Temporal downscaling rainfall and streamflow records through a deterministic fractal geometric approach

Abstract

A deterministic geometric approach, the fractal-multifractal (FM) method, is proposed to temporally downscale (disaggregate) rainfall and streamflow records. The applicability of the FM approach is tested on: (1) two sets of rainfall records—one from Laikakota, Bolivia and the other from Tinkham, Washington, USA; and (2) two distinct sets of streamflow records—for water years 2005 and 2008 from the Sacramento River, California, USA. For the purpose of validation, the available daily records are first aggregated into weekly, biweekly, and monthly records and then the FM method is applied to downscale such sets back into the daily scale. The results indicate that the FM method, coupled with a threshold to capture the high intermittency of rainfall and a smoothing parameter to get the milder texture of streamflow, readily generates daily series (over a year) based on weekly, biweekly, and monthly accumulated information, which reasonably preserves the time evolution of the records (especially for streamflow) and captures a variety of key statistical attributes (e.g., autocorrelation, histogram, and entropy). It is argued that the FM deterministic downscalings may enhance and/or supplement available stochastic disaggregation methods.