Multifractal analysis in wavelets for the analysis of atmospheric data

Dynamic meteorology is the study of atmospheric movements associated with climate and weather. To study these movements, the particulate molecular nature of the atmosphere can be neglected, and the atmosphere can be considered as a continuous fluid. The various physical quantities (pressure, density, temperature and velocity) that describe the state of the atmosphere then have a unique value at each point on this continuum. These variables, and their derivatives, are assumed to be continuous in time and space. The fundamental laws of fluid mechanics and thermodynamics can then be used to describe the movements of the atmosphere in the form of a system of partial differential equations, whose solutions are the various physical quantities.

The system of differential equations modelling atmospheric movements is highly complex, and no general solutions yet exist. A number of simplifications and numerical approximations have to be made to obtain reasonably reliable weather and climate predictions.

In parallel with numerical modelling, analysis of experimental data enables us to gain a better understanding of the physical phenomena involved, and to validate or invalidate numerical models. At present, the reliability of weather predictions obtained from numerical simulations does not extend beyond five or six days. This is largely due to the chaotic nature of observable physical quantities (winds, temperatures, pressures, etc.). What's more, some physical phenomena are observed on several space or time scales: the extratropical Q.B.O. (Quasi Biennial Oscillation) with an average period of 28 months, the E.N.S.O. (El Nino Southern Oscillation) with a period of 4 years, or the 11-year solar cycle. Some oscillations over shorter periods are well known, such as the annual cycle, but understanding all the physical phenomena occurring on different time scales represents a current economic and ecological challenge, leading to the publication of numerous articles on the subject every year.

Numerical simulations used for weather prediction are generally based on models describing the troposphere (lower layer of the atmosphere), and stratospheric data (from the upper layer) are generally considered to have little impact on weather trends at the Earth's surface. However, large stratospheric phenomena persisting over several weeks (or more) occasionally reach the Earth's surface.