MULTIFRACTALITY IN EARTH AND ENVIRONMENTAL SCIENCES

Earth and environmental systems are among the most complex systems known to humankind. Atmospheric circulation, rainfall variability, earthquakes, river flow dynamics, soil heterogeneity, climate fluctuations, ocean turbulence, and ecological interactions all exhibit irregular patterns that cannot be completely explained using classical linear approaches. Traditional statistical models often assume uniformity, stationarity, and single-scale behavior, whereas natural systems operate across multiple spatial and temporal scales. This realization has led scientists toward advanced mathematical frameworks capable of describing complexity more realistically. One such powerful framework is multifractality. Multifractal analysis provides a scientific approach to understanding irregular, nonlinear, and scale-dependent structures observed in Earth and environmental sciences. Unlike ordinary fractal systems characterized by a single scaling exponent, multifractal systems involve a spectrum of scaling exponents representing varying degrees of complexity. This book presents theoretical foundations, mathematical principles and analytical techniques.