In this paper we test the Unified Mulifractal model of atmospheric dynamics in the tropics. In the first part, we empirically investigate the scaling behaviour along the horizontal, in the second part along the vertical. Here we concentrate on the presentation of basic multifractal notions and techniques and on how they give rise to self-organized critical structures. Indeed, we point out a rather simple and clear characterisation of these structures which may help to clarify both the nature of the oft-cited coherent structures and the generation of cyclones. Using 30 aircraft series of horizontal wind and temperature, we find rather remarkable constancy of the three universal multifractal indices H, C₁ and a as well as the value of critical exponents q_D, ?_D associated with multifractal phase transitions and self-organized critical structures. This constancy extends not only from wind tunnel and mid-latitude to the tropics, but also to multifractals generated by Navier-Stokes like equations.