# Fractional derivative models for atmospheric dispersion of pollutants

## TL;DR

This paper explores fractional derivative models to improve the accuracy of atmospheric pollutant dispersion predictions, demonstrating superior performance over traditional and existing variable-coefficient models through real-world comparison.

## Contribution

It introduces simple fractional differential equation models for pollutant dispersion and shows they outperform traditional Gaussian and variable-coefficient models in real experiments.

## Key findings

- Fractional models outperform Gaussian models in accuracy.
- Fractional models outperform variable-coefficient models.
- Better fit to real atmospheric dispersion data.

## Abstract

In the present work, we investigate the potential of fractional derivatives to model atmospheric dispersion of pollutants. We propose simple fractional differential equation models for the steady state spatial distribution of concentration of a non-reactive pollutant in Planetary Boundary Layer. We solve these models and we compare the solutions with a real experiment. We found that the fractional derivative models perform far better than the traditional Gaussian model and even better than models found in the literature where it is considered that the diffusion coefficient is a function of the position in order to deal with the anomalous diffusion.