The Fractal Nature of Drought: Power Laws and Fractal Complexity of Arizona Drought

Abstract

In this study, we explore the possibility that the Drought Monitor database belongs to class of fractal process which can be characterized using a single scaling exponent. The Drought Monitor map identifies areas of drought and labels them by intensity: D₀ abnormally dry, D₁ moderate drought, D₂ severe drought, D₃ extreme drought, and D₄ exceptional drought. The vibration analysis using power spectral densities (PSD) method has been carried out to discover whether some type of power-law scaling exists for various statistical moments at different scales of this database. We perform multi-fractal analysis to estimate the multi-fractal spectrum of each group. We apply Higuchi algorithm to find the fractal complexity of each group and then compare them for different time intervals. Our findings reveal that we have a wide range of exponents for D₀-D₄. Therefore, D₀-D₄ belong to class of multi-fractal process for which a large number of scaling exponents are required to characterize the scaling structure.