Evaluation of the Stepwise Correction Module Used in the Pairwise Homogenisation Algorithm

Abstract

Several benchmarking studies of homogenisation algorithms exist, aiming at the skill of the algorithms as a whole. However, the algorithms consist of different combinations of basic statistical tools. A specific investigation of these techniques can reveal which of them are crucial for the performance. In the past, most effort was put into the detection part, where the positions of the breakpoints are determined. In this paper, the correction part is in focus, where the jump heights are finally calculated and eliminated. We concentrate on the performance of the step-wise correction module used in the Pairwise Homogenisation Algorithm (PHA). Assuming perfect detection, a generic prototype of the module is applied to simulated data. As a skill measure, we use the correct determination of the network-mean trend induced by the breaks. We show that large scatter occurs due to an amplification of the noise, just because the correction is carried out step by step. The mutual use of all stations within a network leads to dependent corrections for the individual stations so that the error variance of the overall correction remains high. A simple but effective technique is presented to increase the performance of stepwise correction. The proposed stepwise method provides largely similar results as the ANOVA method. Both eliminate a possible trend bias induced by the breaks almost entirely, but also add large scatter to the corrected trends. In case that the original data contain no trend bias so that the bias correction does not apply, the data may be even worsened by the homogenisation, if the time series contain six or more breaks.