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8 Fractals and Similarity Approaches in Hydrology

Part 1. Theory, Organization and Scale

  1. Luca G Lanza1,
  2. John Gallant2

Published Online: 15 APR 2006

DOI: 10.1002/0470848944.hsa007

Encyclopedia of Hydrological Sciences

Encyclopedia of Hydrological Sciences

How to Cite

Lanza, L. G. and Gallant, J. 2006. Fractals and Similarity Approaches in Hydrology. Encyclopedia of Hydrological Sciences. 1:8.

Author Information

  1. 1

    University of Genoa, Department of Environmental Engineering, Genoa, Italy

  2. 2

    Commonwealth Scientific and Industrial Research Organisation, Land and Water, Butler Laboratory, Canberra, Australia

Publication History

  1. Published Online: 15 APR 2006


The application of fractals and similarity concepts in hydrology has given rise to a better understanding of the space-time organization of forms and processes that are relevant to the hydrologic cycle. Indeed, a variety of literature results support the conjecture that scaling holds for most hydrological variables in time and space.

This chapter concentrates on fields where fractals and similarity approaches have proved helpful in fostering advances in specific hydrological studies. In particular, precipitation and drainage network morphology are addressed. A few specific applications to the study of natural forms and patterns relevant to the hydrological sciences are presented first, while the application of scaling concepts to the study of processes themselves is later discussed.

Because of its highly irregular behavior, the rainfall process is one ideal candidate to be approached by means of self-similarity and/or (multi)fractal description models. Such models involve increasing complexity and computational burden as soon as the interest moves from the one-dimensional time series to the three-dimensional case, where the full space-time pattern of rainfall is considered. Examples of recent interesting results are presented with reference to the one-, two-, and three-dimensional approaches to rainfall modeling based on similarity concepts.


  • scaling;
  • fractal;
  • multifractal;
  • rainfall;
  • drainage networks