The reduced rate of observed warming since the El Niño event in the year 1998 has provoked two main questions: what are the causes of the so called “pause”, “hiatus” or simply “slowdown” (see e.g. “Hiatus in Context” 2014), and how long may it last. The answers to the first question are legion. They include unpredicted reductions in the radiative forcing and various features of natural internal climate variability. If the answer includes a mode of climate variability it may allow making projections of reasonably expected lengths of a “pause”, e.g. it may last another decade (Chen and Tung 2014). The potential duration of the “hiatus” is also of interest as it may subsequently require a rethinking of our means of climate research and of our understanding of the climate system.

The observation based global mean temperature record allows a simple guesstimate of the potential length of the “hiatus”. More specifically, one can use the observational global mean temperature datasets, e.g., the median of the HadCRUT4.3 data (Morice et al. 2012, version accessed January 6, 2015), to estimate how long periods of zero trends may become under assumed and fixed linear trend magnitudes, e.g., 0.17K per decade. The following analyses base on the residuals from a cubic trend fit to the HadCRUT4.3 data. These residuals can be described by an autoregressive process of fourth order.

In a first step, I add a linear trend of 0.17K per decade to the residuals and then calculate trends over windows of one to thirty years on this index. The Figure shows on the right a boxplot of these trends for individual windows. The red line adds the 5 percentile. Horizontal grey lines mark trends of -0.08K and 0K per decade. The zero trend lines falls below the 5 percentile after 18 years and the negative trend already after 12 years. The left panel of the Figure shows the HadCRUT4.3 data, the residuals and the residuals plus the linear trend.

The above mentioned AR(4) fit allows to simulate an ensemble of 1000 equivalent indices and to repeat the analyses which provides a 90 percent interval for the 5 percentile of the analysis (shown as blue lines in the Figure). The interval allows for a 20 year period of trends of -0.08K and 25 years of no trend.

There are a number of things to discuss here. For one, the analysis uses only one of a number of available temperature indices, but the AR-processes may account for this to some extent. Similarly the AR-ensemble may compensate for not using the full HadCRUT4.3 ensemble. More importantly, by using the HadCRUT4.3 data until 2014, the analysis includes already information about the “slow-down” period. However, considering only the data until the late 1990s does not change the results. The choice of 0.17K per decade is motivated by the recent 25-year trend of 0.177K per decade given by Tung and Zhou (Tung and Zhou 2013).

The presented analyses ignore any hypotheses about potential physical causes of the slow-down and it makes simplifying assumptions about the underlying trend-structure and the time-series properties of the global mean temperature index. However, the residuals from a simple smooth trend line should incorporate any potential signals besides the idealised trend, i.e. natural internal climate modes (e.g., AMO, PDO, ENSO), more strongly varying anthropogenic agents (e.g., aerosols) and naturally induced variations in the radiation forcing (e.g., volcanic or solar activity).

Under the made assumptions, it seems possible that there is a reasonable chance that, under an average 0.17K warming trend per decade, we may witness a 25 year period of no trend. Indeed, there may even be a period of 20 years with a cooling trend of -0.08K.

# References

Chen, Xianyao, and Ka-Kit Tung. 2014. “Varying Planetary Heat Sink Led to Global-Warming Slowdown and Acceleration.” *Science* 345 (6199), 897–903. doi:10.1126/science.1254937. http://dx.doi.org/10.1126/science.1254937.

“Hiatus in Context.” 2014. *Nature Geosci* 7 (3), 157. doi:http://dx.doi.org/10.1038/ngeo2116. http://dx.doi.org/10.1038/ngeo2116.

Morice, Colin P., John J. Kennedy, Nick A. Rayner, and Phil D. Jones. 2012. Quantifying Uncertainties in Global and Regional Temperature Change Using an Ensemble of Observational Estimates: The HadCRUT4 Data Set. *Journal of Geophysical Research* 117 (D8): D08101+. doi:10.1029/2011jd017187. http://dx.doi.org/10.1029/2011jd017187.

Tung, Ka-Kit, and Jiansong Zhou. 2013. “Using Data to Attribute Episodes of Warming and Cooling in Instrumental Records.” *Proceedings of the National Academy of Sciences* 110 (6), 2058–63. doi:10.1073/pnas.1212471110. http://dx.doi.org/10.1073/pnas.1212471110.

[ a pdf-version of this text is available at http://dx.doi.org/10.6084/m9.figshare.1285023 ]