Abstract
The increasing trend curve of global surface temperature against time since the 19th century is the icon for the considerable influence humans have on the climate since the industrialization. The discourse about the curve has spread from climate science to the public and political arenas in the 1990s and may be characterized by terms such as “hockey stick” or “global warming hiatus”. Despite its discussion in the public and the searches for the impact of the warming in climate science, it is statistical science that puts numbers to the warming. Statistics has developed methods to quantify the warming trend and detect change points. Statistics serves to place error bars and other measures of uncertainty to the estimated trend parameters. Uncertainties are ubiquitous in all natural and life sciences, and error bars are an indispensable guide for the interpretation of any estimated curve—to assess, for example, whether global temperature really made a pause after the year 1998.Statistical trend estimation methods are well developed and include not only linear curves, but also change-points, accelerated increases, other nonlinear behavior, and nonparametric descriptions. State-of-the-art, computing-intensive simulation algorithms take into account the peculiar aspects of climate data, namely non-Gaussian distributional shape and autocorrelation. The reliability of such computer age statistical methods has been testified by Monte Carlo simulation methods using artificial data.The application of the state-of-the-art statistical methods to the GISTEMP time series of global surface temperature reveals an accelerated warming since the year 1974. It shows that a relative peak in warming for the years around World War II may not be a real feature but a product of inferior data quality for that time interval. Statistics also reveals that there is no basis to infer a global warming hiatus after the year 1998. The post-1998 hiatus only seems to exist, hidden behind large error bars, when considering data up to the year 2013. If the fit interval is extended to the year 2017, there is no significant hiatus. The researcher has the power to select the fit interval, which allows her or him to suppress certain fit solutions and favor other solutions. Power necessitates responsibility. The recommendation therefore is that interval selection should be objective and oriented on general principles. The application of statistical methods to data has also a moral aspect.
Highlights
A univariate time series is a sample of data values in dependence on time, where for each element of a set of time points, t(i), there exists one corresponding data point, x(i)
Some development may come in the form of Generalized least-squares (GLS) estimation techniques for nonlinear regression functions (Fig. 5), such as the break or the ramp models
The fitting of multiple change-point models is of genuine interest. This is technically challenging and likely necessitates the implementation of advanced optimization techniques, such as genetic algorithms (Michalewicz and Fogel, 2000). The reward of such a technology may consist in a reduction of the problem of fit-interval selection
Summary
A univariate time series is a sample of data values in dependence on time, where for each element of a set of time points, t(i), there exists one corresponding data point, x(i). The methods presented in this review can be applied to evenly and unevenly spaced time series. The target of the learning procedure considered in this article is the trend, which is, loosely speaking, the long-term systematic change of the mean value over time. Statistical science has developed methods for trend estimation and uncertainty determination, which support climate science. This review explains those statistical methods in detail and at a level that is accessible to nonexperts. The explained methods can be applied to any type of climate time series, from the deep past
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