1. For a scientific approach to extreme events Asymptotic analysis of typhoons and tsunami Daniela Bianchi, Department of Physics, Univ. Of Rome “La Sapienza” Sergey Dobrokhotov, Institute of Problem of Mechanics, Moscow Academy of Sciences Fabio Raicich, ISMAR, CNR Trieste Sergiy Reutskiy, Ukrainian Academy of Science, Kharkov Brunello Tirozzi, Department of Physics, Univ. Of Rome “La Sapienza”

2. Poleward heat transport

3. Wind system for water covered Earth

4. Main wind system (Northern summer)

5. Main wind system (Southern summer)

6. Cyclon and Anticyclon

7. Cyclogenesis at mid latitudes

8. Westerlies-Rossby wave

9. Nanmadol

10. Forecast without heat exchange

12. Sonca

13. Forecast without heat exchange

15. Kirogi

16. Real and computed trajectory with heat exchange

17. Real and forecast trajectory

20. Maslov decomposition (1/2) x is the difference among the running point and the typhoon center F is a function with the singularity in the origin of the square root type S is a quadratic function of the coordinates x with different eigenvalues f(x,t), g(x,t) are smooth functions Self-similarity and stability properties

21. Maslov decomposition (2/2)

22. Cauchy Riemann conditions and stability of perturbations

23. Perturbed solutions of SW equations (1/3)

24. Perturbed solutions of SW equations (2/3)

25. Perturbed solutions of SW equations (3/3)

26. Conserved structure of the solution (1/2)

27. Conserved structure of the solution (2/2)

28. Chi variable at each 0.25 degrees for the 00 of 18.09.06 Sanshan positions: 37.1 N, 132.4 E (developed) Yagi positions: 20.5 N, 158.6 E (beginning) 1 : Chi =0.1282 sec^(-1)

29. Computation of the trajectory of the center of typhoons

30. SW+temp. eq. (1/2)

31. Sw+temp.eq (2/2)

32. Lax Wendroff Method (1/4)

33. Lax Wendroff method (2/4)

34. Lax Wendroff method (3/4)

35. Lax-Wendroff Method (4/4)

36. Stability of the vortex

37. Non stability of the vortex

38. Boundary conditions (1/3)

39. Boundary conditions (2/3)

40. Boundary conditions (3/3)

41. Neural Network (1/4)

42. Neural Network (2/4)

43. Neural Network (3/4)

44. Neural Network (4/4)

45. Hugoniot-Maslov Hierarchy 1/15

46. Hugoniot-Maslov Hierarchy 2/15

47. Hugoniòt-Maslov Hierarchy 3/15

48. Hugoniòt-Maslov Hierarchy 4/15

49. Hugoniòt-Maslov Hierarchy 5/15

50. Hugoniòt-Maslov Hierarchy 6/15

51. Hugoniòt-Maslov Hierarchy 7/15

52. Hugoniòt-Maslov Hierarchy 8/15

53. Hugoniòt-Maslov Hierarchy 9/15

54. Hugoniòt-Maslov Hierarchy 10/15

55. Hugoniòt-Maslov Hierarchy 11/15

56. Hugoniòt-Maslov Hierarchy 12/15

57. Hugoniòt-Maslov Hierarchy 13/15

58. Hugoniòt-Maslov Hierarchy 14/15

59. Hugoniòt-Maslov Hierarchy 15/15

60. More phenomenology (1/4)

61. More phenomenology (2/4)

62. More phenomenology (3/4)

63. More phenomenology (4/4)

64. Workshop On Renormalization Group, Kyoto 2005 B. Tirozzi, S.Yu. Dobrokhotov, S.Ya. Sekerzh-Zenkovich, T.Ya. Tudorovskiy Analytical and numerical analysis of the wave profiles near the fronts appearing in Tsunami problems

65. “Gaussian” source of Earthquake

66. Level curves of perturbation

67. Wave profiles at the front at time t at different angles

68. 3D wave profile for elliptic source

69. “Modulated gaussian” source of Earthquake

70. Level curves of perturbation

71. Wave profiles at the front at time t at different angles

72. 3D wave profile for elliptic source

73. The ridge near the source of Eathquake

74. Fronts at different times

75. The set of profiles

79. Simulations for Tyrrhenian Sea Relief data: National Oceanic and Atmospheric Administration (NOAA) National Geophysical Data Center (NGDC) ETOPO2 2-minute Global Relief http://www.ngdc.noaa.gov/mgg/gdas/gd_designagrid.html

80. Rays for imaginary source at Stromboli: 38.8 N, 15.2 E

81. Amplitudes of wave at different points of the coast

82. 3D wave profile

83. Density plot

84. ... Workshop on Extreme Events... Max Planck Institut for Complex System Dresden, 30 October-2 November 2006 Analysis of the tsunami event in Algeria 2003 S. Dobrokhotov (1), B. Tirozzi (2), P. Zhevandrov (3), F. Raicich (4) (1) Institute for Problems in Mechanics, RAS, Moscow, Russia (2) Department of Physics, University “La Sapienza”, Rome, Italy (3) Escuela de Ciencias Fisico-Matematicas, Morelia, Mich., Mexico (4) CNR, Institute of Marine Sciences, Trieste, Italy

85. Valencia Barcelona Ibiza Earthquake data (USGS): t0: 18:44:19 GMT, 21 may 2003 USGS: epicenter 36.96°N, 3.63°E, M=6.9, hf=12 km Borerro: epicenter 36.90°N, 3.71°E, M=6.8, hf=10 km, strike=56°

87. Ellipsoidal deformation M = 6.9 h f = 12 km (Pelinovsky et al., 2001) a = 34 km b = 12 km b 56° a Coordinates: model gridpoints

88. (Dobrokhotov et al., 2006) a 1 = 1.2 10 -2 km -1 Gaussian*cosine deformation = 0 a 2 = 2.7 10 -2 km -1 b 1 = 0.5 10 -2 km -2 b 2 = 4.0 10 -2 km -2 = 56° Coordinates: model gridpoints

97. Wave equation

98. Average of fast oscillating solutions

99. Amplitude of the waves at tsunami front

100. Solutions before and after the scattering of the beach (1/2)

101. Solutions before and after the scattering of the beach (2/2)

102. Graphics 1

103. Graphics 2

104. Graphics 3

105. End