching rate of the pollutant clouds, the topological entropy: the greater its value the more quickly the length of the pollutant cloud grows, and the more foldings and complicated shape it has. Therefore, it can be considered as the measure of the strength of chaos and of the unpredictability of the spreading. The other eligible quantity, the escape rate, describes the rapidity of the approximately exponentially decaying process of particle deposition. Based on the graphs of the non-deposited particles, the users can observe on their own the quite different lifetimes of even identical aerosol particles injected into the atmosphere at very nearby geographic locations at the same time instant. In this way, RePLaT-Chaos can be considered as an educational reconstruction of results obtained from contemporary research regarding atmospheric spreading of pollutant clouds and chaotic advection.

As an outlook, we mention that RePLaT-Chaos has another version called RePLaT-Chaos-edu [64] with the same computational background and fewer simulation parameter options but with a more colorful user interface, designed especially for secondary school students. It is intended to serve as a tutorial about the main features of atmospheric pollutant spreading phenomenon. Therefore, besides allowing students to design their own pollution events, it includes a lot of eye-catching animations and easy-to-understand explanations in order to draw the students' attention to the phenomena. The software was tested with a few group of students and received positive feedback [65].

**Funding:** This research was funded by the János Bolyai Research Scholarship of the Hungarian Academy of Sciences and by the National Research, Development and Innovation Office—NKFIH under grants PD-121305, PD-132709, FK-124256 and K-125171.

**Acknowledgments:** Fruitful discussions with T. Tél on chaotic advection and how to introduce it to students are gratefully acknowledged. The author thanks M. Herein and M. Vincze for testing the application, and G. Drotos, K. Klemm, M. Pinter and I. Takacs for suggestions on wording.

**Conflicts of Interest:** The author declares no conflict of interest.
