Fractal and multifractal scaling behavior have the statistical property of scale invariance which means that the scaling is described by power-laws. This tutorial introduces methods of fractal and multifractal analysis for geophysical data with demonstrations of software that provides analysis of power-scaling for time series and 2 and 3-D data.
The analysis methods for self-similar fractals include: ruler, box-counting, mass; and for self-affine fractals, power-spectral density, and for size versus number; size cumulative-frequency. Roll-off of data at both the upper and lower ends of fractal behavior will be addressed.

Methods applicable to multifractals (non Gaussian, intermittent scaling processes) will be illustrated with examples from atmospheric and climate data. These include: Fluctuation analysis (especially Haar fluctuations); Spike plots and trace moment analysis; Scaling in probability space (power-law probability tails and Black Swan events); and common pitfalls of spectral analysis including spurious oscillations.