the variance spectrum of monthly mean central england temperatures

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CORRESPONDENCE AND NOTES 679 Mason, B. J. and Maybank, J. 1960 Mossop, S. C., Brownscornbe. J. L. 1974 Mossop, S. C., Cottis, R. E. and 1972 Mossop, S. C., Ono, A. and 1970 Ono, A. 1969 and Collins, G. J. Bartlett, B. M. Wishart, E. R. Meteorological Office, Bracknell, Berkshire. 11 February 1975 ' The fragmentation and electrification of freezing water ' The production of secondary ice particles during riming,' ' Ice crystal concentrations in cumulus and stratocumulus ' Ice particles in maritime clouds near Tasmania,' Ibid., 96, ' The shape and riming properties of ice crystals in natural dops,' Ibid., 86. pp. 176-186. Ibid., 100. pp. 427-437. clouds,' Ibid., 98, pp. 105-123. pp. 487-50s. cIouds,'J. Atmos. Sci., 26, pp. 138-147. 551.524.36 : 551.583.14 THE VARIANCE SPECTRUM OF MONTHLY MEAN CENTRAL ENGLAND TEMPERATURES* By RALPH SHAPIRO Manley (1974) has published a series of monthly msan temperatures for central England which is remarkable for its length (1659 to 1973) and perhaps also for its homogeneity. In view of the length of the time series, it is instructive for a first crude analysis of the data to determine its variance spectrum. Fig. 1 shows the raw, unsmoothed spectrum of the time s-xies, as published, following the approach of Blackman and Tukey (1959), with the autocorrelation function truncated at 600 lags (months). The ordinate, on a linear scale, shows the fraction of the total variance contributed by I Figure 1. Power spectrum of monthly mean central England air temperatures covering years 1659-1973. 3780 months Lag=600 Dr. Shapiro's paper confirms, and makes mom preciaa. results reported by J. M. Craddock, based on earlier versions of themame data. See, e.g. The Srorisriclm, 15, pp. 167-190. 1965. ' The analysis of meteorological time series for usa in forecarting '. (Editor)

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CORRESPONDENCE AND NOTES 679

Mason, B. J. and Maybank, J. 1960

Mossop, S. C., Brownscornbe. J. L. 1974

Mossop, S. C., Cottis, R. E. and 1972

Mossop, S. C., Ono, A. and 1970

Ono, A. 1969

and Collins, G. J.

Bartlett, B. M.

Wishart, E. R.

Meteorological Office, Bracknell, Berkshire. 11 February 1975

' The fragmentation and electrification of freezing water

' The production of secondary ice particles during riming,'

' Ice crystal concentrations in cumulus and stratocumulus

' Ice particles in maritime clouds near Tasmania,' Ibid., 96,

' The shape and riming properties of ice crystals in natural

dops,' Ibid., 86. pp. 176-186.

Ibid., 100. pp. 427-437.

clouds,' Ibid., 98, pp. 105-123.

pp. 487-50s.

cIouds,'J. Atmos. Sci., 26, pp. 138-147.

551.524.36 : 551.583.14

THE VARIANCE SPECTRUM OF MONTHLY MEAN CENTRAL ENGLAND TEMPERATURES*

By RALPH SHAPIRO

Manley (1974) has published a series of monthly msan temperatures for central England which is remarkable for its length (1659 to 1973) and perhaps also for its homogeneity. In view of the length of the time series, it is instructive for a first crude analysis of the data to determine its variance spectrum.

Fig. 1 shows the raw, unsmoothed spectrum of the time s-xies, as published, following the approach of Blackman and Tukey (1959), with the autocorrelation function truncated at 600 lags (months). The ordinate, on a linear scale, shows the fraction of the total variance contributed by

I

Figure 1. Power spectrum of monthly mean central England air temperatures covering years 1659-1973. 3780 months Lag=600

Dr. Shapiro's paper confirms, and makes mom preciaa. results reported by J. M. Craddock, based on earlier versions of themame data. See, e.g. The Srorisriclm, 15, pp. 167-190. 1965. ' The analysis of meteorological time series for usa in forecarting '. (Editor)

680 CORRESPONDENCE AND NOTES

Figure 2. Power spectrum of 12 term running monthly mean central England air temperatures covering years 1670-1973.

3769 months Lag=600

each frequency sampled. The abscissa, which is also on a linear scale, shows the frequency per 100 years. Thus, for example, a frequency of 100 corresponds to a period of one year. A random time series displayed in this fashion would show approximately equal variance at all frequencies, differing only because of sampling fluctuations. Much of Fig. 1 displays just such a white noise characteristic. The notable exception is the annual period which is plotted off-scale in Fig. 1 and which accounts for 91 % of the total variance. The peak at 6 months is due to a very slight assymetry in the shape of the annual temperature ' wave ' and accounts for slightly less than 1 % of the total variance. The small but statistically significant peak at 25.5 months and the general tendency toward a somewhat elevated continuum at the low frequencies contribute the only obvious

= * I I .

I ' F R E Q U ~ N C Y PER SO"YCRRS zo t'

Figure 3. Power spectrum of annual mean central England air temperatures covering years 1659-1973. Lag -25

CORRESPONDENCE AND NOTES 68 1

remaining departures from randomness in Fig. 1. The peak at 25.5 months is consistent with other mid-latitude, low-level evidence of the quasi-biennial oscillation. The elevation of the continuum at low frequencies probably reflects some real, long-period variations as well as some early ‘ instrumental ’ changes in the make-up of the time series.

Notable for its absence in Fig. 1 is any evidence of an enhancement of the spectrum at periods near 11 years, the well-known sunspot number period.

The sharpness of the annual period and its first harmonic, though not surprising, is worthy of note. In the case of the annual period, the variance at the frequency 100 is near, or greater than, 3 orders of magnitude larger than the values at the nearby frequencies.

To ensure that none of the significant features of Fig. 1 are introduced or influenced by the large concentration of power at one year, spectra were obtained after filtering the raw time series by a variety of different filters designed to remove the annual period. The results of two of the simplest filtering procedures are shown in Figs. 2 and 3. Fig. 2, constructed in the same fashion as Fig. 1, shows the spectrum of the 12-month running mean. Fig. 3 shows the variance spectrum of the annual mean temperature using an autocorrelation function truncated at a lag of 25 years. Both Figs. 2 and 3 show a ‘ red noise ’ spectrum (continuum elevated at the low frequencies) and a small peak at 25.5 months. Both figures also fail to show any enhancement of variance at periods near eleven years.

REFERENCES

Blackman, €2. B. and Tukey, J. W . The measurement of power spectra from the point of view of communications engineering, New York, Dover Pub.

Manley, G. 1974 ‘Central England temperatures: monthly means 1659 to 1973,’ Quart. J. R. Met. SOC., 100. pp. 389405.

Air Force Cambridge Research Laboratories, Bedford, Massachusetts 01731. 17 February 1975

1959