In the Caribbean zone, the air quality is severely degraded from time to time by the sand mists coming from the African coasts. These are the cause of many respiratory diseases. For this, it is therefore crucial to improve the understanding of the fluctuations of fine particles with a diameter of less than 10 µm (PM10) in order to develop strategies and build tools to predict these dust episodes. A first step consists in characterizing the dynamic properties of PM10 fluctuations. In partnership with the University of the West Indies, the KaruSphère laboratory carried out a spectral analysis of PM10 in Hilbert and Fourier space. These first results show the possibility of carrying out an in-depth dynamic analysis of PM10 concentrations in the Caribbean area in order to quantify more precisely the origin and the threshold of this pollution.