A Deterministic Geometric Representation of Temporal Rainfall: Results for a Storm in Boston

Hydrol. Earth Syst. Sci.

2001

This study of the behaviour of rainfall dynamics at different temporal scales identifies the type of approach most suitable for transformation of rainfall data from one scale to another. Rainfall data of four different temporal scales, i.e. daily, 2-day, 4-day and 8-day, observed over a period of about 25 years at the Leaf River basin, Mississippi, USA, are analysed. The correlation dimension method is employed to identify the behaviour of rainfall dynamics. The finite correlation dimensions obtained for the four rainfall series (4.82, 5.26, 6.42 and 8.87, respectively) indicate the possible existence of chaotic behaviour in the rainfall observed at the four scales. A possible implication of this might be that the rainfall processes at these scales are related through a chaotic (scale-invariant) behaviour. However, a comparison of the correlation dimension and coefficient of variation of each of the time series reveals an inverse relationship between the two (higher dimension for lower coefficient of variation and vice versa). The presence of a large number of zeros in the higher resolution time series (that could result in an underestimation of the dimension) and the possible presence of a higher level of noise in the lower resolution time series (that could result in an overestimation of the dimension) might account for such results. In view of these problems, it is concluded that the results must be verified using other chaos identification methods and the existence of chaos must be substantiated with additional evidence.

Section: Introductionmentioning

confidence: 99%

Rainfall dynamics at different temporal scales: A chaotic perspective

Hydrol. Earth Syst. Sci.

2001

“…As may be seen, the procedure leads to complex and "random-looking" measures dy (i.e., the projection) that resemble environmental time series, such as a rainfall data set as a function of time (Puente and Obregón, 1996). As multifractal measures are relevant in turbulence studies (e.g., Meneveau and Sreenivasan, 1987), the projection sets, dy, may be assigned an interpretation as reflections or transformations of turbulence (Puente and Sivakumar, 2007).…”

Section: The Fractal Multifractal Approachmentioning

confidence: 99%

Nonlinear extensions of a fractal–multifractal approach for environmental modeling

Cortis

Puente

Stoch Environ Res Risk Assess

2008

Self Cite

We present the extension of a deterministic fractal geometric procedure aimed at representing the complexity of the spatio-temporal patterns encountered in environmental applications. The original procedure, which is based on transformations of multifractal distributions via fractal functions, is extended through the introduction of nonlinear perturbations to the underlying iterated linear maps. We demonstrate how the nonlinear perturbations generate yet a richer collection of patterns by means of various simulations that include evolutions of patterns based on changes in their parameters and in their statistical and multifractal properties. It is shown that the nonlinear extensions yield structures that closely resemble complex hydrologic temporal data sets, such as rainfall and runoff time series, and width-functions of river networks as a function of distance from the basin outlet. The implications of this nonlinear approach for environmental modeling and prediction are discussed.

“…Veneziano et al, 2000), among others (e.g. Puente and Obregón, 1996;Obregón et al, 2002;Puente and Sivakumar, 2003) and both chaotic and stochastic signals (with 1/f β power spectra), as classified via phase-space reconstruction techniques .…”

Section: Figmentioning

confidence: 99%

Modeling geophysical complexity: a case for geometric determinism

Puente

Hydrol. Earth Syst. Sci.

2007

Abstract. It has been customary in the last few decades to employ stochastic models to represent complex data sets encountered in geophysics, particularly in hydrology. This article reviews a deterministic geometric procedure to data modeling, one that represents whole data sets as derived distributions of simple multifractal measures via fractal functions. It is shown how such a procedure may lead to faithful holistic representations of existing geophysical data sets that, while complementing existing representations via stochastic methods, may also provide a compact language for geophysical complexity. The implications of these ideas, both scientific and philosophical, are stressed.