Abstract This paper develops a record-based framework for detecting structural changes in climate time series, with a focus on daily air temperature. The approach combines three elements: a linear drift model (LDM) to represent progressive warming with approximately stationary daily variability; the concept of δ records, requiring each new record to exceed the previous maximum record level within a fixed threshold, and filtering out records that have become inflated in the presence of trend; a CUSUM-like statistic, calibrated on a Brownian empirical model, for testing changes in the probability of occurrence of records. Theoretically, the main properties of classical records are recalled, applied to the LDM framework, and a numerical integral for the likelihood of δ -record events is derived. Empirically, we analyzed a series of seasonally adjusted daily temperatures over the period 2000–2025. Removing the annual cycle, the data are well described by a linear warming of about 0. 45\, ^ C 0. 45 ∘ C per decade, with a residual daily variability of about 2\, ^ C 2 ∘ C. The observed numbers of both classical and δ records (with δ equal to one residual standard deviation) are consistent with Monte Carlo performance within the adjusted LDM framework, and the CUSUM bridge statistics remain below the Kolmogorov critical values, indicating that there is no statistically significant breakpoint in record-making. Overall, the results indicate a regime of gradual warming with no detectable structural break in the behavior of extremes and illustrate how record-based utilities may be used for monitoring the non-stationarity of weather extremes.
Hayek et al. (Fri,) studied this question.