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Evidence of global warming induced from the increasing concentration of greenhouse gases in the atmosphere suggests more frequent warm days and heat waves. The concept of an extreme heat event (EHE), defined locally based on exceedance of a suitable local threshold, enables us to capture the notion of a period of persistent extremely high temperatures. Modeling for extreme heat events is customarily implemented using time series of temperatures collected at a set of locations. Since spatial dependence is anticipated in the occurrence of EHE's, a joint model for the time series, incorporating spatial dependence is needed. Recent work by Schliep et al. (J R Stat Soc Ser A Stat Soc 184(3):1070–1092, 2021) develops a space-time model based on a point-referenced collection of temperature time series that enables the prediction of both the incidence and characteristics of EHE's occurring at any location in a study region. The contribution here is to introduce a formal definition of the notion of the spatial extent of an extreme heat event and then to employ output from the Schliep et al. (J R Stat Soc Ser A Stat Soc 184(3):1070–1092, 2021) modeling work to illustrate the notion. For a specified region and a given day, the definition takes the form of a block average of indicator functions over the region. Our risk assessment examines extents for the Comunidad Autónoma de Aragón in northeastern Spain. We calculate daily, seasonal and decadal averages of the extents for two subregions in this comunidad. We generalize our definition to capture extents of persistence of extreme heat and make comparisons across decades to reveal evidence of increasing extent over time. [ABSTRACT FROM AUTHOR]

The analysis of trends and other non-stationary behaviours at the extremes of a series is an important problem in global warming. This work proposes and compares several statistical tools to analyse that behaviour, using the properties of the occurrence of records in i.i.d. series. The main difficulty of this problem is the scarcity of information in the tails, so it is important to obtain all the possible evidence from the available data. First, different statistics based on upper records are proposed, and the most powerful is selected. Then, using that statistic, several approaches to join the information of four types of records, upper and lower records of forward and backward series, are suggested. It is found that these joint tests are clearly more powerful. The suggested tests are specifically useful in analysing the effect of global warming in the extremes, for example, of daily temperature. They have a high power to detect weak trends and can be widely applied since they are non-parametric. The proposed statistics join the information of M independent series, which is useful given the necessary split of the series to arrange the data. This arrangement solves the usual problems of climate series (seasonality and serial correlation) and provides more series to find evidence. These tools are used to analyse the effect of global warming on the extremes of daily temperature in Madrid. [ABSTRACT FROM AUTHOR]

[Display omitted] • Novel statistical tools used to analyze the occurrence of temperature records. • An overall significant increase in the number of records is observed compared to a stationary climate. • The most affected seasons are summer and winter, with 86% and 75% affected stations. • Deviation started in the early 1970s in winter and late 1980s in summer. • The Levante coast is the most affected and the Cantabrian coast the least. This work analyses the effects of global warming in the upper extremes of daily temperature series over Spain. This objective implies specific analysis, since time evolution of mean temperature is not always parallel to evolution of the extremes. We propose the use of several record tests to study the behavior of the extreme and record-breaking events in different temperature signals, at different time and spatial scales. The underlying idea of the tests is to compare the occurrence of the extreme events in the observed series and the occurrence in a stationary climate. Given that under global warming, an increasing trend, or an increasing variability, can be expected, the alternative is that the probability of the extremes is higher than in a stationary climate. Some of the tests, based on a permutation approach, can be applied to sets of correlated series and this allows the analysis of short periods of time and regional analysis, where series are measured in close days and/or locations. Using these tests, we evaluate and compare the effects of climate change in temperature extreme and record-breaking events using 36 series of daily maximum temperature from 1960 to 2021, all over peninsular Spain. We also compare the behavior in different Spanish regions, in different periods of the year, and in different signals such as the annual maximum temperature. Significant evidences of the effect of an increasing trend in the occurrence of upper extremes are found in most of Spain. The effects are heterogeneous within the year, being autumn the season where the effects are weaker and summer where they are stronger. Concerning the spatial variability, the Mediterranean and the North Atlantic region are the areas where the effects are more and less clear, respectively. [ABSTRACT FROM AUTHOR]

AbstractRecord-breaking temperature events are now very frequently in the news, viewed as evidence of climate change. With this as motivation, we undertake the first substantial spatial modeling investigation of temperature record-breaking across years for any given day within the year. We work with a dataset consisting of over sixty years (1960–2021) of daily maximum temperatures across peninsular Spain. Formal statistical analysis of record-breaking events is an area that has received attention primarily within the probability community, dominated by results for the stationary record-breaking setting with some additional work addressing trends. Such effort is inadequate for analyzing actual record-breaking data. Resulting from novel and detailed exploratory data analysis, we propose rich hierarchical conditional modeling of the indicator events which define record-breaking sequences. After suitable model selection, we discover explicit trend behavior, necessary autoregression, significance of distance to the coast, useful interactions, helpful spatial random effects, and very strong daily random effects. Illustratively, the model estimates that global warming trends have increased the number of records expected in the past decade almost two-fold, 1.93 (1.89,1.98) , but also estimates highly differentiated climate warming rates in space and by season. [ABSTRACT FROM AUTHOR]