On the multiple breakpoint problem and the number of significant breaks in homogenization of climate records

Changes in instrumentation and relocations of climate stations may insert inhomogeneities into meteorological time series, dividing them into homogeneous subperiods interrupted by sudden breaks. Such inhomogeneities can be distinguished from true variability by considering the differences compared to neighboring stations. The most probable positions for a given number of break points are optimally determined by using a multiple-break point approach. In this study the maximum external variance between the segment averages is used as decision criterion and dynamic programming as optimization method. Even in time series without breaks, the external variance is growing with any additionally assumed break, so that a stop criterion is needed. This is studied by using the characteristics of a random time series. The external variance is shown to be beta-distributed, so that the maximum is found by solving the incomplete beta function. In this way, an analytical function for the maximum external variance is derived. In its differential form our solution shows much formal similarities to the penalty function used in Caussinus and Mestre (2004), but differs numerically and exhibits more details.

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