Predicting Streamflow from Fractal Geometric Encodings of Yearly and Decadal Records

Abstract:

In an attempt to model the specific complexity of geophysical (hydrological) records --beyond some key statistical qualifiers--, in the past we have developed a deterministic geometric procedure: the fractal-multifractal (FM) method and have introduced some promising variants. We show here that the FM ideas are indeed capable of faithfully encoding both yearly and decadal runoff sets gathered at the Sacramento River on a daily basis, with maximum cumulative errors that are, for a sixty year period, always less than a mere 2.5%. Then, we explain how the time variation of FM parameters at such scales allow us to: (a) closely predict whole decadal information in a rather precise manner, and (b) issue sensible forecasts of yearly information based on the transfer of FM decadal to FM yearly parameters via k-nearest neighbor algorithms. It is also illustrated how the notions provide relevant classifications (for yearly and decadal sets) that allow following the evolution of the geometry of runoff, with potential applications to global climate change.