Tests for equality of variances of monthly climate data using resampling techniques are discussed. The application of a jackknife test to spatially correlated time series is worked out in this paper. Besides this spatial extension, it is also possible to combine the data for the individual calendar months into a single seasonal or annual test statistic. The derivation of the critical values of the test statistic from Student's t-distribution in such multivariate applications is investigated. A modification to improve the use of the t-distribution is given for the case that the distribution of the data is close to the normal distribution. The power of the simple jackknife test is compared with that of a permutation test.
The test is illustrated with a comparison of the variances of monthly temperatures and precipitation amounts in the anomaly simulation, with enhanced greenhouse gas concentrations, and in the control simulation of the high-resolution transient experiment (UKTR) with the Hadley Centre coupled ocean-atmosphere General Circulation Model. Three regions are considered: Central North America, Southern Europe and Northern Europe. For a number of regions and seasons the differences between the variances of the two simulations are significant at the 5% level. In particular, a significant increase in the variance of monthly precipitation over Northern Europe is found in the anomaly simulation for winter, summer and autumn. Limitations of the use of the test to monthly precipitation time series containing a large proportion of zeros are identified.
JJ Beersma, TA Buishand. A simple Test for Equality of Variances in Monthly Climate Data
published, J. Climate, 1999, 12