A comparison of fractal-multifractal techniques for encoding streamflow records

JOURNAL OF HYDROLOGY

卷:542

Article

Maskey, Mahesh L.¹  Puente, Carlos E.¹  Sivakumar, Bellie^1,2 

[1] Univ Calif Davis, Dept Land Air & Water Resources, One Shields Ave, Davis, CA 95616 USA

[2] Univ New South Wales, Sch Civil & Environm Engn, Sydney, NSW 2052, Australia

关键词: Fractal-multifractal;    Streamflow;    Dynamics;    Encoding;    Climate change;   

DOI  :  10.1016/j.jhydrol.2016.09.029

来源: Elsevier

【 摘 要 】

This study introduces the deterministic fractal-multifractal (FM) approach and some of its variants for encoding, for the first time, streamflow data. For this purpose, daily streamflow records gathered over 65 years at the Sacramento River in California, USA are studied. The specific FM representations considered here include three main categories and six cases as follows: (i) the original FM approach, yielding a data set as a fractal transformation of a multifractal measure, and obtained by iterating two and three affine maps; (ii) an extension, defining records as a transformation of an input measure by a general attractor (not a function), also obtained by iterating two and three affine maps; and (iii) two procedures that loop two fractal functions or two general attractors, providing a data set as a weighted projection via the iteration of a total of four affine maps each. Highlighting the results obtained for six different years of records having distinct geometries, it is shown that all six FM variants yield faithful representations, as evidenced by the maximum errors in accumulated records never exceeding a mere 2%. Of all approaches, however, it is shown that the one based on three affine maps, leading to substantial compression ratios of 28:1, is generally the best, for such end up following the geometry of all sets rather closely. As illustrated for the whole 65-year period, the time evolution of the FM parameters may be useful to track and predict changes in streamflow over time. (C) 2016 Elsevier B.V. All rights reserved.

【 授权许可】

Free