Climatological series shift test comparison on running windows

Abstract

The detection and correction of inhomogeneities in the climate series is of paramount importance for avoiding misleading conclusions in the study of climate variations. One simple way to address the problem of multiple shifts in the same series is to apply the tests on windows running along the series of anomalies. But it is not clear which of the available tests works better. 500 Monte Carlo simulations have been done for the ideal case of a 600 normally distributed terms (a 50 years series of monthly differences), with a single shift in the middle and magnitudes of 0 to 2 standard deviations (s) in steps of 0.2 s. The compared tests have been: 1) classical t-test; 2) standard normal homogeneity test; 3) two-phase regression; 4) Wilcoxon-Mann-Whitney test; 5) Durbin-Watson test (lag-1 serial correlation), and 6) squared relative mean difference (simpler than t-test and hence faster to compute). The criterion for qualifying the performance of each test was the ability to detect shifts without false alarms and to locate them at the correct point. Results indicate that, under these precise simulated conditions, the best test are the classical t-test, Alexandersson’s SNHT and SRMD, with almost identical results, followed by the Wilcoxon-Mann-Whitney test, while two phase regression and Durbin-Watson performances are very poor.