Microcanonical multifractal formalism: Application to the estimation of ocean surface velocities

Journal of Geophysical Research: Oceans

Volumn 112, Issue 5, 2007, Pages

  Isern Fontanet, J ^a,b   Turiel, A ^a   García Ladona, Emilio ^a   Font, J ^a  

^a INSTITUT DE CIÈNCIES DEL MAR   (Spain)

^b IFREMER   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ATMOSPHERIC TEMPERATURE; ESTIMATION; OCEANOGRAPHY; TURBULENT FLOW; VELOCITY;

ALTIMETRY; FLOW STRUCTURE; FRACTAL ANALYSIS; GEOMETRY; IMAGE ANALYSIS; IMAGE RESOLUTION; SEA SURFACE TEMPERATURE;

EID: 38549115837     PISSN: None     EISSN: 21699291     Source Type: Journal    
DOI: 10.1029/2006JC003878     Document Type: Article

References (74)

1. Abraham, E., and M. Bowen (2002), Chaotic stirring by a mesoscale surface-ocean ow, Chaos, 12(2), 373-381.
2. Afanasyev, Y. D., A. G. Kostianoy, A. G. Zatsepin, and P. Poulain (2002), Analysis of velocity field in the eastern black sea from satellite data during the black sea's experiment, J. Geophys. Res., 107(C8), 3098, doi: 10.1029/2000JC000578.
3. Amaral, L. A. N., A. L. Goldberger, P. C. Ivanov, and H. E. Stanley (1998), Scale-independent measures and pathologic cardiac dynamics, Phys. Rev. Lett., 81(11), 2388-2391.
4. Arneodo, A. (1996), Wavelet analysis of fractals: From the mathematical concepts to experimental reality, in Wavelets: Theory and Applications, ICASE/LaRC Ser. in Comput. Sci. and Eng., edited by G. Erlebacher, M. Y. Hussaini, and L. Jameson, p. 349, Oxford Univ. Press, New York.
5. Ameodo, A., F. Argoul, E. Bacry, J. Elezgaray, and J. F. Muzy (1995), Ondelettes, Multifractales et Turbulence, Diderot Editeur, Paris.
6. Ameodo, A., et al. (1996), Structure functions in turbulence, in various flow configurations, at reynolds number between 30 and 5000, using extended self-similarity, Europhys. Lett., 34(6), 411-416.
7. Arrault, J., A. Ameodo, A. Davis, and A. Marshak (1997), Wavelet-based multifractal analysis of rough surfaces: Application to cloud models and satellite data, Phys. Rev Lett., 79, 75-79.
8. AVISO User Handbook (1996), Corrected sea surface heights products, 2.0 ed., aVI-NT-011-311-CN, CLS, Toulouse, France.
9. Bacry, E., J. F. Muzy, and A. Ameodo (1993), Singularity spectrum of fractal signals from wavelet analysis: Exact results, J. Stat. Phys., 70, 635-673.
10. Bowen, M., W. Emery, J. Wilkin, P. Tildesley, I. Barton, and R. Knewtson (2002), Extracting multiyear surface currents from sequential thermal imagery using the maximum cross-correlation technique, J. Atmos. Ocean. Technol., 19(10), 1665-1676.
11. Carleman, T. (2005), Sur le problème des moments, Comptes Rendus Acad. Sci. Paris, 174, 16801922.
12. Chapron, B., F. Collard, and F. Ardhuin (1989), Direct measurement of ocean surface velocity from space: Interpretation and validation, J. Geophys. Res., 110, C07008, doi:10.1029/2004JC002809.
13. Chhabra, A., C. Meneveau, R. Jensen, and K. Sreenivasan (1989), Direct determination of the f(alpha) singularity spectrum and its application to fully developed turbulence, Phys. Rev. A, 40(9), 5284-5294.
14. Chigirinskaya, Y., D. Schertzer, S. Lovejoy, A. Lazarev, and A. Ordanovich (1994), Unified multifractal atmospheric dynamics tested in the tropics part 1: Horizontal scaling and self organized criticality, Nonlinear Proc. Geophys., 1, 105-114.
15. Côté, S., and A. Tatnall (1995), The hopfield neural network as a tool for feature tracking and recognition from satellite sensor images, Int. J. Remote Sens., 18(4), 871-885.
16. Daubechies, I. (1992), Ten Lectures on Wavelets, CBMS-NSF Ser. in Appl. Math., Capital City Press, Montpelier, Vt.
17. Davis, A., A. Marshak, and W. Wiscombe (1994), Wavelet based multifractal analysis of non-stationary and/or intermittent geophysical signals, in Wavelets in Geophysics, edited by E. Foufoula-Georgiou and P. Kumar, pp. 249-298, Elsevier, New York.
18. Ducet, N., P. Le Traon, and G. Reverdin (2000), Global high-resolution mapping of ocean circulation from TOPEX/Poseidon and ERS-1 and-2, J. Geophys. Res., 105, 19,477-19,498.
19. Emery, W., A. Thomas, M. Collins, W. Crawford, and D. Mackas (1986), An objective method for computing advective surface velocities from sequential infrared satellite images, J. Geophys. Res., 91, 12,865-12,878.
20. Falconer, K. (1990), Fractal Geometry: Mathematical Foundations and Applications, John Wiley, Hoboken, N. J.
21. Frisch, U. (1995), Turbulence, Cambridge Univ. Press, New York.
22. Garcia, C. A. E., and I. Robinson (1989), Sea surface velocities in shallow seas extracted from sequential coastal Zone Color Scanner satellite data, J. Geophys. Res., 94(C9), 12,681-12,691.
23. Gille, S., and S. L. Smith (2000), Velocity probability density functions from altimetry, J. Phys. Oceanogr., 30, 125-136.
24. Grazzini, J., A. Turiel, and H. Yahia. (2002), Entropy estimation and multiscale processing in meteorological satellite images, Proc. ICPR 2002, 3, 764-768.
25. Gupta, V., and E. Waymire (1990), Multiscaling properties of spatial rainfall and river flow distributions, J. Geophys. Res., 95(D3), 1999-2009.
26. Horn, B., and B. Schunk (1981), Determining optical flow, Artificial Intelligence, 17, 185-203.
27. Hunt J., O. Phillips, and D. Williams (Eds.) (1991), Turbulence and stochastic processes: Kolmogorov's ideas 50 years on, Proc. R. Soc. London Ser. A, 434, 1-240.
28. Isern-Fontanet, J., E. García-Ladona, and J. Font (2003), Identification of marine eddies from altimetry, J. Atmos. Oceanic Technol., 20, 772-778.
29. Isern-Fontanet, J., E. García-Ladona, and J. Font (2006a), The vortices of the Mediterranean sea: An altimetric viewpoint, J. Phys. Oceanogr., 36, 87-103.
30. Isern-Fontanet, J., et al. (2006b), Non-gaussian velocity Probability Density Functions: An altimetric perspective of the Mediterranean Sea, J. Phys. Oceanogr., 36, 2153-2164.
31. Isern-Fontanet, J., B. Chapron, G. Lapeyre, and P. Klein (2007), Potential use of microwave Sea Surface Temperatures for the estimation of ocean currents, Geophys. Res. Lett., 33, L24608, doi:10.1029/ 2006GL027801.
32. Ivanov, P., L. Amaral, A. Goldberger, S. Havlin, M. Rosenblum, Z. Struzik, and H. Stanley (1999), Multifractality in human heartbeat dynamics, Nature, 399, 461-465.
33. Kelly, K. A. (1989), An inverse model fro near-surface velocity from infrared images, J. Phys. Oceanogr., 19, 1845-1864.
34. Kestener, P., and A. Arnéodo (2003), Three-dimensional wavelet-based multifractal method: The need for revisiting the multifractal description of turbulence dissipation data, Phys. Rev. Lett., 91(19), 194501, doi:10.1103/PhysRevLett.91.194501.
35. Kilpatrick, K., G. Podestá, and R. Evans (2001), Overview of the NOAA/NASA advanced very high resolution radiometer Pathfinder algorithm for the sea surface temperature and associated matchup database, J. Geophys. Res., 106, 9179-9197.
36. Kolmogorov, A. N. (1941a), The local structure of turbulence in an incompressible fluid with very large reynolds number, Dokl. Akad Nauk. SSSR, 309, 301-305.
37. Kolmogorov, A. N. (1941b), Dissipation of energy in a locally isotropic turbulence, Dokl. Akad Nauk. SSSR, 32, 16-18.
38. Kuo, N. J., and C. Yan (1994), Using the shape-matching method to compute sea-surface velocities from avhrr satellite images, IEEE Trans. Geosci. Remote Sens., 32(3), 724-728.
39. Lapeyre, G., and P. Klein (2006), Dynamics of the upper oceanic layers in terms of surface quasigeostrophy theory, J. Phys. Oceanogr., 36, 165-176.
40. Lapeyre, G., B. Hua, and P. Klein (2001), Dynamics of the orientation of active and passive scalars in two-dimensional turbulence, Phys. Fluids, 13, 251-264.
41. Le Traon, P., and F. Ogor (1998), ERS-1/2 orbit improvement using TOPEX/ POSEIDON: The 2cm challenge, J. Geophys. Res., 103(C4), 8045-8057.
42. Le Traon, P., F. Nadal, and N. Ducet (1998), An improved mapping method of multisatellite altimeter data, J. Atmos. Oceanic Technol., 15(2), 522-534.
43. Llewellyn Smith, S., and S. Gille (1998), Probability density functions of large-scale turbulence in the ocean, Phys. Rev. Lett., 81(23), 5249-5252.
44. Lovejoy, S., W. Currie, Y. Tessier, M. Claereboudt, E. Bourget, J. Roff, and E. Schertzer (2001), Universal multifiractals and ocean patchiness: Phytoplankton, physical fields and coastal heterogeneityp, J. Plankt. Res., 23(2), 117-141.
45. Meneveau, C., and K. Sreenivasan (1991), The multifractal nature of turbulent energy dissipation, J. Fluid Mech., 224, 429-484.
46. Morrow, R., F. Birol, D. Griffin, and J. Sudre (2004), Divergent pathways of cyclonic and anti-cyclonic ocean eddies, Geophys. Res. Lett., 31, L24311, doi:10.1029/2004GL020974.
47. Munk, W. (2000), Oceanography before, and after, the advent of satellites, in Satellites, Oceanography and Society, Elsevier Oceanogr. Ser., edited by D. Halpern, pp. 1-4, Elsevier, New York.
48. Muzy, J. F., E. Bacry, and A. Arneodo (1991), Wavelets and multifractal formalism for singular signals: Application to turbulence data, Phys. Rev. Lett., 67, 3515-3518.
49. Novikov, E. A. (1994), Infinitely divisible distributions in turbulence, Phys. Rev. E, 50, R3303.
50. Parisi, G., and U. Frisch (1985), On the singularity structure of fully developed turbulence, in Turbulence and Predictability in Geophysical Fluid Dynamics, Proc. Intl. School of Phys. E., Fermi, edited by M. Ghil, R. Benzi, and G. Parisi, pp. 84-87, North Holland, New York.
51. Pascual, A., Y. Faugre, G. Larnicol, and P. LeTraon (2006), Improved description of the ocean mesoscale variability by combining four satellite altimeters, Geophys. Res. Lett., 33, L02611, doi:10.1029/2005GL024633.
52. Rio, M.-H., and F. Hernádez (2004), A mean dynamic topography computed over the world ocean from altimetry, in-situ measurements and a geoid model, J. Geophys. Res., 109, C12032, doi:10.1029/ 2003JC002226.
53. Sachs, D., S. Lovejoy, and D. Schertzer (2002), The multifractal scaling of cloud radiances from 1 m to 1 km, Fractals, 10(3), 1-12.
54. She, Z. S., and E. Leveque (1994), Universal scaling laws in fully developed turbulence, Phys. Rev Lett., 72, 336-339.
55. She, Z. S., and E. C. Waymire (1995), Quantized energy cascade and log-poisson statistics in fully developed turbulence, Phys. Rev. Lett., 74, 262-265.
56. Sreenivasan, K. (1991), Fractals and multifractals in fluid turbulence, Annu. Rev. Fluid Mech., 23, 539-600.
57. SSALTO/DUACS User Handbook (2006), (M)SLA and (M)ADT near-real time and delayed time products, 1rev4 of the 31 January 2006 ed., sALP-MU-P-EA-21065-CLSA, CLS, Toulouse, France.
58. Struzik, Z. R. (2000), Determining local singularity strengths and their spectra with the wavelet transform, Fractals, 8(2), 163-179.
59. Turiel, A. (2003), Relevance of multifractal textures in static images, Elect, Lett. Comput. Vision Image Anal., 1(1), 35-49.
60. Turiel, A., and A. del Pozo (2002), Reconstructing images from their most singular fractal manifold, IEEE Trans. Im. Proc., 11, 345-350.
61. Turiel, A., and N. Parga (2000), The multi-fractal structure of contrast changes in natural images: From sharp edges to textures, Neural Comput., 12, 763-793.
62. Turiel, A., and C. Pérez-Vicente (2003), Multifractal geometry in stock market time series, Physica A, 322, 629-649.
63. Turiel, A., and C. Pérez-Vicente (2004), Multifractal measures: Definition, description, synthesis and analysis: A detailed study, in Proceedings of the "Journées d'étude sur les méthodes pour les signaux complexes en traitement d'image," edited by J.-P. Nadal, A. Turiel, and H. Yahia, pp. 41-57, INRIA, Toulouse, France.
64. Turiel, A., and C. Pérez-Vicente (2005), Role of multifractal sources in the analysis of stock market time series, Physica A, 355, 475-496.
65. Turiel, A., G. Mato, N. Parga, and J. P. Nadal (1998), The self-similarity properties of natural images resemble those of turbulent flows, Phys. Rev. Lett., 80, 1098-1101.
66. Turiel, A., J. Grazzini, and H. Yahia (2005a), Multiscale techniques for the detection of precipitation using thermal ir satellite images, IEEE Geosci. Remote Sens. Lett., 2(4), doi:10.1109/ LGRS.2005.852712.
67. Turiel, A., J. Isern-Fontanet, E. García-Ladona, and J. Font (2005b), Multifractal method for the instantaneous evaluation of the stream function in geophysical flows, Phys. Rev. Lett., 95(10), doi:10.1103/PhysRevLett.95.104502.
68. Turiel, A., C. Pérez-Vicente, and J. Grazzini (2006), Numerical methods for the estimation of multifiractal singularity spectra on sampled data: a comparative study, J. Comput. Phys., 216(1), 362-390.
69. Vigan, X., C. Provost, R. Bleck, and P. Courtier (2000a), Sea surface velocities from sea surface temperature image sequences: 1. Method and validation using primitive equation model output, J. Geophys. Res., 105, 19,499-19,514.
70. Vigan, X., C. Provost, and P. Podesta (2000b), Sea surface velocities from sea surface temperature image sequences: 2. Application to the brazil-malvinas confluence area, J. Geophys, Res., 105, 19,515-19,534.
71. Walton, C. C., W. G. Pichel, F. J. Sapper, and D. A. May (1998), The development and operational application of nonlinear algorithms for the measurement of sea surface temperatures with noaa polar-orbiting environmental satellites, J. Geophys. Res., 103, 27,999-28,012.
72. Waugh, D., E. Abraham, and M. Bowen (2006), Spatial variations of stirring in the surface ocean: A case study of the Tasman sea, J. Phys. Oceanogr., 36, 526-542.
73. Wbal, D. D., and J. J. Simpson (1991), Satellite derived estimates of the normal and tangential components of near-surface flow, Int. J. Remote Sens., 12, 2529-2571.
74. Wu, Q. X., D. Pairman, S. J. McNeill, and E. J. Barnes (1992), Computing advective velociites from satellite images of sea surface temperature, IEEE Trans. Geosci. Remote Sens., 30(1), 166-176.