The impact of atmospheric blocking on the compounding effect of ozone pollution and temperature: A copula-based approach

Ozone pollution and high temperatures have adverse health impacts that can be amplified by the combined effects of ozone and temperature. Moreover, changes in weather patterns are expected to alter ozone pollution episodes and temperature extremes. In particular, atmospheric blocking is a high-impact large-scale phenomenon at mid-high latitudes that has been associated with temperature extremes. This study examines the impact of atmospheric blocking on the ozone and temperature dependence among measurement stations over Europe. We use a copula-based method to model the dependence between both 5 variables under blocking and non blocking conditions. This approach allows to examine the impact of blocks on the joint probability distribution. Our results showed that blocks lead to an increasing strength in the upper tail dependence of ozone and temperature extremes (>95th) in north-west and central Europe (e.g UK, Benelux, north-west of France and Germany). The analysis of the probability hazard scenarios revealed that blocks generally enhance the probability of compound ozone and temperature events by 20% in a large number of stations over central Europe. The probability of ozone or temperature 10 exceedances increases 30% (on average) under the presence of atmospheric blocking. Furthermore, we found that in a number of stations over north-western Europe atmospheric blocking increases the probability of ozone exceedances by 30% given high temperatures. Our results point out the strong influence of atmospheric blocking on the compounding effect of ozone and temperature events, suggesting that blocks might be considered as a relevant predicting factor when assessing the risks of ozone-heat related health effects. 15

4 days. In addition, the tracking algorithm includes possible merging and splittings of the blocking event in time by adopting a blocking overlap area criterion of 7.5 x -6 km 2 between two consecutive days and a maximum distance between blocking centers of 1000 km (Schuster et al., 2019).
The BI was computed through the Free Evaluation System Framework (see Richling et al. (2015) for more details), specifically with the single plug-in corresponding to the blocking-2d (Freva, 2017).

Joint distribution analysis
Recently, copula-based approaches have become very popular to assess interrelations between several random variables (Ribeiro et al., 2019;Salvadori et al., 2016;Hao et al., 2018). A copula is a joint distribution function in which the marginal distributions are independent from the dependence structure and can be modeled separately (Nelsen, 2006). For two random variables random variables X (temperature) and Y (MDA8O 3 ) with marginal distributions F X (x) = Pr(X ≤ x) and F Y (y) = Pr(Y ≤ y) 105 respectively, a copula function allows to construct their joint cumulative distribution as follows: where C is the copula of the transformed random variables U = F X (X) and V = F Y (Y), with the marginals U and V being uniformly distributed on the interval [0,1]. According to the Sklar's theorem, if the marginal distributions are continuous, then the copula function C is unique (Sklar, 1996). The main advantage of using copula functions is the flexibility to model 110 the dependence between multiple variables with different univariate marginal distributions. For each station we use bivariate copulas to model the dependence between temperature and ozone and estimate their joint probability distribution under two different synoptic situations: 1) with blocking (when BI=1), 2) without the presence of blocking (when BI=0). We fit a total of four copulas commonly used: t-student (from the Archimedean family), Clayton, Gumbel and Joe (from the elliptical family) (  (Akaike, 1974) and the copula parameters were estimated via maximum likelihood estimation (MLE). The copula analyses were carried out with the VineCopula and the copula R packages (Schepsmeier et al., 2016;Hofert et al., 2020).
The copula models were used to assess the relationship between temperature and ozone exceedances under blocking (BI=1) 125 and non blocking (BI=0) conditions by constructing the corresponding joint probability distribution (P(X ≤ x, Y ≤ y)). Apart from the general dependence structure, some copulas can measure the dependence of the extremes through the tail dependence parameter (λ u ) (Nelsen, 2006). As linear or rank dependence measures might not be accurate when focusing on extremes (Hao and Singh, 2016), we have further assessed the upper tail dependence of ozone and temperature extremes derived from the copulas under blocking (BI=1) and non blocking (BI=0). We estimate the probability of a compound event at each station, 130 in which Tmax and MDA8O 3 exceed the 95th percentile of their respective distribution. Note that we define compounds of extremes at each station considering the thresholds over the whole distribution (e.g. including non blocked and blocked days) of ozone and temperature. The use of absolute thresholds allows us to quantify the impact of blocks on the probability of exceedances. The probability of exceedances over a certain multivariate threshold was examined based on three different hazard scenarios described by the following joint and conditional joint probabilities, which can be expressed using copula 135 notation (see further details in Serinaldi (2015)): The probabilities in equations 2 and 3 have been widely applied in the literature to assess compounds of extremes (Zscheis-140 chler and Seneviratne, 2017;Hao et al., 2018). Equation 2 represents the scenario in which both variables temperature (Tmax) and ozone (MDA8O 3 ) exceed the 95th percentile, while equation 3 consider the events occurred when either temperature or ozone or both exceed their respective threshold (95th). As blocks normally lead to persistent positive surface temperature anomalies during summer over Europe (Pfahl and Wernli., 2012), it is of interest to evaluate the influence of blocking on the probability of ozone exceedances given high temperatures, which is assessed in the CON D scenario.

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To quantify the significant impact of blocks on the compound ozone and temperature events, we estimated the differences between the probabilities derived from the copulas (i.e ∆P =P 1 -P 0 ). Then, we assess whether the difference between the probabilities when BI=1 and BI=0 are significantly different from zero. To do so, we apply a bootstrap procedure for each probability scenario (i.e. AN D, OR, CON D) in which we drew 100 bootstrapped samples and derived the respective probabilities P 1 and P 0 when BI=1 and BI=0, respectively. For the null hypothesis (H 0 ) there is no difference between the probabilities obtained 150 from the cases BI=1 and BI=0, while the alternative hypothesis indicates that the probability of an extreme event conditioned to a blocking situation is significantly different from the probability under non blocking conditions.

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To investigate the impact of blocks on the relationship between MDA8O 3 and Tmax, the Kendall's tau coefficient (τ ) was calculated during blocking and non blocking days (Fig.3).  by not significant and weaker correlations that show similar magnitude values when BI=1 and BI=0. Ordóñez et al. (2017) analysed the impact of subtropical ridges on ozone, and they found a major impact of subtropical ridges in the central-south European sectors. Nevertheless, they pointed out that influence of ridges for the build-up of ozone pollution is not as clear as in the case of blocks and its impact is more sensitive to the location. Blocks play an important role in warm temperature anomalies in spring and summer over central Europe, while the impact is generally lower over south, mostly due to the position 200 of the block (Sousa et al., 2018). Consistent with our results that show a weaker relationship between MDA8O 3 and Tmax, we can anticipate significant spatial differences in the impact of blocks on the compounds of extremes of ozone and temperature and their joint distribution.

Copula results
Among the different types of copulas presented in the literature, a total of four copulas (table 1) were tested to find the most 205 appropriate fit that characterises the relationship between MDA8O 3 and Tmax at each station. Our copula choice was mainly motivated by their ability to represent joint tail dependence (upper and/or lower). After modelling the dependence between both variables when BI=1 and BI=0 separately, we quantify the effect of atmospheric blocking on compound extremes of ozone and temperature through the differences between probabilities derived from the cases mentioned above (BI=1 and BI=0) for each probability scenario. The impact of blocks on the joint behaviour between MDA8O 3 and Tmax is reflected in the 210 selected copula (Fig S4). When BI=0 a large number of stations are characterized by an asymmetric dependence structure as it is the case of Joe and Gumbel copulas. The Gumbel copula is also selected in a number of stations when BI=1, but in this case the t copula is representative for a major number of stations. On the contrary than the Gumbel and Joe copulas, the t copula belongs to the Elliptical and radially symmetric copulas, but capturing dependence in the extremes in both lower and upper tail et al., 2017), our results show the increasing probability of temperature OR ozone pollution extremes under atmospheric blocking.
From a risk assessment perspective, the scenario CON D is also of interest, as it quantifies the impacts of blocks of ozone 255 pollution extremes events conditioned on high temperature. For the CON D probability, both the computation domain and the critical region evolve when moving along higher temperatures and then, the probability is computed over a reduced subset (e.g. conditioned on temperature extremes) (see Serinaldi (2016) for further details and Fig. S5). As illustrated in Fig In particular, blocks lead to an increasing probability of ozone extremes given high temperatures in the UK (>40%). In a few number of stations over south and north-eastern of Europe, blocks did not show a significant influence in the conditional probability of extremes, with low and non significant values of ∆P . For some of these stations the copula selected when BI=1 is the Clayton copula (Fig. S1), which indicates greater probability of joint extreme low values (lower tail dependence), but 265 not in the upper tail as shown in Fig. 5 (e and f). In such cases, the presence of blocks is not relevant for ozone pollution exceedances that seem to occur independently of temperature extremes. The present study has assessed the influence of atmospheric blocking on the dependence between maximum daily average of 8h ozone (MDA8O 3 ) and daily maximum temperature (Tmax) for the period 1999-2015 during the ozone season (April-270 September). A total of 300 monitoring stations distributed over Europe were included. First, we examined the blocking influence on single extremes events of ozone pollution and temperature, defined on the basis of the 95th percentile of their distribution. Using a copula-based approach, we evaluated the impacts of blocks on compound ozone pollution and temperature events taking into account their dependence. For each station, the dependence between ozone and temperature was modelled independently under blocking (BI=1) and non blocking (BI=0) conditions. The selected copulas described the dependence structure 275 and the joint behaviour of ozone and temperature. We investigated the impacts of blocks on the risks of compound ozone and temperature events under three different hazard scenarios of probability: AN D, OR and CON D, which are commonly used to study multivariate events.
In agreement with previous studies, our results showed that during the ozone season more than 40% of ozone exceedances (>95th) are coincident with blocked days over the central stations (including Germany, east of France and Benelux). The 280 rest of the stations showed a lower frequency (∼ 25%) of ozone exceedances during blocking conditions. The frequency of temperature extremes is larger than ozone extremes under blocking conditions and on average 55% of hot days occur under blocking conditions. The highest frequency is observed in the northern Europe (Scandinavia) with more than the 70% of temperature-blocked extremes, while the lowest frequency is observed in the southern Europe, witch is consistent with the literature (Brunner et al., 2018;Sousa et al., 2018). The analysis of the dependence between ozone and temperature revealed 285 that atmospheric blocking is a key importance in some regions that showed a strong relationship between ozone and temperature under blocking conditions (e.g. central and eastern Europe). In particular, we found a great impact over the stations in the UK and Benelux where the blocks lead to positive and higher correlation values, while a weaker relationship is observed under non blocking conditions. The copula-based approach confirms the dependence between ozone and temperature under the influence of atmospheric blocking. Moreover, the copulas showed that blocks have a major effect on the upper tail dependence in some 290 stations over the UK, north-west and west of France, Benelux and north of Germany, which suggests that compound ozone and temperature extremes are highly associated and influenced by atmospheric blocking.
Overall, we found that blocks enhanced the probability of occurrence of compound ozone and temperature extremes in a large number of stations included in this study. Our results showed that blocking significantly increased by ∼ 15%-20% (i.e. ∆P > 0.15) the probability of co-occurrent ozone and temperature exceedances the stations over central, north-west and east 295 of Europe. In fact, the probability of combined ozone and temperature extremes under non blocking conditions is rather small everywhere (P 0 < 0.025). Blocks significantly increase the probability that either ozone or temperature (or both) exceed the 95th percentile. The highest probability values are observed over central and eastward stations in which blocking increase the probability of extremes events ozone or temperature more than 35%. The analysis of the join distribution considering the conditional hazard scenario (CON D) showed a smaller impact of blocks in some stations where the probability of ozone 300 pollution extremes conditioned on high temperature did not show significant differences in terms of magnitude under non