Statistical tests for comparison of daily variability in observed and simulated climates

Abstract

Tests for differences in daily variability based on the jackknife are presented. These tests properly account for the effect of autocorrelation in the data and are reasonably robust against departures from normality. Three measures for the daily variability are considered: process, within-month, and innovation variance. The jackknife statistic compares the logarithm of these measures. The standard errors of this logarithm are obtained by recomputing the variance estimates for all subsamples wherein one month is omitted from the complete sample. A simple extension of the jackknife procedure is given to obtain a powerful multivariate test in situations that the differences in variance have the same sign across the region considered or over the year. As an illustration the tests are applied to near-surface temperatures over Europe simulated by the coupled ECHAM/LSG model. It is shown that the control run of the model significantly overestimates the process variance in winter and spring and the within-month variance in all seasons. Significant differences are also found for the innovation variances of the daily temperatures, but the sign of the differences varies over the year. In a perturbed run with enhanced atmospheric greenhouse gas concentrations the daily temperature variability over Europe significantly decreases in winter and spring compared with the control run.