Multifractal objective analysis: Conditioning and interpolation

Stochastic Environmental Research and Risk Assessment

Volumn 15, Issue 4, 2001, Pages 261-283

  Salvadori, G ^a,b   Schertzer, D ^c   Lovejoy, S ^d  

^a UNIVERSITY OF SALENTO   (Italy)

^b POLITECNICO DI MILANO   (Italy)

^c CNRS   (France)

^d MCGILL UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035538787     PISSN: 14363240     EISSN: None     Source Type: Journal    
DOI: 10.1007/s004770100070     Document Type: Article

References (33)

1. Belli G, Cambiaghi M, Chigirinskaya Y, Kwak D, Lanza A, Marsan D, Naud C, Quinto E, Ratti SP, Ravera A, Salvadori G, Scannicchio D, Schertzer D, Schmitt F (1995) Radiation Protection Research Action, Commission of the European Communities (D.G. XII), Contract FI3P-CT93-0077, Final Report, (available upon request to the Commission of the European Communities - D.G. XII)
2. Barnsley M (1988) Fractals Everywhere. Academic Press, San Diego
3. Backer KH, Dürfler M (1990) Dynamical Systems and Fractals. Cambridge University Press, Cambridge
4. Cressie N (1992) Statistics for Spatial Data. J. Wiley & Sons, New York
5. Creutin JD, Obled C (1982) Objective analyses and mapping techniques for rainfall fields: an objective comparison. Wat. Res. Res., 18(2): 413
6. Crilly AJ, Earnshaw RA, Jones H (1991) Fractals and Chaos. Springer-Verlag, New York
7. Falconer KJ (1988) The Geometry of Fractal Sets. Cambridge University Press, Cambridge
8. Falconer KJ (1990) Fractal Geometry. J. Wiley & Sons, Chichester
9. Feder J (1989) Fractals. Plenum Press, New York-London
10. Gilchrist B, Cressman G (1954) An experiment in objective analysis. Tellus, 6: 309
11. Goodin WR, McRae GJ, Seinfeld JH (1979) A Comparison of Interpolation Methods for Sparse Data. J. Appl. Meteo., 18: 761
12. Kaye BH (1989) A Random Walk through Fractal Dimensions. VCH, Weinheim, FRG
13. Korvin G (1992) Fractal Models in the Earth Sciences. Elsevier, New York
14. Kottegoda NT, Rosso R (1997) Probability, Statistics, and Reliability for Civil and Environmental Engineers. McGraw-Hill, New York
15. Lavallée D (1991) Multifractal Analysis and Simulation Techniques and Turbulent Fields. PhD Thesis, McGill University, Physics Dept., Montréal, Canada
16. Lavallée D, Lovejoy S, Schertzer D (1991) On the determination of the codimension function. In: Schertzer D, Lovejoy S (eds.) Non-Linear Variability in Geophysics. Kluwer Academic Publishers, p. 99
17. Lovejoy S, Schertzer D, Ladoy P (1986) Fractal characterization of inhomogeneous measuring networks. Nature, 319: 43
18. Matheron G (1970) Random functions and their application in geology. In: Merriam DF (ed.) Geostatistics. Plenum, New York, p. 79.
19. Mandelbrot BB (1983) The Fractal Geometry of Nature. Freeman, S. Francisco
20. Nicolis C (1993) Optimizing the global observational network: a dynamical approach. J. Appl. Meteo., 33: 1751
21. Panofsky H (1949) Objective weather-map analysis. J. Appl. Meteo., 6: 386
22. Raffy M (1994) The role of spatial resolution in quantification problems: spatialization method. Int. J. Remote Sensing, 15: 2381
23. Ripley BD (1981) Spatial Statistics. J. Wiley & Sons, New York
24. Rohatgi VK (1976) An Introduction to Probability and Mathematical Statistics. J. Wiley & Sons, New York
25. Salvadori G (1993) Multifrattali Stocastici: Teoria e Applicazioni. PhD Thesis, Diss. 93/1316, Biblioteca Nazionale, Roma (Italy); TDR.1993.1278, Biblioteca Nazionale, Firenze (Italy); (in Italian)
26. Salvadori G, Ratti SP, Belli G, Lovejoy S, Schertzer D (1994) Multifractal objective analysis of seveso ground pollution. Tox. Envir. Chem., 43: 63
27. Salvadori G, Ratti SP, Belli G (1997) Fractal and multifractal approach to environmental pollution. Environ. Sci. Poll. Res., 4(2): 91
28. Schertzer D, Lovejoy S (1987) Physical modelling and analysis of rain and clouds by anisotropic scaling multiplicative processes. J. Geophys. Res., 92: 9693
29. Schertzer D, Lovejoy S (1992) Hard and soft multifractal processes. Physica A, 185: 187
30. Schertzer D, Chigirinskaya Y, Lovejoy S, Ratti SP, Salvadori G, Belli G (1995) Multifractal analysis of chernobyl fallout: self-organized criticality and hot spots. Proc. "Mathematics and Computations, Reactor Physics, and Environmental Analyses", Portland (Oregon), April 30-May 4, 1995, Amer. Nucl. Soc. Publisher, Illinois, p. 743
31. Shiryaev AN (1996) Probability, 2nd edn., Springer-Verlag, New York
32. Tessier Y, Lovejoy S, Schertzer D (1994) The multifractal global rain-gauge network: analysis and simulation. J. Appl. Meteo., 33: 1572
33. Thiessen AH (1911) Precipitation averages for large areas. Mon. Wea. Rev., 39: 1082