Atmospheric fields exhibit extreme variability over a wide range of spatial and temporal scales; they are also intermittent, which means that their activity is often concentrated at smaller and smaller scales. Conventional statistical tools fall short in capturing this and detecting extremes. However, characterization of geophysical fields with their underlying complexities and correlations is ever important in prediction, modelling and understanding the weather conditions we live in, which is even more relevant now in the context of climate change.The heterogeneous properties of atmospheric fields come form the governing non-linear equations of the turbulence (Navier-Stokes), which still remains as an unsolved problem regardless its ubiquitousness. By using the concept of multiplicative cascades, it is possible to statistically reproduce the symmetries of said equations for geophysical fields; and multifractal tools expand upon this for characterizing the variability across scales by assuming same elementary process at each scale. In this dissertation, the scale invariant framework of UM, and the derived analysis technique of Joint Multifractals (JMF) are used for studying various fields in a two folded way – by examining the fields individually, and jointly, in real and in controlled situations. The fields are studied in four focus areas: rainfall and kinetic energy, rainfall and wind, temperature and humidity, and rainfall and particles.Using UM, rainfall intensity and rainfall kinetic energy (at TARANIS observatory, ENPC) are studied and a scale invariant relationship is postulated that doesn’t rely on any assumptions of drop size distribution. This equation is backed by theoretical formulation, and is shown to provide reliable estimates on par with commonly used equations in literature. Since kinetic energy requires relatively complex instrumentation, such a relation allows reliable retrieval of energy indirectly from commonly available precipitation data. This approach is further tested with rainfall simulations inside sense-city using JMF.The effect of rainfall on available wind power and power extracted by turbine are not well known. Towards this, high-resolution data from a meteorological mast (at pays d’Othe wind farm, France) are analysed along with turbine power in the purview of Rainfall Wind Turbine or Turbulence (RW-Turb) project. JMF tools were used to study various directly measured and derived fields in RW-Turb according to rainy and dry conditions, and an overall increasing correlation with rainfall rate is observed in joint analysis, which is worth exploring in future.The third focus area of temperature and humidity is explored partly with RW-Turb project and partly with sense-city. Few known days (rainy and dry) were simulated inside sense-city climate chamber in Descartes campus where ENPC is, for mimicking temperature and pressure variation observed in real conditions. Using JMF, the joint correlation between the fields in real and simulated conditions is evaluated, with efforts to account for the gap in estimation.For the fourth focus area, aerosol concentration (nm and µm) from Cherbourg-Octeville, France was analysed along side rain measurements for understanding scavenging of atmospheric particles by rainfall (below cloud scavenging). Preliminary analysis showed multifractal behaviour; this is of specific interest since the concentrations does not always follow the expected decreasing trend with rainfall. Along with this, multifractal properties of light attenuation by aerosols and their implications in atmospheric visibility are also studied using UM framework.Using the various results obtained, the unifying aspect of atmospheric fields - extreme variability, intermittency and scale invariance are illustrated. Through analysis of observational and controlled data, and numerical simulations, the utility of UM in trend detection, simulations and predictions are also commented on.