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Tornadogenesis and Fractal Geometry. Huaqing Cai NCAR/ASP/ATD. Comparison of Garden City and Hays Mesocyclone. From Wakimoto and Cai, MWR, 2000. Markowski ( MRW , 2002)

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Tornadogenesis and fractal geometry

Tornadogenesis and Fractal Geometry

Huaqing Cai


Comparison of garden city and hays mesocyclone
Comparison of Garden City and Hays Mesocyclone

From Wakimoto and Cai, MWR, 2000

Markowski (MRW, 2002)

Perhaps the most remarkable observational finding during the last 10 years is that the differences between tornadic and nontornadic supercells may be subtle, if even distinguishable, even in dual-Doppler radar analyses of the wind fields just prior to tornadogenesis.”

Comparison of Garden City and Hays Mesocyclone

From Wakimoto and Cai, MWR, 2000

What is a fractal
What is a Fractal ?

  • The term “fractal” was first introduced by B. Mandelbrot in 1970s

  • Fractal, i.e., that which has been infinitely divided

  • Scale invariance

  • Self-similarity

  • A fractal structure is the same “from near or from far”

Applications of fractal geometry in atmospheric sciences
Applications of Fractal Geometry in Atmospheric Sciences

  • Area-perimeter relation for rain and cloud (Lovejoy, Science, 1982)

  • Predictability of atmosphere (Zeng and Pielke, JAS, 1992)

  • Breaking waves (Longuet-Higgins, JPO,1993)

  • Isoconcentration surface in a smoke plume (Praskovsky et al.,JAS, 1996)

Vorticity is scale dependent.

How vorticity is dependent on scale ?

Does it follow the power law ?

Or does it scaling with scale according to e1-D,

where e is the scale, D is a constant (fractal


Vorticity as a fractal
Vorticity as a Fractal

R = 0.993

L = 0.3—9.6 km

Garden City


L=1.8 km

Comparisons of the Garden City and Hays Fractals Suggest that:

  • Two different mesocyclones could look very similar on certain scales

  • Fractal geometry provided a method to look at the same mesocyclone from different scales at the same time

  • The vorticity line could have some indications of a mesocyclone’s tornado potential

0.6 km that:

0.9 km

0.3 km

Tornadic that:


Pseudo vorticity as a fractal
Pseudo-Vorticity as a Fractal that:

xpv= | (Vr)max – (Vr)min | / D

x = 2* xpv for Rankine Vortex

Kellerville that:





Self similarity between tornado and mesocyclone scale
Self-Similarity Between Tornado and Mesocyclone Scale that:

Tornado Scale

0.3 km

0.9 km

0.6 km

Mesocyclone Scale

Summary and future work
Summary and Future Work that:

  • Fractal geometry provided a new perspective to look at a mesocyclone from difference scales at the same time.

  • The different slopes of the vorticity (Pseudo-vorticity) lines may be an indicator of a mesocyclone’s tornadic potential

  • Vorticity (Pseudo-vorticity) line technique is not a tornadogenesis theory, it does not tell you why a mesocyclone produces a tornado, it just tells you which one might be produce tornado.

Summary and future work continued
Summary and Future Work (Continued) that:

  • More case studies, using both dual-Doppler and single Doppler data and different radars such as WSR-88Ds and DOWs, will be needed to verify the hypothesis proposed here.