During the last 25 years a number of writers have called attention to a short cycle in weather elements and have given estimates of its mean length varying from 2.5 to 3.5 years. The diversity in these estimates is due in part to the practice of some investigators of using data with a time interval of 12 months, which leads to high values of the intervals; others employed consecutive 12-month means and derived values of 2.5 to 3.0 years.
In the present paper various statistical criteria and methods are employed to show the extent to which a given succession of meteorological data, such as yearly means of temperature, differs from a purely fortuitous sequence of similar data. In high latitudes the mean interval between two consecutive maxima or minima is less than 3.0 years, which is the mean interval for a perfectly fortuitous sequence. This and other criteria indicate a systematic and persistent tendency to a recurrence of similar phases which differs from that due to chance alone and this period of recurrence is approximately 2.0 to 2.5 years.
Two methods of investigation, the empirical and the analytical, are discussed and contrasted. The empirical method is illustrated by Wolfer's determination of the epochs of maxima and minima of the solar spots, by Brückner's determination of the epochs of the 35-year cycle, and by Wallén's investigation of the 2.5-year cycle in temperature, rainfall, and lake levels in Sweden.
It is maintained that analytical methods applied to meteorological data, illustrated by Brunt's periodogram analysis of Greenwich temperatures and Beveridge's periodogram of wheat prices in Europe for 300 years, have led to negative results in that no stable periodicity of uniform length has been certainly shown to exist.
In the present investigation two 12-month means per year have been employed, one centered on January 1 and the other on July 1. The adequacy of data in this form for disclosing satisfactorily a cycle of 2.0 to 2.5 years in length is shown by both empirical and analytical methods.
Contemporaneous curves showing meteorological conditions for a number of stations have been drawn for the regions studied, viz. northern Europe and northern United States.
By careful scrutiny and comparison of these curves the epochs of maxima and minima of the short cycle have been determined for pressure and temperature in Europe since 1740 and for temperature in the United States since 1780. Similar phases of pressure over southwestern Europe and of temperature over northern Europe and the northern United States are nearly coincident; the deviations from coincidence are shown to correspond to the accidental errors of observation. Epochs of maxima and minima have also been derived for the pressure in Greenland, which are in general opposite to those in southwestern Europe. The epochs of pressure and temperature for Portland, Oreg., are shown to differ markedly in phase from those for stations in the upper Mississippi Valley. The epochs of maximum and minimum storm velocity in the United States and of maximum and minimum interdiurnal variability of pressure at St. Louis have been derived and it is found that when the temperature over the northern boundary of the United States is low, storm areas move rapidly and the day-to-day fluctuations in pressure and temperature at St. Louis are large. Variations in temperature at New Orleans occur later than at St. Paul, the average difference in the epochs of the short cycle being about four months.
The variations of rainfall show the short cycle with less regularity than those of pressure and temperature, in conformity with the more nearly fortuitous character of this element. In general the epochs of maximum rainfall over northern Europe occur near the epochs of minimum pressure over southern Europe.
It is found that the period under discussion has a mean length of about 28 months, subject to systematic variations in length attributed to the 11-year sunspot period, the 35-year Brückner variation, and to a long secular change, perhaps indicative of a 300-year cycle. The latter is indicated by the general increase in length from about 2.0 years at the middle of the eighteenth century to about 2.5 years at the present time. The 35-year cycle is suggested by a shortening of the period at or near the wet epochs, and a corresponding lengthening at the dry epochs of the Brückner cycle. The 11-year variation seems to be shown by a secondary decrease in the length a few years after the epochs of maxima of sun spots.
A 28-month periodicity is shown to exist in the variations of the mean latitude of sun spots, which shifts systematically from one hemisphere to the other over a range of about 10°. The 11-year and the 35-year variations are shown also to exist in the length of this solar period.
A fairly large correlation exists between the latitude of spots, (regarding north latitude as positive and south latitude as negative), and the temperature at St. Paul one year later, the coefficient being —.56.
Wolfer's smoothed sun spot relative numbers since 1750, with the 11-year variation eliminated, disclose secondary maxima with a tendency to recurrence every 2.3 years, as an average. The 11 and 35 year, as well as the long secular variations are evident in the recurrence of these maxima.
A new graphical scheme is described which facilitates the accurate evaluation of the mean length of the period at any time.
The substance of this paper was published in Mo. Weather Rev., January, 1924, 52: 38. The writer desires to express his appreciation of the suggestions and criticisms offered by Prof. C. F. Marvin during the final revision.