T-Scale Origin

...in which comparisons are made with the Beaufort and Fujita Wind-Speed Scales

The international tornado intensity scale has a sound scientific basis and is closely related to the Beaufort Scale in its scientific formulation. The history of the wind-speed scales is briefly summarised here.

THE INTERNATIONAL BEAUFORT SCALE

In the year 1805 Sir Francis Beaufort proposed an empirical wind scale for use at sea which was an immediate success. Another empirical scale was devised for use on land. In the twentieth century (in 1921) the Beaufort Scale was quantified by introducing a three-halves power law relating wind velocity to Beaufort force number.

Quoting from the Met. Office’s Meteorological Glossary:

"The introduction of anemometers led to the necessity for a scale of equivalents between Beaufort numbers estimated by experienced observers and the velocity of the wind in miles per hour. Experiments showed that the relation could be expressed approximately by the equation v = 1.87 times B ^3/2 mph, where B is the corresponding Beaufort number".

At a meeting in 1926 the International Meteorological Committee accepted Dr. George Simpson’s table of equivalents [of which I give a part here]

Using v = 0.837 B^3/2 metres per second or v = 1.87 B ^3/2 mph

Part Of The Beaufort Scale
Beaufort Scale Metres / Second Miles / Hour
B0 0 - 0.5 0 – 1
B1 0.6 - 1.7 2 - 3
B2 1.8 – 3.3 4 – 7
B8 15.3 – 18.2 34 - 40
B10 25.2 – 29.0 57 - 65

THE INTERNATIONAL TORNADO SCALE
In 1972 Dr. Terence Meaden who had been researching the incidence, strengths and damage paths of tornadoes in Britain proposed that the best means of creating a tornado intensity scale was to base it on an extension of the internationally-recognised Beaufort scale.

After testing the tornado scale for three years the International Tornado Intensity Scale was announced at a meeting of the Royal Meteorological Society in 1975 and published next year in the UK (Meaden 1975-76) and in the USA (Abbey 1976).

The theoretical basis was that the Beaufort formula was employed and extended upwards by setting T0 at gale force B8. This meant that

B = 2 (T + 4) and T = (B/2 – 4) where T is the scale number on the T–Scale

In this way all the world’s known tornadoes occupy a scale running from T0 to T10. The majority of British tornadoes range up to T6 while the most violent known tornado for Britain approached T8.

Let us stress that the tornado intensity scale, besides being mathematically exact, relates precisely to the well-proven Beaufort Scale whose bicentenary (1805-2005) is soon to be recognised.

On the matter of relating degrees of observed damage to T–Scale numbers, we quote from a major 1985 research paper (Meaden 1985):

In the absence of actual wind-speed measuring instrumentation "the direct estimation of tornado wind-speeds is best achieved by studying the evidence of certain kinds of structural damage (as for instance to engineered structures), or by analysing ciné-film or video film sequences of entrained debris, the flight and impact of projected missiles, photographs of the shapes of funnel clouds, and so on. Good evidence like this is not often available, and is only acquired gradually during many years of patient data accumulation. Hence, in order to facilitate a rapid understanding of tornadic strengths in day-to-day examples, and to permit meaningful intercomparisons to be readily drawn between them, the straightforward scale of intensities devised by TORRO has been used in the basic British/European tornado data bank. The intensity numbers on this scale represent wind-speed bands pertaining to their damage potential . The assignment of an intensity number simplifies discussion of a tornado’s most significant attribute, its maximum known strength; at the same time, it greatly aids information retrieval. Of the many uses to which it can be put, one of the most important is certainly the statistical analysis of past incidents within a selected region to establish tornado-risk probabilities at different levels of intensity."

It is important to note the straightforward relationship between T–Scale and B scale, namely:

Relationship Between the International Tornado Intensity Scale And Beaufort Scale
Tornado Scale 0 1 2 3 4 5 6 7 8 9 10
Beaufort Scale 8 10 12 14 16 18 20 22 24 26 28

and the following useful formulae:

v = 2.365 (T+4)^ 3/2 metres per second v = 8.511 (T+4)^3/2 kilometres per hour

v = 5.289 (T+4)^ 3/2 miles per hour v = 4.596 (T+4)^3/2 knots.

On both the Beaufort and the Tornado scales mean gale-force wind is identical at 18.9 m/sec (42.3 mph) for B = 8 and T = 0.

Also, mean hurricane speeds are identical at 34.8 m/sec or 77.7 mph for B = 12 or T = 2.

THE FUJITA SCALE
T.T. Fujita set his tornado force 1 (more precisely F1.0) to equal minimum hurricane speed, i.e. he chose not the normal Beaufort mean hurricane force 12.0 but what amounts to B11.53 instead (about 73 mph). This peculiarity ensured that there could never be an exact equivalence between F and B scales.

Having noted the existence of the Beaufort scale as being useful for speeds below hurricane speed, Dr. Fujita reflected that, in case the highest wind speeds in tornadoes might be found to approach Mach 1 (738 mph or 330 metres per second), he should allow for that when proposing his tornado damage scale.

So he set out a three-part graph running from 0 mph to beyond 750 mph, in which he had to forge a link between Beaufort at one end and the Mach scale at the high end, where he chose F12 to be Mach 1. This also had the effect of making F0 equal to B7.7 (not B8)

He achieved the link by interposing a third section to a special design that nonetheless followed the usual 3/2 power law, but in order to make the mismatch work Dr. Fujita assigned arbitrary constants to his new line (Fujita 1973; Fujita and Pearson 1973)).

A major consequence is that there are no exact numerical relations between the Beaufort and Fujita Scales:

Relationship Between Beaufort And Fujita Scales
Fujita Scale 0.00 1.00 2.00 3.00 4.00 5.00 6.00
Beaufort Scale 7.70 11.53 15.40 19.20 23.10 26.90 30.80

Another consequence is that study of Fujita’s three-part graph reveals that there are abnormal cusp singularities at the two places where the different curves meet each other.

If there had been a world scientific committee meeting at this time, Fujita’s non-rigorous and arbitrary handling of the matter would never have been accepted.

Moreover, because Fujita’s scale was given F numbers from F0 to F12, only the part up to F5 is of any use for all known tornadoes, rendering it very cramped in practical use. Only 0.07 per cent of recorded US tornadoes have been known to reach F5, so F5 is rarely assigned. Most tornadoes only reach F3 or 4 in America, and in other countries seldom exceed F3. Therefore, the majority of tornadoes around the world are cramped into the restricted range F0 to F2 or 3.

TABLES RELATING THE TORRO AND FUJITA SCALES

TORRO Scale Vs Fujita Scale
T–Scale 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0
Fujita Scale 0.1 0.6 1.1 1.6 2.2 2.7 3.2 3.7 4.2 4.8 5.3
Fujita Scale Vs T–Scale
Fujita Scale 0.00 1.00 2.00 3.00 4.00 5.00
T–Scale -0.15 1.80 13.70 5.60 7.50 9.50

REFERENCES
Abbey, R. F. (1976). Page 187 of Risk probabilities associated with tornado windspeeds, in Proc. Symposium on tornadoes, Lubbock, Texas, June 1976.

Fujita (1973). Tornadoes around the world. Weatherwise. 26, 56-62.

Fujita, T.T. and Pearson, A.D. (1973) Results of FPP classification of 1971 and 1972 tornadoes. Preprints 8th Conference on Severe Local Storms, Denver. October 1973. Pp. 142-145

Meaden, G.T. (1975-76). Tornadoes in Britain: their intensities and distribution in time and space. J. Meteorology, 1, 242-251 (based on a lecture to the Royal Meteorological Society in 1975).

Meaden, GT (1985) A study of tornadoes in Britain, with assessments of the general tornado risk potential and the specific risk potential at particular regional sites. Prepared at the request of HM Nuclear Installations Inspectorate Health and Safety Executive.

More information on the International Tornado Intensity Scale, including damage equivalents, is to be found at http://www.torro.org.uk