**Nomenclature**

reality, most of air pollution signals are usually nonstationary [9, 14, 47]. The Fourier transform-based technique treats the signal as a sum of predefined basis functions. If the analyzing signal is well matched with the bases, it performs better; otherwise the performance is degraded [10]. Here, the SPEC highlight energy fluctuations linked to PM10 coming from African dust between May and September (large-scale sources) [9] and from the eruption of Soufrière on Montserrat in February 2010 (mesoscale sources) [48]. However, the SPEC does not detect energy fluctuation related to anthropogenic pollution, i.e., local sources. This shows HS is a robust method in timefrequency domain. Indeed, based on the EMD method, this TFR is fully data adaptive, and the signal decomposition is performed without any predefined basis functions.

In this paper, we investigated scaling and time-frequency properties of PM10 data in Hilbert frame. The performances obtained in the Hilbert space are compared with those achieved in the Fourier space. Firstly, with the Hilbert spectral analysis (HSA), a

<sup>10</sup><sup>5</sup> Hz which corresponds to time scales 6*:*1 hours⩽*T*⩽55*:*4 days with an estimated spectral exponent *β<sup>h</sup>* = 1.02 0.10. As HSA methodology has a very local ability in both physical and spectral spaces, the influence of intermittent dust events with huge fluctuations is included in the amplitude-frequency space which is not the case in Fourier spectrum. Thereafter, PM10 data are illustrated in time-frequency representations with the Hilbert spectrum and spectrogram. The results provide the evidence that HS-based TFR performs better than SPEC. The higher resolution in TFR offers better fluctuations of PM10 energy for *f* < 1μ Hz. This is due to the fact that it is impossible to increase the TF resolution at the desired level in SPEC. The major asset of HS is that the time resolution can be as precise as the sampling period and the frequency resolution depends on the choice up to the Nyquist limit. In addition, contrary to SPEC which introduces a noticeable amount of cross-spectral energy terms during the use of window function with overlapping, HS is fully adaptive to datasets due to the decomposition of the signals. These first results suggest a substantial possibility to perform a profound dynamical analysis of PM10 concentrations for the Caribbean area in order

The authors would like to thank Guadeloupe air quality network (Gwad'Air) and the French Met Office (Météo France Guadeloupe) for providing air quality

PM10 particulate matter with an aerodynamic diameter 10 μm or less

⩽*f*⩽4*:*57

power law behavior is clearly observed on the frequency range 2*:*<sup>09</sup> <sup>10</sup><sup>7</sup>

These results confirm the superiority of HS over STFT in TFR.

to quantify the origin and the threshold pollution.

The authors declare no conflict of interest.

**Acknowledgements**

and meteorological data.

**Conflict of interest**

**Abbreviations**

**98**

SPEC spectrogram

PSD power spectral density

**5. Conclusion**

*Functional Calculus*


*φ* phase function of the intrinsic mode function
