Introduction
The climate suffers changes at different time scales driven by several external
and internal factors. Human-induced changes in greenhouse gases, land use,
etc., have been especially prominent in the last centuries, modifying the
energy balance and therefore inducing climate changes . The
attribution of recent climate change to each factor is an attempt to ascertain the
causes for recent changes observed in the Earth's climate and quantify their
relative relevance. However, although the main factors perturbing the climate
at a global scale have been extensively
characterized , fewer exercises
focusing on regional scales are available .
Beyond the average state, the footprint of climate change is manifested
through shifts in extreme weather. In recent years there has been an
increasing interest in quantifying the role of human and other external
influences on climate in specific weather
events . Therefore,
trying to attribute extreme events to climate change at regional scales
presents particular challenges for science.
In the last decades, Europe has experienced a prominent increase in the
occurrence of extremely warm episodes, especially during
summertime . The impacts of such events on
human health are important, observing high rates of mortality when such
extremes occur. Some examples are the summers of
2003 and 2010 , when
persistent episodes of high maximum temperatures in western and eastern
Europe took place. Several studies show that days exceeding the 95th
percentile of the daily maximum temperature (Tx) series, usually called
extremely hot days (EHDs; ), cause also an increase in
mortality, especially among the elderly and people with cardiovascular
diseases . Many works have tried to investigate the
causes of these trends, concluding that these are largely influenced by
anthropogenic activity ,
with summers like that of 2003 expected to become more frequent under
several climate change scenarios . However, extreme
events are also driven by unpredictable internal variability. Indeed, some
authors argued that the summer of 2010 was the result of
the internal variability of the climate system, rather than a clear response
to global warming.
Many works have analysed the influence of the large-scale dynamics on the
variability of extreme temperature indices using several methodologies. For
example, and related
the influence of the atmosphere dynamics and sea surface temperature (SST) to
heat waves using methods based on empirical orthogonal functions (EOFs) or canonical correlation analysis (CCA). Other studies use circulation
types
(CTs; ).
These are guided by the results obtained by , who pointed out
that recent climate changes can be interpreted in terms of changes in the
frequency of occurrence of atmospheric circulation regimes. Some patterns
related to anticyclonic and blocking situations favour the development of warm
extreme events over
Europe .
Therefore, trends in the appearance of these situations could be the cause of
the observed trends. Many studies using CTs have provided information in relation to the
increase observed in the frequency of such patterns since the second half of
the past
century .
On the other hand, based on the robustness of the evidence from multiple
models, the last IPCC report concludes that it is likely
that human influence has altered sea level pressure (SLP) patterns globally
since 1951. In that way, climate change induces changes in circulation that
can further modify the occurrence of extreme events.
However, not all studies find strong links between trends in the occurrence
of extreme episodes and trends in the frequency of CTs.
, and , among others, found
that trends in extreme temperatures are mainly due to the increase of
temperature within the CTs, rather than the increase of the frequency of
occurrence of the CTs. This could suggest that trends in extremes can be in
addition linked to other forcings, such as global warming, teleconnection
phenomena , dryness of soil, increase
of the SST, etc. Discrepancies in relating both kind of trends (in frequency
of the CTs and EHDs) might be due to the way that CT classifications are
built. An example of this can be found in , where a
study on the relationship of trends in extreme Tx indices and changes in
the frequency of CTs is presented. In this work an established CT
classification previously obtained by the authors was used. This
classification, as well as the majority of classifications proposed in the
literature, is obtained using a huge number of days corresponding to a long
period of time (general CT classifications, hereafter). The problem of these
classifications for their application to the analysis of extremes is the low
statistical load that these specific atmospheric situations, drivers of
extreme occurrence, have against the rest of atmospheric situations. This
means that these particular situations would be assigned to generalist
clusters, since the assignation is controlled by statistical rules that look
for a global optimum. Therefore, relating the frequencies of such generalist CTs
to extremes might not be appropriate.
On the other hand, the use of single composites instead of CTs could solve the above problem, but it has some drawbacks.
One is the restriction of the explanation of all extreme occurrences to a unique atmospheric pattern, when there could be
several quite different synoptic situations driving to same kind of extreme. Another drawback is the impossibility of its
application in attribution exercises since the efficiency would be 100 %, while the experience says that quite similar
atmospheric conditions do not necessarily lead to the same effects at the surface, since other forcings could act. Therefore, the use of CT classifications built specifically for the analysis of extremes
is the most reasonable methodology for associating large-scale atmospheric
conditions to extreme events.
Another aspect to consider is how trends in the frequency of extremes are
obtained. Most studies trying to relate local changes (using local series) to
changes in dynamics could be problematic for attribution exercises since
other forcings, different to dynamics, would have an important control on the
variability of these particular events. Regional series composed of a number
of local series contain the information of bigger areas (usually of
homogeneous orography), filtering out the local noise. Therefore, these are
more appropriate for this kind of studies. In principle, series representing
a larger area are more homogeneous, and large-scale dynamics has a larger
control on its variability. Statistical downscaling is based precisely on
this fact, where estimations of local variability are based on predictors,
normally large-scale atmospheric fields (representing the dynamics) and the
training of statistical models to consider the effects of other forcings
which act at more local scales . In addition, the
larger homogeneity of regional series than local ones is manifested on its
extended use in processes of homogenization of climate series. Most methods
of homogenization use reference series, formed by the combination of local
series to test the relative homogeneity of the local
ones . In addition, the analysis of frequency of
regional series is largely extended on hydrology and water resource
applications . Therefore, regional series should
be used in attribution works in order to reinforce the signal imposed by the
dynamics on regional variability. However, it should be checked whether the
regional series represent the behaviour of their constituent local ones.
Using suitable regionalization procedures should assure this compliance.
This study focuses on mainland Spain and the Balearic Islands for
several reasons. First, this region has experienced a significant increase in
Tx during summer in the last
decades .
Furthermore, trends would have continuity during all of this century considering
the results of the AR4 , which also provides information about the great
sensitivity of the region to future changes, especially in the projections of
Tx in summer. Second, the complex orography of the study area causes a
large spatial variability of climate impacts that the same atmospheric synoptic
situation has , making of great interest the studies based on
looking for regional differences. In addition, the availability of a
high-resolution gridded data set developed over the region in the last
years for the analysis of variability
facilitates carrying out studies like this.
In this work a novel way of attributing observed trends in the frequency of
EHD occurrence to trends in the frequency of CTs is presented. Unlike
previous works, here it is proposed a CT classification built based on the
definition of extreme (without using general classifications). For the
construction of these classifications, regional information contained in the
adopted definition of extreme is used, reinforcing on this way the relationships
between EHD variability and dynamics. Furthermore, different CT
classifications are obtained in order to test the impact that different
combinations of atmospheric fields (used for defining the CTs) have on the
final results, this being another important difference with respect to other
previous works. In addition, the results of the Tx regionalization in
summer contribute to give new insights supplementing the results of previous
works performed over the Iberian Peninsula (IP). This contribution is
organized as follows: Sect. describes the data sets employed.
In Sect. the regionalization procedure necessary
for adopting the definition of extreme and the analysis of the obtained regions
are presented. Section shows the method followed
for characterizing the CTs based on the regional extreme definition as well
as a comparative study of the six obtained CT classifications using different
combinations of variables. The way of obtaining the links (efficiencies)
between the CTs and EHD occurrences, the exercise of attribution and its
results, and an analysis of the stability of such links are explained
in Sect. . Main conclusions and discussions are in
Sect. .
Regional series and EHD
This section describes the method of
regionalization followed to identify the regions whose constituent local
series have similar temporal variability. As was discussed in the
introductory section, regional series respond better to changes imposed by
dynamics filtering out the signals controlled by other forcings affecting the
variability of local series. The definition of EHDs from a regional point of
view, the analysis of the variability of the regional series, and the
analysis of the coherency of the regions as well as the differences among them are
also exposed in this section.
Clustering procedure for regionalization
The procedure applied is similar to that employed by
and . First, a Principal Component Analysis
in S-mode is applied to the correlation matrix calculated
using daily anomalies of Tx (obtained with respect the seasonal cycle).
Only the three first EOFs following the scree plot test were
retained, explaining more than 80 % of total variance. Second a two-step
clustering method is applied to the loadings of each grid point in the
retained EOFs. The Ward algorithm is employed for obtaining the
number of groups and centroids that are used as seeds for a definitive
K-means clustering . A more detailed explanation of the
regionalization method can be found in .
Regions
The eight obtained regions as a result of the regionalization process
applied to the summer maximum daily temperatures (16 June to 15
September) of the Spain02 database for the period
1951–2008.
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The aim of this study is not to perform an exhaustive analysis of the
regions, but rather to use the regional series as a tool for achieving the
attribution goal, so only some aspects related to the time variability of
these series are presented below. Figure shows the
eight obtained regions. Their names have been established according to their
geographical locations: SW, NE, E, Cs (southern central), NWs (south of northwest), NWe (east of northwest), NWw (west of northwest) and N. Regional series
have been constructed by averaging the time series of the grid points
belonging to the same region. Table (first four
columns) shows some statistics of the regional series: mean, trend, standard
deviation and 95th percentile. A meridional gradient of mean and percentile
values is observed, with the warmest regions being located in the southern half of
the country (SW and Cs).
Statistics summarizing the eight regional series. The
second and third columns show the mean and trend (∘C decade-1) of the daily
maximum temperature series. The standard deviation of the de-trended series
is shown in the fourth column. The fifth column exhibits the 95th percentile.
Finally, the sixth column shows the EHD trends (days/decade). Bold values
(asterisks) indicate significant values at 95 % (90 %) confidence
level (estimated with the Mann–Kendall test). Values are obtained for the
period 1951–2008, but for EHD trends the 1958–2008 period is considered.
Confidence intervals (95 % of significance) for Sen's trends are
indicated in parentheses for Tx and EHD trends.
Region
T¯max
T¯max trend
SD
95th p
EHD trend
SW
32.5
0.13* (-0.03/0.29)
0.98
37.8
1.00 (0.32/1.67)
NE
27.5
0.40 (0.23/0.58)
1.07
33.1
1.19 (0.34/2.1)
E
29.7
0.13* (-0.01/0.27)
0.92
33.5
0.63* (0.00/1.33)
Cs
31.2
0.28 (0.1/0.44)
1.08
36.1
1.66 (1.00/2.42)
NWs
28.4
0.32 (0.16/0.50)
1.04
34.3
1.54 (0.85/2.22)
NWe
24.7
0.12* (-0.03/0.26)
0.91
30.0
0.45* (0.00/1.15)
NWw
24.5
0.27 (0.08/0.46)
1.09
30.6
0.63 (0.00/1.38)
N
24.4
0.32 (0.14/0.49)
1.08
31.2
1.05 (0.47/1.67)
The temporal variability of the regional series is presented in
Fig. . Solid black lines represent the Tx mean
seasonal series. For all regions two different periods are observed,
confirming the results obtained in previous works that analysed the evolution
of summer Tx series over the IP and in further
Mediterranean regions . The first lies between 1951
and 1977, when temperatures dropped significantly, with 1977 being the coldest
year for most regions. The second period (1978–2007) is characterized by a
significant rise of Tx. The 1990s were an especially warm decade, with the
hottest year occurring for most regions. In particular, 1994 was the hottest for
eastern (NE, E and Cs), 1991 for western (SW and NWs) and 1990 for northern
regions. During the last decade, a decrease of the standard
deviation is observed in the central, southern and eastern regions, and an increase in
the northern ones (N, NWe and NWw).
Extremely hot day definition
Temporal evolution of the eight regional series (see Fig. ). The seasonal mean series of maximum temperature
are represented by the black bold curve (right y axis). The yearly number of
regional EHDs and its running mean series (of 11 years) are depicted
by vertical bars and the grey curve, respectively (left y axis).
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The definition of extreme is adopted using the 95th percentile of the regional
series (fifth column of Table ). These percentiles are
calculated using the entire period of the Spain02 data set (1951–2008; Sect. ). Thus, a day is defined as an EHD when any of the regional
Tx series exceeds its 95th percentile. In this way, an ensemble of 863
EHDs were identified in the period 1951–2008.
Figure shows the seasonal frequency (bars) and running mean series (11 years) of the regional EHD occurrences
(grey line). A noticeable increase is observed in the frequency of EHDs since the 1990s. This finding is in agreement with other studies
that found significant increases in climate extreme indices related to Tx over the IP and
Europe . Comparing for all regions the evolution of seasonal Tx (black curves) and seasonal frequency of EHDs (bars) of
Fig. , it is observed that the warmest year does not necessarily coincide with the year of the highest EHD occurrences.
In general, the year with most extreme occurrences was 2003, especially in the northern regions (N, NWe, NWs and NE), coinciding with the
extraordinary heat wave that affected many countries of western Europe . The persistence of EHDs
(number of consecutive EHDs) during this year was also extraordinary in most of our regions, reaching up to 10 days in NE, N, NWe and NWs,
and up to 16 days in the SW region. In Cs and NWw the maximum number of EHD occurrences took place in the early 1990s, whereas in the E region
it curiously occurred in two consecutive years (1958 and 1959).
Daily co-occurrence of EHDs between pairs of regions.
Non-diagonal elements indicate the probabilities of having a simultaneous EHD
between all possible pairs of regions. Diagonal (bold values) indicates the
probabilities of having an EHD exclusively over a given region.
Region
SW
NE
E
Cs
NWs
NWe
NWw
N
SW
0.11
NE
0.37
0.16
E
0.25
0.44
0.40
Cs
0.57
0.47
0.40
0.08
NWs
0.62
0.47
0.25
0.59
0.05
NWe
0.38
0.38
0.16
0.31
0.54
0.07
NWw
0.44
0.26
0.15
0.27
0.44
0.56
0.26
N
0.3
0.46
0.22
0.32
0.44
0.60
0.35
0.19
A trend analysis of the seasonal EHD series has been performed in order to
use them for the attribution exercise. Trends and their statistical
significance have been obtained by using Sen's
algorithm and the Mann–Kendall test, respectively.
In addition, to be able to connect these trends to the trends in the
frequency of CTs, EHD trends have been calculated for the period 1958–2008
instead of 1951–2008. The election of this period is in accordance with the
non-availability of atmospheric data used for obtaining the CTs in the period
1951–1957 (see Sect. ). The sixth column of
Table shows the trends obtained for each region as
well as the confidence intervals (95 % of confidence) of these trends.
All regions have positive and significant trends (95 % of significance in
all regions but 90 % in NWe and E). Largest trends are observed in the
inner regions (Cs, NWs and NE), showing a pattern very influenced by the
distance to sea, similar to that reported in and
in , which analysed spatial warming patterns over the IP.
Another important aspect of the obtained regions is its internal coherency
and differences among them. Coherency of the regions can be estimated
attending to the degree of representation of the region with respect to its
constituent series. Thus, a regional EHD should be a signal of many EHD local
occurrences at the same time in many of their grids. In this sense, the mean
percentage of grid points belonging to the same region that experiences local
EHD occurrences when a regional EHD is observed has been obtained for each
region. Results show that around 60 % of grid points for most regions
have a local EHD when a regional EHD occurs, confirming that regional series,
obtained by averaging all the constituent series, are a good thermometer of
the global behaviour of the region. NWs and E regions are the most and least
homogeneous, with percentages of 65 and 52 %, respectively. In
addition, if the 90th local percentile is considered, more than 80 % of
grid points overcome this percentile when in the region an EHD occurs.
Differences among the regions can be obtained by calculating the probability of
simultaneous EHD occurrence among them. Table shows
a symmetric matrix with these probabilities. The symmetry of the matrix is in
accordance with the number of EHDs in the different regions being the same
because of the use of the 95th percentile of each region (all regions have
the same number of EHDs during the comparison period, 1951–2008). Diagonal
values of the matrix show the probability of occurrence only in this region
(without EHD occurrences in the remaining regions). Results indicate that the E
region is the most distinctive (40 % of non-simultaneous occurrences),
whereas NWs shares many episodes with many of the regions (5 % of
occurrences only in this region). The lowest probability of simultaneous
occurrence is between E and NWs regions (15 %), and the largest between
NWs and Cs (62 %). In general, there are important regional differences,
which points to the conclusion that a given large atmospheric pattern could
have a different effect over the various regions.
Characterization of EHD circulation types
As discussed above, links between EHD occurrences and CTs could not be well
established when general CT classifications are used. We propose the obtainment
of specific CT classifications based on the variable to study, in this case
EHD occurrence. Before obtaining the final CT classification, main synoptic
situations leading to EHD occurrences at the different regions are
characterized. In addition, since the results could depend on the atmospheric
fields used for characterizing these situations, six different combinations
are examined. This will permit testing the sensibility of the final results
to the chosen fields.
Clustering procedure for CT characterization
To characterize the atmospheric patterns drivers of EHD occurrences, a
similar procedure to those used for general CT classifications is followed.
The main difference is that only days characterized as EHDs are used for the
clustering. The two-step method applied in is used
here. In the first step, a principal component analysis in T mode (PC-ModeT) clustering is
performed . This clustering allows obtaining the necessary
seeds for the second clustering step, defining the number of clusters (a
priori unknown). Second, a K-means algorithm is applied over the retained
PCs, using for initializing the clustering the seeds obtained in the previous
step. The geographical window for clustering is identical to that employed
in , which covers completely the IP and Balearic
Islands (35–45∘ N and 10∘ W–6∘ E). Performing
the clustering using larger windows might lead to inclusion of more noise in
the classifications, obtaining probably some clusters representing further
dynamical structures with little influence on the regional climate
variability of the IP. Despite the windows employed covering a small area, the
results of clustering are representative of bigger
areas , so a larger window is used for
representation of the centroids (composites of the clusters), allowing for
better visualization of the synoptical structures.
Six CT classifications have been obtained. Three of them consider the
atmospheric fields individually (SLP, T850, Z500). The other three consist of
the combination of all possible pairs of fields (SLP–T850, SLP–Z500 and
Z500–T850). The number of clusters of each CT classification depends on the
retained PCs used for the PC-ModeT clustering, this being double the
retained PCs . For classifications with only one
atmospheric field, six clusters are obtained, whereas eight clusters are
obtained if two fields are considered. Therefore, three or four PCs are
retained if fields are considered individually or in pairs, respectively. In
all cases the explained variance by these PCs is over 90 %.
Dispersion of the EIs (see main text for the
definition of the index). The numbers denote the range–standard deviation of
the EIs obtained for each region and CT classification. The last
column shows the CTs with EIs (in brackets) above 1 for the best
classification of each region (bold numbers).
Region
SLP
Z500
T850
SLP–Z500
SLP–T850
Z500–T850
CTs
SW
1.4–0.54
1.4–0.56
1.9–0.80
1.4–0.53
2.0-0.72
1.6–0.58
CT1(1.1),CT2(1.0),CT3(2.0)
NE
0.8–0.29
1.7–0.65
1.7–0.71
3.1–1.01
2.1–0.72
3.3-1.13
CT2(3.4),CT7(1.5)
E
4.6–1.76
3.2–1.22
3.7–1.43
10.2-3.48
8.3–2.82
8.4–2.84
CT4(1.0),CT8(10.2)
Cs
0.5–0.18
1.2–0.46
2.2–0.80
2.0–0.65
2.6–0.86
3.4-1.13
CT2(3.4),CT3(1.1)
NWs
0.8–0.33
1.3–0.46
1.7-0.74
1.5–0.53
1.7–0.58
1.5–0.59
CT1(1.0),CT2(1.7) (SLP–T850)
NWe
2.0–0.76
1.0–0.42
1.7–0.66
2.3–0.74
3.0-0.97
1.4–0.48
CT2(3.0),CT5(1.0)
NWw
0.9–0.38
1.2–0.48
1.6–0.61
1.3–0.53
1.9–0.64
2.1-0.71
CT1(1.0),CT6(2.1)
N
1.3–0.65
1.1–0.41
1.7–0.66
2.0–0.66
4.0-1.33
1.36–0.59
CT2(4.0),CT6(1.2)
Efficiencies before and after the allocation process (in
percentage) for the CTs of the best classification (last column) for each
region.
Region
CT1
CT2
CT3
CT4
CT5
CT6
CT7
CT8
Classification
SW
53.3–17.6
51.3–44.4
66.7–18.5
31.9–24.8
3.2–0.5
0.0–0.0
20.5–4.9
0.0–0.0
NWs
46.7–15.4
63.5–54.9
39.8–11.1
38.3–29.8
3.2–0.5
6.6–1.4
38.6–9.2
0.0–0.0
SLP–T850
NWe
25.2–8.3
74.8–64.7
10.2–2.8
21.3–16.5
48.4–7.0
14.3–3.0
41.0–9.8
0.0–0.0
N
17.0–5.6
80.0–69.2
1.9–0.5
26.6–20.7
25.8–3.7
55.0–11.6
41.0–9.8
0.0–0.0
NE
26.5–6.7
77.1–72.2
12.0–4.0
45.0–34.0
25.3–8.7
3.1–0.6
59.7–21.5
8.5–0.4
Cs
3.7–0.9
77.1–72.2
51.3–17.2
42.2–31.9
41.4–14.2
1.0–0.2
6.5–2.3
4.3–0.2
Z500–T850
NWw
50.0–12.6
25.4–23.8
39.3–13.2
27.5–20.8
1.0–0.4
67.7–12.0
3.2–1.2
0.0–0.0
E
17.9–5.1
19.8–8.8
27.3–12.3
50.0–37.0
2.2–0.3
39.5–6.0
6.3–4.7
91.0–6.7
SLP–Z500
Evaluation of the CT classifications for EHD description
The way of selecting those days defined as EHDs (any EHD occurrence over
almost one region) makes an ensemble of situations affecting the various regions in a different
way. For a given region, some of the CTs will have
great influence on its EHD occurrences, but some others do not have (or
little) influence, affecting other regions more. On the other hand,
using clustering techniques for classifications, as well as to force
the clustering of a great number of events to a reduced number of clusters (6
or 8), causes the existence of noise in the classifications. A question
arising is if there is any classification, among the six obtained here, that
characterizes better the EHD occurrence for each of the regions. In order to
address this question, an index, effectiveness index (EI), is defined. This
index is calculated as the ratio between the number of EHD occurrences and
non-occurrences in the region under a given CT. Therefore, for a given CT
classification and region, there is a set of EIs. The best classification is
chosen from that whose standard deviation and range of the EIs are the
largest, since it separates better the most- from the least-influential CTs. In
addition, those CTs with EI >1 for a given region are defined as “extreme
CTs”, because the probability of extreme occurrence is larger than the non
occurrence.
Centroids of the CTs for the SLP–T850 classification. SLP and T850
are represented by contours, black lines for SLP and colour lines for T850.
Shading denotes the regional EHD efficiencies associated with each CT. The
top left corner shows the number of the represented CT. Right corner
indicates the frequency (in percentages) of each CT, before and after applying
the allocating method (Sect. ).
![]()
Same as Fig. but for the Z500–T850
classification. Z500 and T850 are represented by geopotential high contour
levels (shaded black lines) and isothermals (colour lines).
![]()
Same as Fig. but for the SLP–Z500
classification. SLP and Z500 are represented by isobars (black lines) and
contour levels (blue shaded lines).
![]()
Table shows the range and standard deviation (range–SD)
obtained for all the regions and CT classifications. Last column shows for
each region its best (highlighted in black) CT classification with its
extreme CTs. Results indicate that two synoptic variables characterize better
the EHDs for most regions; therefore, hereinafter the remaining analysis will
focus only on the CT classifications formed by two atmospheric fields.
Z500–T850 is the best one for NE, NWw and Cs (inner-eastern regions and
northwestern). SLP–Z500 characterizes better the E region. SLP–T850 is the
best for SW, NWe and N (western and northern regions). T850 classification is
the best for the NWs region. However, in this area SLP–T850 performs quite
similar. Hence, and for the shake of clarity in the analysis, SLP–T850 has
been considered as the best classification in this case.
Figures – show the centroids
(composites) of the CTs (contours) belonging to the CT classifications formed
by two atmospheric fields as well as their efficiencies (shaded) over the
different regions. Efficiency is defined as the conditional probability of
having an EHD in a region under a given CT. Another interesting parameter is
the contribution of a given CT to the occurrence of the EHDs in a given
region. The contribution is assessed by calculating the ratio between the
number of observed EHDs under a CT and the total EHDs observed in the region.
Tables and depict the
efficiencies and contributions values.
The efficiency patterns are quite similar for the three CT classifications.
However, for each region the efficiency is higher for the classification that
gives larger spreads in the EI (Table ). Some examples
follow. The efficiency pattern related to CT8 is equivalent in all
classifications and shows high efficiency over the E region. The efficiency
is higher for the SLP–Z500 classification, which has the largest EI for
E region. Similar results are found for CT5 of SLP–T850, CT6 of Z500–T850 (best)
and CT5 of SLP–Z500 in the NWw region, and for CT3 of SLP–T850 (best),
CT3 of Z500–T850 and CT1 of SLP–Z500 over the SW region. These results suggest that
some CTs belonging to different classifications are equivalent; i.e. they give
similar efficiency patterns. In fact, this can be corroborated by calculating
the common days of the mentioned CTs (not shown). This highlights the need
for studies on the sensitivity of the CT classification to the atmospheric
variables employed.
The comparison of the atmospheric situations, among the different
classifications, associated with similar efficiency patterns, enables some
conclusions to be drawn about the main drivers related to the EHD occurrences.
Regarding the T850 variable, the regional efficiency shows the highest values
in regions where temperatures are near and above 20 ∘C. This feature
is very common in many CTs of the different classifications such as the
CTs 2, 3, 4, 6 and 8 of SLP–T850 and the CTs 1, 2, 3, 4, 5, 7 and 8 of the Z500–T850
classification. The wind provenance, inferred considering the SLP field, is
also an important factor contributing the occurrence of EHDs in some regions,
because of the warm advection over specific regions. Many CTs are related to
situations of wind blowing from inner towards coastal areas, causing the
highest efficiencies in the latter. The inner IP regions are highland
plateau areas where high temperatures are observed (see
Table ). When wind blows from this area towards the sea
through valleys, air is adiabatically compressed, causing an important warming
in lowland regions. Some examples of these situations can be identified in
the classifications by analysing the efficiencies and contributions of some
CTs. Five regions are mainly affected by this: NWw, especially when wind blows
from the east because of the presence of high pressures over western Europe
(CT5 of SLP–T850 and SLP–Z500); SW in northeastern wind conditions (CTs 1 and 3
of SLP–T850 and CT1 of SLP–Z500) as a result of the presence of high pressure
over the Mediterranean and relative low pressures over the southwest of the
IP; the E region under strong western zonal wind (CT8 of SLP–T850 and
SLP–Z500), induced by the location of high and low pressures over the
Atlantic and Mediterranean, respectively; and the NE and N regions in southwestern wind situations
(CT6 of SLP–T850 and SLP–Z500). Conversely, CTs with weak SLP gradients
(stagnant situations linked to thermal lows) are specially important in the
EHD occurrences at Cs and NE (CT4 of SLP–T850 and SLP–Z500), and N, NWe and
NWs (CT2 of SLP–T850) regions. Such situations were also pointed out
by like those more relevant guiding hot
extremes in summer over the IP. Regarding the Z500 field, EHDs are associated
with large amplitude ridges over the IP. Regions with the highest
efficiencies are located to the west of the ridge axis, where there are high
stability and warm advection. The efficiency and contribution are only
important in the E region when zonal wind at 500 hPa is strong (CTs 5 and 8 of
Z500–T850 and CT8 of SLP–Z500). This pattern usually takes place when hot
episodes over the IP are ending up. The analysis of the CT transitions (not
shown) for consecutive EHD episodes reinforces this result. The hottest areas
travel from western to eastern regions, following the ridge movement.
Contributions (in percentage) of the CTs belonging to the
best classification (last column) for each region.
Region
CT1
CT2
CT3
CT4
CT5
CT6
CT7
CT8
Classification
SW
28.5
23.3
28.5
11.9
1.2
0.0
6.7
0.0
NWs
24.6
28.5
16.8
14.1
1.2
2.3
12.5
0.0
SLP–T850
NWe
14.0
35.4
4.5
8.2
18.5
5.3
14.0
0.0
N
9.2
36.8
0.8
10.0
9.6
20.0
13.6
0.0
NE
13.9
35.1
5.4
18.9
9.7
1.2
14.3
1.5
Cs
2.0
36.4
24.0
18.4
16.4
0.4
1.6
0.8
Z500–T850
NWw
28.1
12.4
19.0
12.4
0.4
26.9
0.8
0.0
E
9.5
10.3
12.9
23.3
0.9
14.7
2.2
26.3
SLP–Z500
Linking EHD trends to CTs
Significant and positive EHD regional trends were found for all regions
(Sect. ). An interesting question is whether there is
any relation between these trends and changes in the frequency of occurrence
of the CTs. Therefore, the existence of trends in the frequency of CTs should
be assessed. The main problem is that frequencies of CTs only can be obtained
during extreme episodes. There are atmospheric situations, similar to that
described in the centroids, that were not included in the previous
clustering step because EHDs did not occur in any region. As was discussed
above (Sect. ), the same atmospheric patterns could lead
to some different weather situations. To take this into consideration, the rest
of the days initially not considered for characterization have to be assigned to
one of the obtained clusters. For this reason, links (efficiencies) between
CTs and EHD occurrences have to be recalculated. The method of assignation of
such days is presented below.
Thresholds of the different CTs used for
distance/correlation in the allocation process.
Classification
CT1
CT2
CT3
CT4
CT5
CT6
CT7
CT8
SLP–T850
0.06/-0.26
0.06/0.57
0.06/0.40
0.06/0.67
0.05/0.18
0.08/0.36
0.06/0.61
0.07/0.39
Z500–T850
0.07/0.18
0.05/0.14
0.05/-0.09
0.05/0.02
0.05/-0.06
0.05/0.27
0.06/0.36
0.07/0.31
SLP–Z500
0.06/0.10
0.07/0.59
0.06/-0.12
0.06/0.72
0.06/0.17
0.08/0.47
0.05/0.47
0.08/0.04
Number of days classified within each CT. Each box shows
the number of days classified before and after the allocation process. CT9
denotes the unclassified days.
Classification
CT1
CT2
CT3
CT4
CT5
CT6
CT7
CT8
CT9
SLP–T850
135–410
115–133
108–389
94–121
93–644
91–433
83–347
65–677
0–1446
Z500–T850
136–539
118–126
117–349
109–144
99–289
96–541
62–172
47–902
0–1538
SLP–Z500
123–432
121–273
110–243
108–146
90–647
86–563
79–106
67–908
0–1282
Allocation method
Each CT is the result of a set of similar atmospheric conditions being its associated centroid the mean value (composite) of this ensemble or
population. However, there is some dispersion inside each group. To allocate an atmospheric situation (not considered as an EHD) into the CTs means
finding the population where such situation fits better. For this task the election of some metrics is fundamental. Two metrics have been used for
assignation: the Spearman correlation and the Euclidean distance. The former measures the spatial similarity of two fields
, whereas the latter evaluates the differences in the intensity of patterns .
Both metrics are relevant and complementary . The population of a given CT is characterized by the distribution
of the distances to and correlations with the centroid using only the days considered in the characterization (Sect. ).
To obtain the population of each CT, the atmospheric data are first standarized by grid point; then correlations and distances to the centroid are
obtained. Mean and standard deviation for standardization are obtained using all days (extremes and non-extremes) of the study period. A
criterion
to allocate a situation into a given CT is that the distance to (correlation with) the centroid be lower (higher) than some given thresholds. Hence,
the election of these thresholds is a problem to solve. On the one hand, thresholds could be fixed to certain percentiles of the populations, but
this could be problematic because this would have strong subjectivity. On the other hand, thresholds could be the maximum (minimum) values of
distance (correlation) obtained from days clustered for the characterization of the CT leaders to EHD occurrences (Sect. ).
We have chosen the latter option because this is free of subjectivity. Table shows the thresholds considered for all CTs and
classifications. Some thresholds of certain CTs are too broad, allowing the assignation of more days into them. These CTs are those with higher
noise inside them, and probably they are formed by a larger heterogeneity of situations. By contrast, there are CTs more homogeneous with thresholds more restrictive. In general the most homogeneous CTs agree with
atmospheric patterns having high efficiency in most regions simultaneously.
Finally, a given day is allocated to the CT on which distance and
correlation are lower and higher, respectively, than the thresholds defined
for it. Days that can not be assigned to any CT are then allocated to a new
group (unclassified group, CT9; ). This way of assignation
might derive from the allocation of a situation to more than one of the
established centroids. In these cases, it is allocated to the nearest cluster
considering only the Euclidean distance. The use of this criterion is in
accordance with the lower spread of the Euclidean distance populations than that observed for
correlation.
Analysis of the allocation
Table shows the number of days belonging to the different CTs
before and after the allocation process. Approximately 70 % of the days for
all classifications are assigned, whereas the rest are allocated to the
unclassified cluster (CT9), with Z500–T850 (SLP–Z500) being the one with
most (fewest) unclassified days (33 % vs. 28 %). There is a large
variability in the increase of the days belonging to the different CTs. CT1,
CT6 and CT8 have the largest increase (10 times) in all classifications,
whereas others like CTs 2 and 4 of SLP–T850 and CTs 2 and 4 of Z500–T850 present small changes
(less than 20 % of the initial clustered days). The assessment of the quality of the
clusters before and after the allocation is of major relevance. In order to
ensure the reliance of the assignation method, the
explained cluster variance (ECV) of each classification
(Table. ) is analysed. Results show few differences among
the classifications. Z500–T850 classification has the best quality, observing
even an increase in the quality of clusters after the allocation. The quality
of the other classifications worsens slightly after the allocation, with the
SLP–T850 classification being slightly better than the SLP–Z500 one. On the other
hand, when comparing the quality for the three classifications after the
allocation (ECV >46 % in all cases; see Table. ) with
some others obtained using general CT classifications, even
better results are observed in our classifications. Hence, in an ECV lower
than 40 % was obtained in summer, and in of
47.2 %. These results support the suitability of the method followed for
allocation.
It is instructive to explore the consequences after applying the allocation
procedure on the properties of the groups or CTs. One consequence of the
larger number of classified days is the decrease in the efficiency of the CTs
(see Table ). Obviously, the lower the increase of the
number of days, the smaller the decrease of the efficiency. This effect stands out
in CTs 2 and 4 for the SLP–T850 and Z500–T850 classifications, which have the
highest efficiencies in most regions. Changes in the efficiency after the
allocation also affect the EI used for deciding the best CT
classification for each region (Sect. ). Following the
same criterion as above, results remain unaltered for most regions, except for E
and NWw regions, which are now better characterized by the SLP–T850
classification.
The shape of the populations of distances and correlations of each CT can be
also affected. The net effect of the allocation process is to include new
days located further from the centroid. Nevertheless, a small number of
clusters hardly change the populations after the assignation (CTs 2 and 4 of SLP–T850,
CTs 2 and 4 of Z500–T850 and CTs 4 and 7 of SLP–Z500), which are coincident with the ones with
higher efficiency. Figure shows two examples of the
correlation histograms before and after the allocation process (top) as well
as the empirical cumulative distribution function (bottom). The left and right panels
show an example of great and small changes in population, respectively.
Once the allocation is performed, an analysis of trends in the frequency of
CTs is carried out. Table shows the trends obtained
for each CT of the different classifications. Trends and their statistical
significance are obtained following the same methods (Sen's algorithm and
Mann–Kendall test for trend and its statistical significance, respectively)
as used for estimating the regional EHD trends. Results indicate that
only two CTs of each classification have trends with statistical significance
(one more but without significance). Considering this and their associated
efficiencies (Table ), it could be said that trends in
CTs would be linked to the increase of EHD occurrences in northern regions
(mainly N and NE). It is interesting also to observe that the CT9 (formed by
the unclassified days) has a negative trend for the three classifications,
meaning that in time a larger number of days are assigned to the
centroids linked to EHD occurrences.
Explained variance by the clusters (in %) for the
three CT classifications before and after the allocation process.
Z500–T850
SLP–T850
SLP–Z500
Before
49.97
49.65
49.48
After
50.06
47.02
46.59
Histograms and empirical cumulative distribution functions of the
correlations for CT3 of Z500–T850 (left) and CT2 of Z500–T850 (right). Each panel
shows the populations before and after the allocation process.
![]()
Trends in the frequency of CTs for the different CT
classifications. One (two) asterisk indicates trends at 90 % (95 %) of
the confidence level (Mann–Kendall test).
Classification
CT1
CT2
CT3
CT4
CT5
CT6
CT7
CT8
CT9
SLP–T850
0.00
0.26*
0.00
0.00
-0.43
0.51*
0.00
0.00
-1.3
Z500–T850
0.28
0.45**
0.00
0.00
0.00
-0.53
0.80**
0.00
-0.80
SLP–Z500
0.00
0.57*
0.00
0.00
0.00
0.57*
0.00
-0.30
-0.50
Attribution of EHD trends
Temperature changes can be linked to several factors, one of them being the
changes in atmospheric circulation. Trends in the EHDs could be considered
also as an indicator of temperature changes. In this subsection, a model to
attribute regional EHD trends to trends in the frequency of CTs is presented.
The regional EHD trend in a given region, Tr, can be written as the sum of
two terms:
Tr=Tcr+Tor,
where Tcr is the trend attributable to changes in atmospheric circulation
and Tor the trend related to other factors. Now, Tcr can be described
as a linear function of the changes in the frequency of the CTs. We propose
the simple model
Tcr=∑i=1nTiϵir,
where the subscript i denotes the CT number, from 1 to n (the number of
CTs); Ti is the frequency trend of the CTi
(Table. ); and ϵir denotes the efficiency
of the CTi over the region r (Table. ), calculated
after the allocation process.
Regional EHD trends (days/decade). The first three
columns show the trends obtained from the attribution exercise considering
the different classifications. Last column shows the observed trends derived
from regional series.
Region
TSLP–T850r
TZ500–T850r
TSLP–Z500r
Tr
SW
0.11
0.18
0.15
1.00
NWs
0.15
0.29
0.15
1.50
NWe
0.15
0.21
0.11
0.45
N
0.22
0.42
0.12
1.10
NE
0.17
0.51
0.12
1.20
Cs
0.09
0.35
0.12
1.60
NWw
0.08
0.09
0.13
0.63
E
0.08
0.30
0.06
0.60
Using this simple model Tcr can be calculated for all regions using the
different CT classifications. The results are summarized in
Table . The last column depicts the observed
regional EHD trend. With independency of the CT classification, the
reproduced trends are in all cases smaller than those observed for a given
region, but they are strongly dependent on the CT classification, except for
SW and NWw regions where few differences are appreciated among
classifications. In general terms, the Z500–T850 classification (that of the
best quality; see Sect. ) obtains the
highest reproduced trends except for NWw. Using this classification a fraction
between 40 and 50 % of the observed trends is attributed to changes in the
frequency of CTs in the E, NE, NWe and N regions, about 20 % in the
western and southern regions (SW, Cs and NWs), and only 14 % in NWw.
Within-type variations in the efficiency
In the exercise of attribution, links between CTs and EHD occurrences,
established by the efficiency, have been taken as long-term mean values of
the efficiency throughout the entire study period (1958–2008), because our main
goal is to attribute long-term regional EHD trends. On the other hand, if our
purpose were to describe the variability at higher frequencies, an analysis of
the stability of links (obtaining the links using higher frequencies) should
be carried out. The instability of links is frequently known in the literature as
within-type variations (WT). Some of the limitations of the use of CTs for
downscaling purposes is precisely the existence of WT, meaning that other
factors could be controlling the links. For example, the scarcity of
precipitation in spring would lead to drier soils, and during summer
land–atmosphere processes would be more
intense , enhancing air temperature
and efficiency. Another example is the persistence of atmospheric situation
drivers of high Tx; this also would cause an enhancement of
land–atmosphere processes. Persistence might be originated by the existence
of SST anomalies caused by teleconnection
phenomena . In order to evaluate the possibility
of using the CTs obtained here for downscaling of annual EHD in the different
regions, an analysis of the stability in the efficiency for the different
regions has been carried out. To do so, annual efficiency series have been
obtained, and, in a way similar to other
works , running mean series of
31 years are derived for the analysis of the stability.
Within-type variations. The lines represent the moving average
(31 years) of the efficiencies for the CTs composing the best CT
classification (colour) for each region (panel) after the allocation process.
![]()
Figure shows the obtained running mean series for
every region and for the CTs composing the best CT classification for each
region (that with the highest dispersion of the EI after the allocation
process; see Sect. ). In general terms,
those CTs with the highest efficiencies in each region increase its
efficiency by 10 % throughout the study period (1958–2008). This is the case
of CT2 in the regions Cs, NWs, NWe, NWw and N, and CT4 in the E region.
Anyway, there are some other important WT variations in CTs affecting the
inner regions more, pointing to a rise of the efficiency. Some examples
follow: CT-3/4 for Cs, CT-1/2 for SW and CT-1/3/7 for NWs. Another
interesting result is the increase of the efficiency of CT4 in the northern
regions (NWw, NWe and N), while it decreases in the E region, confirming once
again the remarkable regional differences existing over the studied area.
Among all the regions, the least affected by WT is the NE region, where only
CT1, with low efficiency over the region, increases its efficiency. This last
result is curious because this region was noted by as one of
the Spanish regions where larger WT in Tx were observed during the second
half of the past century, observing warming in Tx inside many of the CTs
obtained by these authors. Differences between our results and those found
in could be in the variable analysed, in our case extreme
events and in their case Tx mean. Hence, the increase of Tx mean may not
mean an increase in the efficiency of EHD occurrence.
Some reasons for the
increase in the efficiency found in the CTs can be linked to the increase of
the persistence of CTs. To evaluate this possible influence, the correlation
between the de-trended seasonal frequency series and mean seasonal
persistence series of the CTs with the most important WT have been
calculated. Results show positive and significant correlations, between 0.6
and 0.7, which support the influence of the persistence on the efficiency
rise. In addition, the decline of soil moisture observed over the IP since
the 1970s could be another factor contributing to higher
efficiencies.
Conclusions and discussions
This work sets as its intention the attribution of regional trends in EHD occurrences
observed at eight Spanish regions (during the period 1958–2008) to changes
in the frequency of atmospheric situations linked to the occurrence of such
events. The study is centred in summer, when EHDs have a larger relevance. The
method followed is based on the procurance of CT classifications using
regional information contained in the same definition of extreme. This differs
from others studies based on general CT classifications. Therefore, a
regionalization of daily Tx series is carried out, deriving from this
exercise the regional series used for adopting the definition of extreme. In
addition, the internal coherency of the regions and differences among them
are also analysed. Later, a characterization of the atmospheric situations,
drivers of EHD occurrences in the different regions, has been obtained,
centring these classifications only on those days defined as EHDs. In this
way, six CT classifications each using a different combination of
atmospheric fields have been obtained, and an analysis for finding the most
suitable classification for each region has been performed. Links between
CTs and EHD occurrences have been defined by means of the efficiency that a
given CT leads to a regional EHD in each region. To establish such links, the
CT classifications obtained in the characterization step have been extended
to the rest of days (non-EHDs). To do so, a method of allocation of these days
to the centroids obtained in the characterization is presented. Finally, the
method of attribution is presented as well as an analysis of the stability of
the links between large-scale dynamics and EHD occurrence. The main
conclusions are summarized below.
Eight regions with different daily Tx variability are identified. Regions have high internal coherency and important differences
among them. Positive and significant regional EHD trends are found across most regions. Generally, such trends are larger in central and northern regions, and lower in the SE and NWe regions.
To find CT classifications describing the extreme occurrences, it is convenient to base them on the variables to analyse, as well as on a characterization
of the associated atmospheric patterns using exclusively those days defined as extremes. The method proposed here produces CT classifications of similar quality to
those obtained in general CT classifications which use other clustering techniques. However, this method ensures a more precise allocation of the extreme days to the correct clusters than general CT classifications.
The choice of the most suitable combination of atmospheric variables to define the CTs becomes of major relevance. This study finds that classifications using
combinations of two atmospheric variables generally perform better than those using only one. In the case of the studied area, SLP–T850 characterizes better the EHD
occurrences for most regions. However, other combinations, such as Z500–T850, have better results in the Cs and NE regions. In addition, Z500–T850 is the CT classification
with the best quality, whereas SLP–Z500 has the worst quality in terms of the explained variance by the clusters.
In the different obtained classifications, only a small number of CTs have significant trends of its seasonal frequency, a result which is in line with other studies
using general CT classifications . Such trends depend on the atmospheric variables used for the classification, with the largest
trends occurring in the classification of the best quality (Z500–T850). CT2 of the Z500–T850 and SLP–T850 classifications have the largest trends. This atmospheric pattern is
associated with high occurrence of EHDs in most regions simultaneously, specially in the central and northern regions.
Part of the EHD trends observed in some regions can be attributed to changes in the CT frequencies. However, the trends reproduced by the attribution method are in
all cases lower than the observational ones, indicating that part of the trend has to be attributed to other factors. The attributed trends have a great dependence on the
region, as well as on the CT classification. Thus, the best-quality classification, Z500–T850, is able to attribute the larger part of the observed regional EHD trends for
most regions except for NWs. Considering this classification, a fraction between 30 and 50 % of the observed trends is attributed in the E, NE, NWe and N regions, about 20 % in
the western and southern regions (SW, Cs and NWs), and hardly 14 % in the NWw.
Some of the most-influential CTs in terms of leading to EHD occurrences in the different regions present WT variations in relation to their efficiency, except for NE. Approximately
the most efficient CTs have increased their efficiencies by 10 % during
the study period. These changes may be associated, among other
things, with the increase of the persistence of such CTs through time.
The attribution exercise reveals that the observed regional EHD trends can be
only partially attributed to changes in the atmospheric dynamics and that
they have an important regional component. This suggest that there are other
factors involved in the EHD trends – such as global warming, soil–atmosphere
feedbacks or changes of surface properties – that contribute to
increasing positive changes in EHD frequency. A fact that reinforces this
asseveration is that the trends in central regions are less affected by
changes in atmospheric dynamics. This could be related to a depletion of soil
moisture that enhances the positive land–atmospheric feedback, as
previously stated by other authors . This also supports the WT
variations mentioned above.
The links obtained here between regional EHD and CTs, and the allocation
method followed, can be used for estimating the role of the atmospheric
dynamics in the long-term regional changes of EHD occurrence over the
different regions under different climate change scenarios. This is a natural
extension of this work. In addition, the methodology applied here could be
extended to other extreme events such as floods, droughts, heat waves, etc.
The robustness of the regional series as well as the identification of the
best large-scale atmospheric variables characterizing such events could be of
crucial importance when trying to relate regional extreme behaviour to
atmospheric dynamics.