Assessing internal changes in the future structure of Dry-Hot compound events. The case of the Pyrenees

. Impacts upon vulnerable areas such as mountain ranges may become greater under a future scenario of adverse climatic conditions. In this sense, the concurrence of long dry spells and extremely hot temperatures can induce environmental risks such as wildfires, crop yield losses or other problems, the consequences of which could be much more serious than if these events were to occur separately in time (e.g. only long dry spells). The present study attempts to address recent and future changes in the following dimensions: duration (D), magnitude (M) and extreme magnitude (EM) of 10 compound Dry-Hot events in the Pyrenees. The analysis focuses upon changes in the extremely long dry spells and extremely high temperatures that occur within these dry periods, in order to estimate whether the internal structure of the compound event underwent a change in the observed period (1981-2015) and whether it will change in the future (2011-2100) under intermediate (RCP4.5) and high (RCP8.5) emission scenarios. To this end, we quantified the changes in the temporal trends of such events, as well as changes in the bivariate probability density functions for the main Pyrenean 15 regions. The results showed that to date the risk of the compound event has increased by only one dimension –magnitude (including extreme magnitude) – during the last few decades. In relation to the future, increased in risk was found to be associated with an increase both in the magnitude and the duration (extremely long dry spells) of the compound event, mainly in the eastern and southern regions of the Pyrenees.


Regionalization
The Pyrenees constitute a mountainous system presenting high climatic variability, which can be summarized quite easily in order to explain the major part of the compound behavior of Dry-Hot events. In this sense, the authors consider that many regions are of no particular interest for the present analysis, because situations of long dry spells and extremely hot temperatures, for instance, display a practically identical synoptic behavior pattern throughout the region. For example, a 100 subtropical ridge produces a dry environment and above-average temperatures throughout the Pyrenees (Lemus-Canovas et al., 2019a). This does not occur when spatial patterns of precipitation are investigated, because spatial variability is much greater. Interestingly, with northern advection in this area, precipitation can be abundant on the Atlantic and northern slopes, but scarce or non-existent on the southern slopes (Lemus-Canovas et al., 2018). This variability therefore differs depending on the variables analyzed. 105 The use of clustering techniques is very common in the creation of regions of climate variables. For example, Carvalho et al., (2016) regionalized temperature and precipitation in Europe; Carro-Calvo et al., (2017) performed similar tasks for tropospheric ozone; and more recently, Lemus-Canovas et al., (2019b) employed these techniques by combining precipitation with circulation types to establish rainfall regions in the Alps. In the present paper we conducted a combined regionalization of temperature and precipitation, (as both variables constitute the basis of Dry-Hot events) by applying the k-110 means algorithm to the daily series of temperature and rainfall (normalized) of spring and summer. In order to obtain a robust regionalization, a maximum of 100 iterations was established. To decide the optimal number of clusters, we https://doi.org/10.5194/nhess-2021-5 Preprint. Discussion started: 14 January 2021 c Author(s) 2021. CC BY 4.0 License.
performed an iteration from k = 2 to k=15, obtaining 14 different classifications (see Fig. S1 in the Supplement). Total variance can be explained by the increase in k clusters, as shown in the Scree test (Cattell, 1966) in Fig. S2. Such a representation shows two points,k = 5 (40%) and k = 8 (48%)which could be considered as a "slope change", and 115 therefore possible delimiters of the number of regions. Despite the use of the Scree test, the decision is subjective, and a compromise is therefore needed between the degree of complexity and the descriptive capacity of the regionalization (Carro-Calvo et al., 2017). Consequently, we decided to use 8 clusters, which explain 48% of the variance (Fig. S2).

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For the construction of the regionalized series, the daily values of all cells were averaged in order to work with a series that is smoother than if the centroids were used. The main reason for working with averaged regional series was to avoid the downscaling process in the application of the bias correction method. Thus, inflation and modification of the trend represented by the climate model (Maraun 2013) were avoided, among other undesirable effects. This and other aspects 130 relating to the application of the bias correction are explained in section 2.4. https://doi.org/10.5194/nhess-2021-5 Preprint. Discussion started: 14 January 2021 c Author(s) 2021. CC BY 4.0 License.

Event definition
As previously stated, the Dry-Hot events are characterized by means of the following dimensions: duration (D), magnitude (M) and extreme magnitude (EM), corresponding to the spring months: March, April and May (MAM); and to the summer months: June, July and August (JJA); both seasons are analyzed independently. D is defined as the number of consecutive 135 days on which precipitation is below 1 mm (Fig. 2). This threshold was chosen to be consistent with previous studies (Orlowsky and Seneviratne 2012;Donat et al., 2013;Lehtonen et al., 2014;Manning et al., 2019), as well as to avoid the drizzle effect, which systematically causes climate models to overestimate precipitation (Gutowski et al., 2003).
To ensure that independent and extreme spells were obtained, those with a duration greater than the 90th percentile were selected annually. Additionally, M was defined as the maximum temperature values (Tx) observed during the period in 140 which D occurred, while EM differs from M on providing Tx values greater than the 90th percentile. A schematic summary of the variables studied is presented in Figure 2.

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Analyzing the EM subset enables us to characterize the greater risk of the simultaneous occurrence of both variables: D and EM, which in turn may significantly increase the risk of wildfires, for example. To estimate the trend of the events and to assess the statistical significance of these trends we employed Sen's slope (Sen, 1968) and Mann-Kendall's non-parametric test (Mann, 1945).

Bias correction and evaluation 150
Bias correction techniques are commonly used to correct the data simulated by the RCM by means of the observed data; among these techniques, the most popular and widely used is Quantile Mapping (QM). Bias correction by QM is frequently used to downscale simulations at the station level or in high-resolution grid boxes; however, it induces inflation problems in the corrected series (Maraun, 2013) and is unable to generate daily subgrid variability (Maraun et al., 2017). The above mentioned issues tend to be exacerbated in mountain areas, where many local processes may not be represented following 155 the QM process ).
In the present study 1) we aggregated all observed data computed from D, M and EM at each regional level (Fig. 3), calculating the mean of such variables from the grid cells belonging to each of the regions of the study area; 2) we extracted the time series from the cell closest to the centroid of each region for each RCM (table 1); 3) we applied the Empirical QM method (EQM), which estimates the values of the empirical cumulative distribution function (CDF) of the observed and 160 modelled time series for each quantile (Gudmundsson et al., 2012) of the variables D, M and EM.
The bias correction was evaluated by means of a 5-fold cross validation of 7 years (4 folds for adjustment and 1-fold for validation). Cross-validation should not be applied on validating free-running climate simulations against observed series, as the climate models are temporarily stochastic and could induce severe errors in the assessment process of the daily series . However, herein we work with annually aggregated data of the variables, D, M and EM (see 165 section 2.3), where the RCM is expected to be able to reflect the seasonality component and trend.
The evaluation of the EQM -which is not intended to focus on the individual performance of each model, but rather on the overall result -is based on estimating the bias both in magnitude and in trend. It is assumed that once the EQM is applied, the bias in the trend of the respective variables (D, M and EM) should be lower between the bias-corrected data and the raw RCM, than between the observed data and the bias-corrected data because, as described below, it is the RCM that is capable 170 of modelling the future trend based on the drivers of future climate.
To estimate the bias in the trend, the decadal trend was computed by means of Sen's slope. Furthermore, we also estimated the bias in the variability between the observed data and the bias-corrected data by means of the coefficient of variation The procedure discussed in this section, which involves applying the regional average of observations, is intended to avoid, 175 among other problems, modification of the trend by the EQM (Cannon et al., 2015), which should be more similar to the trend projected by the RCMs than to the observed data, because the future climate will be driven by factors other than the current ones, which are measured by the RCMs.

Characterization of the variables underlying the compound event and of the role they play in potential risks
Extremely long dry spells (D) have a main north-south pattern in which the northernmost areas present extreme D values of 180 fewer than 20 days in spring and summer, and the southernmost areas provide values that can exceed 70 days, mainly in https://doi.org/10.5194/nhess-2021-5 Preprint. Discussion started: 14 January 2021 c Author(s) 2021. CC BY 4.0 License. summer (Fig. 3). A second spatial pattern enabled the Atlantic and Mediterranean coastal areas to be differentiated. The former area presented the lowest number of extreme spells throughout the study area in spring and summer. On the other hand, the Mediterranean area showed a very high number of extreme dry spells, especially in summer, when these lasted on average up to 90 days. These spatial patterns showed that, despite the small size of the study area, the D patterns are very 185 diverse. However, the present paper did not only focus upon variable Dwe also examined the combination of this variable and extremely long dry periods. In this sense, it is important to emphasize the difference between analyzing only the Tx values of 190 the days comprising D, which we called M, and analyzing the Tx values >90th percentile (EM). This difference is illustrated in the Tx anomalies of both periods (Fig. 4).

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Such anomalies are clearly more positive on examining the EM variable with respect to M. This indicated that the average magnitude of days with extreme temperature within extreme dry spells was, in some cases, more than 10 times greater than the average thermal magnitude of all days contained in the dry spell. In addition, we observed a clearly opposite spatial pattern to that in Fig.4, in which the most extreme positive anomalies were reached in the areas exhibiting the lowest number of extreme dry spells (Fig. 3). This was mainly due to the fact that in these areas the number of days with precipitation (and 200 therefore with a moderate Tx) is very high by default (Lemus-Canovas et al., 2019a). Consequently, although the spells are short, they give rise to an extremely positive thermal anomaly, mainly on the hottest days of the spell (See EM for Summer in Fig. 4). In contrast, in the south of the Pyrenees, most days present hardly any precipitation, especially in summer, and dry spells and a positive thermal anomaly are therefore not synonymous (see M for summer in Fig. 4). A similar explanation can be found in the seasonal differences: summer is the dry season in most of the study area, which usually presents high thermal 205 values and no precipitation; consequently, thermal anomalies of M and EM are generally lower than those observed in spring.
Before analyzing the future projection of the variables D, M and EM, we reviewed the observed trends of such variables for each region and season. In the case of D (Fig. 5a), a non-significant trend was observed (p-value ≤ 0.05) at the 95% confidence level. A high intrannual variability of the duration of extreme dry spells was detected.
This did not occur on assessing the EM and M trends (Fig. 5c,b, respectively), as both variables displayed a tendency to increase. This trend presented a higher slope in the spring and in the case of the EM. Indeed, the annual values of EM for spring and summer were almost all positive, whilst this was not the case on evaluating only M. At an intra-regional level, the main differences were observed in summer for EM, when the Mediterranean regions NMED and SMED accounted for a higher slope than the other regions. On the contrary, in spring growth was practically the same for all regions for EM and M.

Assessing the reliability of the bias-corrected projections
We evaluated the EQM in order to estimate the bias in D, EM and M (Fig. 6), as well as the bias in trend (Fig. 7), assuming 225 that this should be lower between the raw RCM and the bias-corrected data of the RCM, than between the observed data and bias-corrected data of the RCM. We also estimated the bias in the variability between the observed data and the biascorrected data (Fig. S3). As in the case of Rajczak et al. (2016), the results showed that the EQM was capable of adjusting the mean bias of the variable D, although it showed a high spread. RCMs tend to overestimate wet days, and in the opposite case, they greatly underestimate the dry days, an issue that can be resolved by EQM (Fig.6). The bias of the variables M and EM was also satisfactorily corrected, with a low degree of deviation. The results of the bias in magnitude was satisfactory in all regions. 235 Analysis of the bias in the trend also provided satisfactory results (Fig. 7). For all variables, in particular EM and M, the bias was clearly lower between the BC RCM and the raw RCM, which indicated that the trend of the RCM was respected on applying the EQM. In the case of D, the bias was higher and more variable in all models. However, we also observed a decrease in the bias between the BC RCM and the raw RCM in relation to the BC and the observed data.  Finally, and in accordance with the results shown above, evaluation of the bias in the variability (Fig. S3) revealed that this 245 was higher in D than in EM or M.

future changes in the magnitude of intervention of the variables underlying the compound event
The regional projections showed an increase in the duration of D events (Fig. 8a); these were only abundant in the case of the scenario of high greenhouse emissions (RCP8.5) and were consistent across all regions. However, the scenario projected by the RCP4.5 contrasts greatly with the previous one. In a moderate scenario, no region, with the exception of the 250 continental regions WCONT and ECONT, showed any statistical significance in the duration of D events during spring. In summer, and under this same scenario, there was a statistically significant trend towards an increase in D events, but with a much flatter slope, especially in the HIPY and SMED regions. In the case of the hot extremes (EM), the previously detected increase was evident under both scenarios (Fig. 8b). However, 260 special attention should be paid to the greater increase in EM in relation to M (Fig. 9). Moreover, the rate of warming during the hot extremes was variable albeit more consistent in a high-emission scenario (RCP8.5) (Fig. 9). Interestingly, under this scenario and during the spring, the EM trend was above M throughout the study area, with particular incidence in the CANT and WATL regions. In summer, the increase in EM was greater than that in M in the Mediterranean regions, especially in NMED, as well as along most of the northern slope of the Pyrenees (EATL and 265 WATL). In the intermediate scenario, there was greater equilibrium between the EM and M trends. The HIPY region is of special interest; it presents the highest average elevation in the study area, with several glaciers and a multitude of snowcapped mountains remaining, due to its being the region exhibiting the lowest overall EM trend. It is of particular interest to analyze these D and EM events jointly to ascertain whether the compound risk of these two variables will be equally distributed or whether each of the two variables will have a different weighting in the joint event.
This evaluation is shown in Figure 10 for the CANT and NMED dipole regions, where the multivariate coordinates of the 275 anomalies of events D and EM are shown; these are divided into three periods: (2011-2040, 2041-2070 and 2071-2100)  by the thermal increase, as opposed to an increase in the duration of such events (D). The same assessment can be extrapolated to the NMED region for the spring in a RCP4.5 scenario. Nonetheless, in the case of summer for this same scenario, a small increase in the duration component was observed. In the RCP8.5 scenario, a very considerable increase in risk was perceived as a result of the increased weight of the magnitude, especially in the last two periods in both seasons and 285 regions. The increase in the D dimension continued to be very weak for the CANT region, regardless of the season analyzed.
On the other hand, in the NMED region, there was a remarkable increase in dimension D, which rose by an average of 10 days (summer, 2071-2100) with respect to the historical average . In this case, we detected that the increase in the compound risk occurred in both dimensions (up to 7ºC in summer), thus implying a much higher risk than in the CANT dipole region. 290 A very similar phenomenon was detected between the EATL region, conditioned by a more oceanic and temperate climate, 295 and the SMED region, with drier and warmer conditions (Fig. 11). Although in RCP4.5 the compound risk increased with a rise in extreme temperatures (EM) in both seasons of the year, in an extreme scenario (RCP8.5), and mainly in the SMED region, the compound risk increased as a result of an increase in both dimensions (D and EM).  These results were summarized in Figure 12, which shows the future patterns of Dry-Hot compound events according to the D and EM variables of the CANT and NMED regions, which act as a dipole in the study area. Each season and emission scenario present a different pattern, summarized below: • Spring | RCP4.5: Increase in one-dimensional compound risk based on (extreme) magnitude. No major shifts between dipole regions. 305 • Summer | RCP4.5: Increase in one-dimensional compound risk mainly based on (extreme) magnitude. Although a greater increase in EM was quantified in the Mediterranean and continental regions (see Fig. 10 and Fig. 11), a small increase was also reported in the second dimension when the duration of the dry event showed an increase.
• Spring | RCP8.5: Increase in risk resulting from a certain two-dimensional component, particularly in the Mediterranean and continental regions. The increase in (extreme) magnitude was slightly greater in the 310 Mediterranean and continental regions. There was a big increase in the second dimension in the above mentioned regions, and a small one in the dipole regions.
• Summer | RCP8.5: Increase in two-dimensional compound risk in Mediterranean areas, greater than the previous pattern. The increase in the opposite regions was practically the same as the Spring | RCP8.5 pattern, mainly in the EM dimension. The increase in EM in the last period in the Mediterranean regions was the highest of the four 315 patterns described.
https://doi.org/10.5194/nhess-2021-5 Preprint. Discussion started: 14 January 2021 c Author(s) 2021. CC BY 4.0 License.  Fig. S5). However, the WATL region, which is adjacent to the CANT region, was influenced by both climates (Atlantic and Mediterranean) and therefore did not reflect a similar behavior pattern to that of the CANT region (see Fig. 1 to verify the heterogeneity of this region).

Discussion
The results of the present research reveal that up to the present there has been a general increase in the compound risk of 325 Dry-Hot events due to an increase in the thermal component; thus, the duration dimension is excluded, as pointed out in various recent studies (Hao et al., 2018;Manning et al., 2019). A significant finding of our study indicates that there will be a significant increase in the future compound risk in relation both to the magnitude dimension (extreme temperature) and the duration dimension (duration of extreme dry event). Therefore, it was estimated that in the future the compound event will exhibit a more balanced distribution between the two dimensions, with the D dimension gaining prominence. Polade et al.,330