Trends in distributional characteristics: Existence of global warming

What type of global warming exists? This study introduces a novel methodology to answer this question, which is the starting point for all issues related to climate change analyses. Global warming is defined as an increasing trend in certain distributional characteristics (moments, quantiles, etc.) of global temperatures, in addition to simply examining the average values. Temperatures are viewed as a functional stochastic process from which we obtain distributional characteristics as time series objects. Here, we present a simple robust trend test and prove that it is able to detect the existence of an unknown trend component (deterministic or stochastic) in these characteristics. Applying this trend test to daily temperatures in Central England (for the period 1772–2017) and to global cross-sectional temperatures (1880–2015), we obtain the same strong conclusions: (i) there is an increasing trend in all distributional characteristics (time series and cross-sectional), and this trend is larger in the lower quantiles than it is in the mean, median, and upper quantiles; (ii) there is a negative trend in the characteristics that measure dispersion (i.e., lower temperatures approach the median faster than higher temperatures do). This type of global warming has more serious consequences than those found by analyzing only the average.