Fractal dimensions for rainfall time series

Breslin, MC and Belward, JA (1999) Fractal dimensions for rainfall time series. Mathematics and Computers in Simulation, 48 4-6: 437-446. doi:10.1016/S0378-4754(99)00023-3


Author Breslin, MC
Belward, JA
Title Fractal dimensions for rainfall time series
Journal name Mathematics and Computers in Simulation   Check publisher's open access policy
ISSN 0378-4754
Publication date 1999
Sub-type Article (original research)
DOI 10.1016/S0378-4754(99)00023-3
Volume 48
Issue 4-6
Start page 437
End page 446
Total pages 10
Place of publication North Holland
Publisher Elsevier
Collection year 1999
Language eng
Subject C1
780101 Mathematical sciences
230199 Mathematics not elsewhere classified
Abstract Fractals are objects which have a similar appearance when viewed at different scales. Such objects have detail at arbitrarily small scales, making them too complex to be represented by Euclidean space. They are assigned a dimension which is noninteger. Some natural phenomena have been modelled as fractals with success; examples include geologic deposits, topographical surfaces and seismic activity. In particular, time series data has been represented as a curve with dimension between one and two. There are many different ways of defining fractal dimension. Most are equivalent in the continuous domain, but when applied in practice to discrete data sets lead to different results. Three methods for estimating fractal dimension are evaluated for accuracy. Two standard algorithms, Hurst's rescaled range analysis and the box-counting method, are compared with a recently introduced method which has not yet been widely used. It will be seen that this last method offers superior efficiency and accuracy, and it is recommended for fractal dimension calculations for time series data. We have applied these fractal analysis techniques to rainfall time series data from a number of gauge locations in Queensland. The suitability of fractal analysis for rainfall time series data is discussed, as is the question of how the theory might aid our interpretation of rainfall data. (C) 1999 IMACS/Elsevier Science B.V. All rights reserved.
Keyword Computer Science, Interdisciplinary Applications
Computer Science, Software Engineering
Mathematics, Applied
Fractal Dimension Methods
Rainfall Time Series
Fractional Brownian Motion
Q-Index Code C1

Document type: Journal Article
Sub-type: Article (original research)
Collection: School of Mathematics and Physics
 
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Created: Tue, 10 Jun 2008, 13:26:59 EST