Geophysical extremes, scaling and fractal support induced by zero-values

In the era of the data-driven research, the zero-values of geophysical fields require increased attention in order to improve understanding of their effective impacts on the prediction of extreme geophysical phenomena.

In everyday life, we use the idea that zero denotes the absence of quantity, whereas in geophysics, it refers to a chosen reference point, not necessarily the absence of a physical phenomenon.  It then results from the removal of the background field, either by design of the measured quantity or due to the current limitations of empirical detection.

Regardless of their origin, the presence of zeros in data significantly alters the resulting statistical distributions and influences the estimates of statistical parameter. Regarding universal multifractals (UM), two approaches have been favoured over the last thirty years to mimic the appearance of zeros and/or quantify their influence on the resulting UM estimates. The first, among the most widely used, relies on multiplying of a UM field by an independent fractal model, the ‘beta-model’, i.e. to assume the field has physically a fractal support. The second consist of thresholding the UM singularities and ignoring the fluctuations below the threshold, i.e. assuming that there is a detection of low field values.

This presentation will revisit these two approaches, emphasizing the significant resulting differences in the theoretical behaviour of the multifractal phase transitions, which are responsible for the behaviour of multifractal extremes. Then practical methods for preliminary detection of the most appropriate zero-creation mechanism within the data will be illustrated with concrete examples from geophysical fields.