The Application of Fractal Dimension in the Analysis of Cloud Structure

Fractal dimension is the measure of how convoluted the boundary of a fractal becomes when iterated. Due to the complex nature of cloud boundaries, it is speculated whether this non-Euclidean geometric procedure can better describe the geometry of our atmosphere. To calculate the fractal dimension, the box counting ratio method is employed on infrared imagery, and the dimension is calculated over several systems at several different cloud top temperatures. It is shown that a positive correlation exists between fractal dimension and cloud top temperature. It is further hypothesized that if a symmetric fractal pattern exists in the microscale and synoptic scale shape of a cloud, then a similar connection may exist through all scales. By using knowledge of cloud top temperature alone, we may know the exact boundary extent of the cloud, much as we do in symmetric fractal patterns such as the Mandelbrot set. This can improve the accuracy of radiation models in the future.