Trends in distributional characteristics : Existence of global warming

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Does global warming exist? The answer to this question is the starting point for all the other issues involved in climate change analysis. In this paper, global warming is defined as an increasing trend in certain distributional characteristics (moments, quantiles, etc) of global temperatures, and not only on the average. Temperatures are seen as a functional stochastic process from which we obtain distributional characteristics as time series objects. 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 Central England temperatures (1772-2016) and to Global cross-sectional temperatures (1880-2015), we obtain the same strong conclusions: (i) there is an increasing trend in all the distributional characteristics (time series and cross-sectional) and this trend is larger in the lower quantiles than in the mean, median and upper quantiles; (ii) there is a negative trend in the characteristics measuring dispersion (lower temperatures approach the median faster than the higher ones).The paper concludes by clearly answering the opening question in the afirmative and showing that global-local warming is not only a phenomenon of an increase in the average temperature but also of a larger increase in the lower temperatures producing a decreasing dispersion. This type of warming has more serious consequences than the one found by using only the average.
Climate change, Global-Local warming, Functional stochastic processes, Distributional characteristics, Trends, Quantiles, Temperature distributions
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