Turbulent and turbulent-like systems are ubiquitous in the atmosphere but there is a gap between classical models and reality. Advances in nonlinear dynamics, especially modern multifractal cascade models, allow us to close the gap, to investigate the weather and climate at unprecedented levels of accuracy, comparing theories, models and experiments over huge ranges of space-time scales.

Using new stochastic modelling and data analysis techniques, this book provides an overview of the nonclassical, multifractal statistics. The authors demonstrate that by generalizing the classical turbulence laws, it is possible to obtain emergent laws of atmospheric dynamics. These higher level laws are empirically validated from weather to lower-frequency macroweather scales to even lower frequency climate scales, and length-scales of millimetres to the size of the planet. By generalizing the notion of scale, atmospheric complexity is reduced to a manageable scale-invariant hierarchy of processes, thus providing a new perspective for modelling and understanding the atmosphere. This new synthesis of state-of-the-art data and nonlinear dynamics is systematically compared with other analyses and global circulation model outputs. Applications of the theory are graphically demonstrated with many original multifractal simulations.

This thorough presentation of the application of nonlinear dynamics to the atmosphere is an important resource for atmospheric science researchers new to multifractal theory. It will also be of use to graduate students in atmospheric dynamics and physics, meteorology, oceanography and climatology.