| Summary: | Forgetting some fundamental issues related to climate may have detrimental effects in its research. A first issue that need not be forgotten is the fact that the very notion of climate relies on statistics. For example, according to a popular definition (U.S. Global Change Research Program: Climate Literacy, The Essential Principles of Climate Sciences, 2009), climate is the long-term average of conditions in the atmosphere, ocean, and ice sheets and sea ice described by statistics, such as means and extremes. In turn, long-term average conditions cannot be assessed correctly if inappropriate statistical models and assumptions are used. For example, statistical methods commonly used in climate research are based on the classical statistical paradigm that assumes independence of processes in time, or on the slightly modified model of Markovian dependence. However, substantial evidence has been accumulated from long time series, observed or proxy, that climate is characterized by long-term persistence, also known as long memory or long-range dependence. Such behaviour needs to be described by processes of Hurst-Kolmogorov type, rather than by independent or Markovian processes. Consequently, it should be remembered that the Hurst-Kolmogorov dynamics implies dramatically higher uncertainty of statistical parameters of location and high negative bias of statistical parameters of dispersion. It also implies change at all scales, thus contradicting the misperception of a static climate and making redundant the overly used term “climate change”. The fundamental mathematical properties of Hurst-Kolmogorov processes is another issue that must not be forgotten, in order to avoid incorrect or misleading results about climate.
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