Multifractal analysis in hydrology

Application to Time Series

by Ioulia Tchiriguyskaia (writer), Daniel Schertzer (writer), Eric Sauquet (writer), Pietro Bernardara (writer), Michel Lang (writer)
july 2007
eBook [ePub]
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This book provides a simplified description of the procedures to be used to perform an analysis of hydrological data within a multifractal framework. After a review of multifractal theory and the presentation of one model for identifying scale invariance properties, examples of applications to rainfall and discharge time series are given. It will be of interest to teachers and researchers in this field, both nationally and abroad.

Chapter 1. Multifractal theory
How can phenomena be observed at different scales?
 The scale ratio
 Observations on and scales of hydrological processes
A statistical description of multifractal processes
 The codimension function c(y)
 The statistical moments function K(q)
General properties of multifractals
Multifractals and extremes
 The divergence of moments
 Effect of the sample size
 Diagnosis on the presence of extreme values
Description of multiplicative cascade models
 General description
 Properties of series generated by a multiplicative cascade
 Comment on conservative and non-conservative fields
The universal multifractal model
 Comment on the estimation of universal multifractal parameters
 The universal multifractal model and extremes
Chapter 2. Application of multifractals to rainfall and discharge series
Multifractal analysis of rainfall and discharge series
 Spectral analysis
 Analysis of scale of moments laws
 Fitting the universal multifractal parameters
 Comment on extreme values
  Fractional integration and differentiation
 Table of notations used
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Language(s): English

Publisher: Éditions Quae

Edition: 1st edition

Collection: Update Sciences & technologies

Published: 30 july 2007

Reference eBook [ePub]: 02056EPB

Reference eBook [PDF]: 02056NUM

EAN13 eBook [ePub]: 9782759213993

EAN13 eBook [PDF]: 9782759200627

Interior: Two-colour

Pages count eBook [PDF]: 59

Size: 2,8 Mo (ePub), 2,4 Mo (PDF)