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Nonlinear extensions of a fractal–multifractal approach for environmental modeling

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Abstract

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

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Acknowledgments

This work was supported in part by the Director, Office of Science, of the US Department of Energy under Contract No. DE-AC02-05CH11231.

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Authors and Affiliations

  1. Earth Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, 94720, USA

    Andrea Cortis

  2. Department of Land, Air and Water Resources, University of California, Davis, CA, 95616, USA

    Carlos E. Puente & Bellie Sivakumar

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  1. Andrea Cortis
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  2. Carlos E. Puente
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  3. Bellie Sivakumar
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Correspondence to Andrea Cortis.

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Cortis, A., Puente, C.E. & Sivakumar, B. Nonlinear extensions of a fractal–multifractal approach for environmental modeling. Stoch Environ Res Risk Assess 23, 897–906 (2009). https://doi.org/10.1007/s00477-008-0272-0

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