(a) Dependence of overall minimum of the test statistic on the time scale of aggregation, shown over different time periods (coloured dots and lines) for the reanalysis time series. Dashed lines show statistical fits of a linear model in log-log space to each period and its extrapolation to sub-daily time scales. The different time scales of aggregation are obtained by successively aggregating the daily test statistics to longer time scales. The CMIP5 1870-1950 distribution of the daily test statistic is shown for comparison. (b) The year of emergence (that is ‘detection’ at any time) of global climate as a function of time scale. The figure is derived by finding, for each time scale and backwards in time from 2018, the first year in which any point does not exceed the 97.5th percentile of the CMIP5 1870-1950 reference distribution of the daily test statistic from (a). Over the last 20 years, climate change would have been detectable in any individual 365-day period, whereas over the last 10 years any 180-day period was detectable in reanalyses and observations. Over the last seven years, detection was possible for any individual day, and would have likely been possible even for shorter time periods. Detection in the experimental daily observational dataset (OISST+BEST) occurs slightly earlier than in daily reanalyses.