Keywords: time series, orthogonal polynomials, exact zeros
Rainfall for each 6-day period for Adelaide from 1839 to 1977 inclusive. December 31 of the previous year is included in the non-leap years to make 15 6-day periods for each year.
|Year||1839 - 1977|
|Period||1 - 61 for each year|
Data file (tab-delimited text)
|Cornish, E. A. (1954). On the secular variation of rainfall at Adelaide. Australian J. Physic., 7, 334-346.|
|Andrew, D. F., and Herzberg, A. M. (1985). Data: a Collection of Problems from many Fields for the Student and Research Worker. Springer, New York.|
The data was extended from Cornish's data by R. G. Jarrett, CSIRO, Melbourne, with the help of the Bureau of Meteorology.
Andrews and Herzberg (1985) write
Cornish analyzed the data by first fitting orthogonal polynomials up to fifth order to each year. Each set of coefficients, the constants, the linear terms, etc, was then examined separately for significant changes over the years. The main result was a 23 year cycle in the linear coefficients, which was related to a cycle of amplitude about 30 days in the onset of the winter rains. This cycle agrees with the known sunspot cycle. Another result was the gradual increase in the magnitude of the quadratic coefficient, indicating a gradual lengthening of the winter rains. A subsequent analysis in 1968 confirmed these results, although the 23 year cycle appears to be less well-defined over the last 30-40 years.
There are obviously many other ways in which the data can be analyzed. One of the major difficulties in any analysis, however, is the variability in the rainfall. Even using six-day totals, about 25% of the observations are zero and there are also some outliers, particularly due to thunderstorms during the summer months.