It has been shown by others that in the future, extreme temperature events are likely to become more frequent, attain higher peak temperatures and last longer. Furthermore, there are likely to be more extreme weather events lasting for several days or weeks per season. One such event, a hot spell, is defined as a sequence of days/nights with maximum/minimum temperatures above a certain threshold. The duration and severity of hot spells, such as the Russian heat wave of 2010, are often attributed to persistent atmospheric circulation patterns such as blocking events. Quasiperiodic climate patterns such as the El Niņo-Southern Oscillation (ENSO) and the North Atlantic Oscillation (NAO) are also known to influence global weather patterns and to cause or aggravate persistent hot spells.

This study employs Extreme Value Analysis (EVA), in particular an peak-over-threshold approach, to investigate the frequency and intensity of extremely high temperature events over Europe, for the period of 1951-2010, and their relationship with blocking events, the NAO and ENSO. Furthermore, we investigate the two aforementioned events: summers of 2003 and 2010 to establish their dependence on the different atmospheric patterns. We use the ERA-Interim reanalysis data to analyze the circulation patterns leading up to the events and, through the application of covariates in the EVA, associate their existence with blocking events, the NAO and ENSO.

The frequency and magnitude of extreme temperature events can be modeled as a marked point process. That is, if the occurrence of a hot day exceeding a defined threshold, u, is modeled as a point in time, X, the expected waiting time until the next non-overlapping event is distributed randomly in time and independent of previous events, i.e. a non-homogenous process set (0,1) following a Poisson distribution P(X ≥ u) ~ Pois (λ) . Considering the magnitudes of these excesses as a series of marks, the intensity of the events can be modeled as a Generalized Pareto Distribution (GPD), which shares the same properties as a Poisson process. The GPD has three parameters: scale, shape and location. If these excesses are independent and identically distributed GPD random variables, then the excesses also follow a Generalized Extreme Value (GEV) distribution. It, therefore, follows that a marked point process can be adopted by determining parameters for both distributions (Poisson and GPD) from Maximum Likelihood Estimates (MLEs) of the GEV parameters. It should be noted that the Poisson process is a poor model for instances where natural clustering is present, as is the case with hot spells which contain several dependent points exceeding a threshold. In these instances the simplest solution is to decluster the data using some arbitrary definition of cluster separation; alternatively, the dependency between the events can be conditioned on the first exceedance in a sequence. We have adopted a cluster separator of 1 day falling below the threshold, to determine the occurrence rate of excesses over time, then fitted the point process on the maximum of each cluster.

The point process models only the frequency of events and their magnitude but does not describe the duration of the hot spells. Therefore, to construct a more complete characterization of hot spells, components for the dependence between excesses within each spell and the duration of the spell have to be defined. We apply a Generalized Linear Model to estimate the duration of hot spells with successive days in a spell modeled as a GPD conditional upon the previous day's excess to characterize dependence of excesses within a spell.

To investigate the influence of a time varying signal (i.e. blocking) on the occurrence of extreme temperatures, we introduce a non-stationary model as a covariate in the location and log-transformed scale parameters of the distributions. Improvements to the model obtained by introducing covariates are examined using the deviance statistic wherein the difference in negative log-likelihood values between two models is tested for significance against the Chi-squared distribution.

A preliminary analysis on summertime (JJA) temperature records of 5 stations representing different climate regions in Europe, applying a point process to the daily maximum temperature excesses over the 95th percentile was carried out. For comparison, all time series were limited to the same reliable blended record available on ECA&D (1951-2010). We used three covariates; a simple blocking frequency, a NAO and an ENSO index. With the NAO index as a covariate, a statistically significant impact was found at stations in East and Central Europe; while the ENSO index demonstrated a statistically significant impact at stations in North Europe. The blocking index used in the preliminary phase was based on a three-dimensional potential vorticity (PV) field over the North Atlantic, which has been shown to be significant in relation to minimum winter temperatures. However our preliminary results were not statistically significant for the summer maximum temperatures. We now employ a more highly defined blocking index based on the 500 hPa geopotential height (Z500), shown to be effective in describing hot spell events in Europe by other research. Our analysis is carried out at a number of stations throughout Europe to capture the effects of different atmospheric patterns (blocking, NAO and ENSO) on countries neighboring both the Atlantic Ocean and the Mediterranean Sea (East Europe), and the North Sea (North Europe).

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