The uncertainty of break positions detected by homogenization algorithms in climate records

Abstract

Long instrumental climate records suffer from inhomogeneities due to, e.g. relocations of the stations or changes in instrumentation, which may introduce sudden jumps into the time series. These inhomogeneities may mask or strengthen true trends. Relative homogenization algorithms use the difference time series of a candidate station with neighboring stations to identify such breaks (changepoints). Modern multiple breakpoint methods search for the optimum segmentation, which is characterized by minimum internal variance within the segments and maximum external variance between the segment means.We analyse the accuracy of these homogenization methods and concentrate on the uncertainty in the position of the break. Due to unavoidable random noise in the difference time series, the segmentation method may find a shifted break position, which attains a higher external variance than the true one. Different lengths of potentially exchanged subsegments are considered; that one providing the largest external variance will be chosen as possibly erroneous optimum. We will show that the variances of shifted segmentations can be approximated by a Brownian motion with drift, where the signal-to-noise ratio (SNR) defines the drift size.Available formulae for one-sided and continuous Brownian motion with drift are expanded to two-sided and discrete processes as they occur in praxis. The error probability increases strongly for SNRs lower than 1. Thus, when the internal variance is larger than the variance introduced by the breaks, the probability of finding the right break position is small.

The joint influence of break and noise variance on the break detection capability in time series homogenization

“…As mentioned above, we focus in this study on the break detection of such modern multiple breakpoint methods (Caussinus and Mestre, 2004;Hawkins, 2001;Lu et al, 2010;Picard et al, 2005Picard et al, , 2011. While Lindau and Venema (2016) concentrated on the errors in the positions of the breaks, here we analyze the deviation of the estimated inhomogeneity signal from the true one.…”

“…While Lindau and Venema (2016) concentrated on the errors in the positions of the breaks, here we analyze the deviation of the estimated inhomogeneity signal from the true one. We consider the difference time series between two neighboring stations as raw information consisting of two components: the break and the noise series.…”

On the reduction of trend errors by the ANOVA joint correction scheme used in homogenization of climate station records

“…Uncertainties occurring during the detection part are discussed in Lindau and Venema (2016). For this purpose, differences with neighbouring station are considered.…”

Detecting breakpoints in artificially modified- and real-life time series using three state-of-the-art methods

“…In the case of climatic time series, since instrumental meteorological recordings began [26] it has always been a problem to determine if a conspicuous change occurring in the data is just an artefact, or an actual breakpoint [27]. Thus, numerous studies exist dealing with climate conditions -regardless whether the subjects of the analysis are instrumental [28] or proxy data -where, e.g.…”

“…The fact that BPs can be triggered by non-climate factors (e.g. instrument exposure, land use, location changes) has also been studied [27,30,31,31].…”