In the last decades, extremely hot summers (hereafter extreme
summers) have challenged societies worldwide through their adverse
ecological, economic and public-health effects. In this study, extreme
summers are identified at all grid points in the Northern Hemisphere in the
upper tail of the June–July–August (JJA) seasonal mean 2 m temperature (T2m)
distribution, separately in ERA-Interim (ERAI) re-analyses and in 700 simulated
years with the Community Earth System Model (CESM) large ensemble for
present-day climate conditions. A novel approach is introduced to
characterise the substructure of extreme summers, i.e. to elucidate whether
an extreme summer is mainly the result of the warmest days being anomalously
hot, of the coldest days being anomalously mild or of a general shift
towards warmer temperatures on all days of the season. Such a statistical
characterisation can be obtained from considering so-called rank day
anomalies for each extreme summer – that is, by sorting the 92 daily mean T2m
values of an extreme summer and by calculating, for every rank, the
deviation from the climatological mean rank value of T2m.
Applying this method in the entire Northern Hemisphere reveals spatially
strongly varying extreme-summer substructures, which agree remarkably well
in the re-analysis and climate model data sets. For example, in eastern India
the hottest 30 d of an extreme summer contribute more than 65 % to the
total extreme-summer T2m anomaly, while the colder days are close to
climatology. In the high Arctic, however, extreme summers occur when the
coldest 30 d are substantially warmer than they are climatologically. Furthermore, in
roughly half of the Northern Hemisphere land area, the coldest third of
summer days contributes more to extreme summers than the hottest third, which
highlights that milder-than-normal coldest summer days are a key ingredient
of many extreme summers. In certain regions, e.g. over western Europe and
western Russia, the substructure of different extreme summers shows large
variability and no common characteristic substructure emerges. Furthermore,
we show that the typical extreme-summer substructure in a certain region is
directly related to the region's overall T2m rank day variability pattern.
This indicates that in regions where the warmest summer days vary
particularly strongly from one year to the other, these warmest days are
also particularly anomalous in extreme summers (and analogously for regions
where variability is largest for the coldest days). Finally, for three
selected regions, thermodynamic and dynamical causes of extreme-summer
substructures are briefly discussed, indicating that, for instance, the
onset of monsoons, physical boundaries like the sea ice edge or the
frequency of occurrence of Rossby wave breaking strongly determines the
substructure of extreme summers in certain regions.
Introduction
During the last decades, numerous high-impact hot-temperature extremes
occurred on approximately seasonal timescales, including the extremely hot
European summer in 2003 (Fink et al., 2004; Schär
and Jendritzky, 2004), the 2010 Russian heat wave (Barriopedro et al., 2011), the hot and dry summer of 2015 in
Europe (Dong et al., 2016; Hoy et al., 2017;
Orth et al., 2016), the hot and humid summer of 2015 in western India and
Pakistan (Wehner et al., 2016), and the concurrent heat waves
across the Northern Hemisphere in the summer of 2018 (Vogel et al., 2019). It is well known that individual
heat waves on timescales of up to a few weeks cause societal challenges,
for example serious public-health issues (e.g.
Fouillet et al., 2006). However, the large socio-economic and ecological
impacts of the seasonal events listed above (e.g.
Ciais et al., 2005; Buras et al., 2019) illustrated that many economic
sectors such as agriculture, tourism and re-insurance are particularly
susceptible to temperature extremes on seasonal (as opposed to synoptic)
timescales. Therefore, understanding the statistical properties of entire
extremely hot summers (hereafter referred to as “extreme summers”) as well
as their physical causes is a research topic of high societal relevance.
The concept of an extreme summer is closely related to the concept of a heat
wave, even though there are important differences. An individual heat wave
is commonly understood to be a single, quasi-continuous episode of
abnormally hot surface weather with a duration ranging from days to weeks (Russo et al., 2015; Zschenderlein et al., 2019).
Heat waves are thus strongly influenced by individual synoptic flow features
such as atmospheric blocks (Brunner et al., 2017;
Pfahl and Wernli, 2012; Röthlisberger and Martius, 2019; Zschenderlein
et al., 2019), stationary ridges (Sousa et al., 2018) or
recurrent Rossby wave patterns (Röthlisberger et al.,
2019). In contrast, extreme summers have a fixed duration (of 3 months),
which is beyond the timescale of these synoptic flow features.
Consequently, extreme summers require a temporal organisation of the
relevant synoptic flow features, which can occur either “by chance”
(internal atmospheric variability) or favoured by more slowly varying
processes. Possible candidates for the latter are soil moisture fluctuations (Fischer
et al., 2007; Lorenz et al., 2010; Seneviratne et al., 2010), sea ice
dynamics (Cohen et al., 2014), or large-scale modes of
variability in the ocean and atmosphere (e.g.
Schneidereit et al., 2012). Understanding how this temporal organisation of
weather within seasons occurs is challenging, as it requires a seamless
approach (Hoskins, 2013), which couples weather system dynamics
to these slower varying processes.
Like any other summer, an extreme summer will inevitably contain cooler and
hotter days, which constitute the upper and lower parts of the daily mean 2 m temperature (T2m) distribution during that summer. However it is currently not known which
part of the T2m distribution is particularly anomalous during an extreme
summer. Thus, extreme summers with distinct “substructures” might occur,
some of which are schematically illustrated in Fig. 1. For example, a summer
might be an extreme summer because the hottest days of the season are
particularly anomalous, with the remainder of the summer days being only
moderately warmer than or even close to climatology. Such an extreme-summer
substructure was observed in large parts of Europe in the summer of 2015, when
the anomalies of the seasonal hottest days exceeded those of the seasonal
mean by almost a factor of 2 (Dong et al., 2016). Hence the
hottest days of the 2015 summer contributed overproportionately to the
seasonal mean anomaly. However, also other substructures are plausible: a
suppression of cool summer days, a uniform shift in the entire summer
temperature distribution or any combination of these three options.
Schematic surface temperature evolution during extreme summers
with different substructures: an extreme summer arising from just one heat
wave (orange), from a suppression of cool summer days (green), from a
shift in the entire T2m distribution (blue) and from a general shift towards
higher temperatures and a heat wave (red). The schematic climatological
surface temperature evolution is depicted in grey.
Knowledge about the extreme-summer substructure is relevant for at least two
reasons. Firstly, the societal impact of an extreme summer featuring one period (or
several periods) of extremely hot temperatures (i.e. hottest summer days
being hotter than normal) will likely differ from the societal impact of
an extreme summer resulting primarily from a suppression of cool summer days
(i.e. coldest summer days being milder than normal) or from an extreme
summer characterised by a uniform shift in the entire temperature
distribution (i.e. all summer days warmer than normal). Secondly, also
the physical and meteorological causes of extreme summers with such distinct
substructures conceivably differ. Thus, identifying the substructure of
extreme summers is likely a starting point for understanding also their
physical causes.
The purpose of this study is to characterise extreme summers statistically
by quantifying their substructure. To do so, we define extreme summers in
the upper tail of the June–July–August (JJA) mean 2 m temperature (T2m)
distribution. Thereafter, the extreme-summer substructure is assessed by
decomposing the seasonal mean T2m anomaly of a particular extreme summer
into the contributions from all rank days of that season (i.e. the
contribution from the coldest day, the second-coldest day, etc.). This
decomposition thus allows quantifying the contributions from all parts of
the T2m distribution (e.g. the coldest, middle and hottest thirds of summer
days) to the seasonal T2m anomaly of an extreme summer.
Here we use the ERA-Interim (ERAI) re-analysis data set to study the substructure
of past extreme summers. However, extreme summers are by definition
extremely rare events. Thus, in order to yield robust results, a
climatological investigation of the extreme-summer substructure requires
much longer data records than provided by ERA-Interim or any other currently
available high-quality re-analysis data set. We therefore complement
ERA-Interim with a 700-year present-day climate simulation (for details, see
Sect. 2.2) to address the following research goals:
Propose and illustrate a simple method for decomposing, at each grid point,
the seasonal mean temperature anomaly into its contributions from each rank
day.
Use this decomposition to analyse the substructure of extreme summers
separately at selected grid points.
Quantify and compare the spatial variability in extreme-summer substructures
in the Northern Hemisphere in both re-analysis and climate model data.
Illustrate physical causes of the observed (and simulated) extreme-summer
substructures in selected regions.
Data and methodsERA-Interim
We use ERA-Interim re-analysis data (Dee
et al., 2011) covering the period 1979–2018. ERA-Interim is originally
produced with a T255 spectral horizontal resolution and 60 hybrid σ–p levels in the vertical. We interpolated the data horizontally to a
1∘ by 1∘ grid and vertically to pressure and isentropic
levels. The ERA-Interim data are provided at 6-hourly time intervals; in this
study however, we aggregated all data to a daily temporal resolution.
Besides the T2m fields, we also use potential vorticity (PV), total
precipitation, 250 hPa meridional winds and sea ice concentration.
Furthermore, we remove a (40-year) linear trend from all JJA T2m data at
each grid point. Our analyses hereafter are based on the detrended data,
except for Figs. 2, 8 and 9, which are more easily understood based on the
non-detrended data (Figs. 2 and 8) or where the absolute T2m values are
important (Fig. 9).
Steps in computing RDAd,kERAI values at the grid point
closest to Zurich, Switzerland (47∘ N, 9∘ E). Values
for the 1994 summer are highlighted in red. Panel (a) shows ERA-Interim T2m
at 47∘ N, 9∘ E, for all 40 ERA-Interim summers. The sorted
T2m values (Td,kERAI) are shown in panel (b) and the
RDAd,kERAI values in panel (c). Note that for illustrating
purposes Fig. 2 presents non-detrended T2m data.
CESM
Besides ERA-Interim, the Community Earth System Model version 1 (CESM;
Hurrell et al., 2013) is used to perform present-day climate simulations
using restart files from the CESM large ensemble project
(CESM-LE.; Kay et al., 2015). We use atmospheric fields at daily temporal resolution,
with a horizontal resolution of approximately 1∘ and 30 vertical
levels. The original CESM-LE data contain a 35-member ensemble of
simulations started on 1 January 1920 and integrated forward in time until
2100. These 35 “macro-ensemble” members were rerun for the period from 1 January 1990 to 31 December 1999 in order to obtain temporally
high-resolution three-dimensional model output. To further increase the
number of simulated JJA seasons, a “micro-ensemble” with additional 35
members was initialized from member one of the macro-ensemble, on 1 January
1980, by adding an O(10-13) perturbation to the initial atmospheric
temperature field of each micro-ensemble member. These additional micro-ensemble
runs are then integrated forward in time until 31 December 1999. Fischer et al. (2013) have shown that at the latest
after a decade, the micro-ensemble members exhibit a similar spread in
atmospheric variables compared to members of the macro-ensemble. Thus, for
the period 1990–1999, the micro-ensemble members can be regarded as
additional independent members, yielding a total of 70 ensemble members
covering the 10-year period from 1990 to 1999, i.e. 700 years of present-day
climate. As for ERA-Interim data, a linear trend is removed from all JJA T2m
data at each grid point and in each ensemble member. Note, however, that due
to the ensemble set-up, this trend is calculated over only 10 years.
Decomposing a seasonal T2m anomaly to quantify the season's substructure
To examine the substructure of a particular July–August (JJA) season k,
we decompose its seasonal T2m anomaly (SAk) into contributions from
the ranked D daily T2m values of season k, where D is the number of
days in season k (e.g. for JJA, D=92). We thus aim to quantify how much
each rank day (i.e. coldest day, second-coldest day, etc.) of season k
contributes to the seasonal anomaly SAk. This decomposition of
SAk is illustrated for the example grid point 47∘ N, 9∘ E (near Zurich, Switzerland), in Fig. 2 and introduced
more formally below. It is applied to both data sets separately in exactly
the same fashion, and, therefore, a superscript M∈{ERAI,CESM} will only be
used where it is necessary to explicitly distinguish between the two
data sets. All the important statistical quantities used in this study are
summarised in Table 1. Furthermore, bear in mind that all these quantities
are calculated at each grid point individually.
Definitions and descriptions of important quantities used in this
study.
SymbolFormal definitionDescriptionTd,kDaily mean T2m with rank d in season k (Fig. 2b)SMk1D∑d=1DTd,kSeasonal mean T2m of season kC1K⋅D∑k=1K∑d=1DTd,kClimatological JJA seasonal meanSAkSMk-CSeasonal anomaly of season kRDMd1K∑k=1KTd,kRank day mean of rank dRDAd,kTd,k-RDMdRank day anomaly of rank d in season k (Figs. 2c, 3b–e, 4b–e)XM1N∑k∈XSMkMean of N considered extreme summersXAXM-CMean anomaly of N considered extreme summers (Figs. 3a, 4a)SFcold,k1D∑d=1D3RDAd,k/SAkFractional contribution from the coldest third of summer days of season k to SAkXFcold1N∑k∈X1D∑d=1D3RDAd,k/XAFractional contribution from coldest third of extreme-summer days to XA (Fig. 5)V1K⋅D∑k=1K∑d=1D(RDAd,k)2Variance of all RDAd,k values at a particular grid point (Figs. 6a, 7a)VFcold1K⋅D∑k=1K∑d=1D3(RDAd,k)2/VFractional contribution from the coldest third of all summer days to V (Figs. 6b, c, 7b, c)
We start by ranking all daily mean T2m values within their respective season
k (Fig. 2a, b) and computing seasonal means (SMk), i.e.
SMk=1D∑d=1DTd,k,k=1,…,K,
where Td,k is the daily mean T2m value with rank d in season k
(i.e. the temporal ordering of the days is lost; see Fig. 2b). At each grid
point we thus compute KERAI=40 seasonal mean values for ERA-Interim and
KCESM=700 values for CESM.
The climatological seasonal mean (C) is also calculated from the ranked
daily mean T2m values (Td,k) as
C=1K⋅D∑k=1K∑d=1DTd,k=1D∑d=1D1K∑k=1KTd,k.
Hereby, 1K∑k=1KTd,k is the average T2m value
of all K days with rank d in their respective season, e.g. for d=1
the average coldest day of the season and for d=92 the average hottest day
of the season. Hence, C is computed as the mean over the average T2m
values for each rank. These rank day T2m means (bold grey contour in Fig. 2b) are hereafter referred to as
RDMd=1K∑k=1KTd,k,d=1,…,D.
Using the RDMd, the seasonal T2m anomaly of any season k
(SAk) can be decomposed into contributions from each of the D rank
days:
SAk=SMk-C=1D∑d=1DTd,k-∑d=1DRDMd=1D∑d=1DTd,k-RDMd=1D∑d=1DRDAd,k,
where in the last equality the rank day anomaly of the day with rank d in
season k is introduced as RDAd,k=Td,k-RDMd. In other words,
the seasonal mean anomaly SAk is expressed as the average rank day
anomaly (see also Fig. 2c).
This decomposition of SAk thus allows assessing the exact
contribution from each (ranked) day of season k to SAk. For
example, if for a particular season kSAk=1 K and RDA92,k=3 K (i.e, the hottest day of season k is 3 K warmer than the respective rank
day mean) this day contributed 3/92=0.0326 K, or 3.26 %, to the
seasonal anomaly SAk. In the following we split the 92 d of each
JJA season k into three parts according to their rank and focus on the
relative contributions to SAk from the coldest, middle and hottest
third of the 92 d of season k by calculating
SFcold,k=1D∑d=1D3RDAd,k/SAk.
The notation [x] hereby stands for x rounded to the nearest
integer. For computing contributions to SAk from the middle and
hottest thirds of the summer days (SFmiddle,k and SFhot,k), the
sum in Eq. (5) runs from D3+1 to D23 for SFmiddle,k and from D23+1 to D for SFhot,k. By construction, the sum of the three
fractions amounts to 1.
Identification and substructure of extreme summers
Extremely hot summers at each grid point in the Northern Hemisphere are
identified in the ERA-Interim (CESM) data set as the five (35) hottest JJA
seasons, yielding two sets of extreme summers, XM={k1,…,kNM}, M∈{ERAI,CESM}, with NERAI=5 and NCESM=35 members,
respectively. Hence, ERA-Interim extreme summers correspond to the 12.5 %
hottest summers (5 out of 40), while the CESM extreme summers correspond to
the 5 % hottest summers (35 out of 700).
An analogous procedure to that described in Sect. 2.3 is employed to
quantify the contributions from each of the three thirds of the extreme-summer days to the average T2m anomaly of the N considered extreme
summers. The mean of these extreme summers (XM) is calculated as
XM=1N∑k∈XSMk and is used to compute the
mean anomaly of these extreme summers, XA=XM-C. The relative contributions
from the three thirds of the summer days to the extreme-summer anomaly XA are calculated as, for example,
XFcold=1N∑k∈X1D∑d=1D3RDAd,k/XA.
The quantities XFcold, XFmiddle and XFhot again add
up to 1 and quantify the relative contributions from the three thirds to the
average T2m anomaly of all extreme summers at a particular grid point. Note
that the quantities XFcold, XFmiddle and XFhot
characterise the mean extreme-summer substructure at a particular grid
point, while SFcold,k, SFmiddle,k and SFhot,k characterise
the substructure of a single season k.
Results and discussionExtreme-summer T2m anomalies
Figures 3a and 4a depict the average T2m anomalies during extreme summers in
the two data sets (XAERAI and XACESM, respectively). In both
data sets, XA exhibits considerable spatial variability. The ERA-Interim
extreme summers have temperature anomalies of up to 3 K over western Russia,
while over some tropical ocean areas XAERAI is less than 0.5 K (Fig. 3a). The XACESM field exhibits a generally similar spatial pattern to
XAERAI, with larger values over land than over the oceans (Fig. 4a).
However, XACESM generally exceeds XAERAI, as the summers
XCESM are statistically more extreme than the summers XERAI. In
the following, we decompose the extreme-summer T2m anomalies (XA) shown in
Figs. 3a and 4a using the methodology described in Sect. 2.3 and 2.4, first
at few selected grid points and then for all Northern Hemisphere grid
points.
Extreme-summer T2m anomaly and extreme-summer substructure for
selected grid points in ERA-Interim. Panel (a) depicts XAERAI; panels (b)–(e) show RDAd,kERAI for the five ERA-Interim extreme
summers in colours and for the remaining summers in light grey. Crosses in
panel (a) indicate the grid points for which the RDAd,kERAI values
are shown in panels (b)–(e).
Extreme-summer T2m anomaly and extreme-summer substructure for
selected grid points in CESM. Panel (a) displays
XACESM, and panels (b)–(e) show in red the maximum
and minimum (dotted) 90th and 10th percentile (dashed) and the
median (solid red)
RDAd,kCESM of the 35 CESM
extreme summers. The 5th- to 95th-percentile range of the
RDAd,kCESM of all JJA seasons
is depicted in grey. Crosses in panel (a) indicate the grid points for
which the rank day anomalies are shown in panels (b)–(e).
Extreme-summer substructures at selected grid points
The rank day anomalies (RDAd,kERAI) for the five ERA-Interim
extreme summers at a grid point located in eastern India (21∘ N, 81∘ E; Fig. 3a, b) reveal a similar substructure in at least
four of the extreme summers. The largest RDAd,kERAI values (up to 5 K)
occur in the hottest 30 d of each season, while for the 60 coldest summer
days in each extreme summer, RDAd,kERAI does not exceed 1.5 K. The
contributions of the coldest, middle and hottest third of all extreme-summer
days to XAERAI at this grid point (i.e.
XFcoldERAI, XFmiddleERAI and XFhotERAI) are
13 %, 20 % and 67 %, respectively. For the 2005 summer, the
contributions were -1 %, 6 % and 95 %, and, hence, almost the entire
seasonal T2m anomaly resulted from the hottest 30 d of the summer being
hotter than normal.
A comparison between the ERA-Interim and CESM extreme-summer substructures
at this grid point (Figs. 3b and 4b) reveals remarkable qualitative
similarities between the extreme-summer substructure at 21∘ N, 81∘ E, in the two data sets. At this grid point, also the seasons
XCESM exhibit their largest RDAd,kCESM values for the 30 hottest
summer days. Moreover, despite the different number of seasons in the two
data sets, the XFcoldCESM, XFmiddleCESM and XFhotCESM values of 11 %, 24 % and 65 %, respectively, are
not far off the respective values for the seasons XERAI. Figures 3b and
4b further reveal that the largest RDAd,kCESM values reach much
larger values (up to 8 K) than the RDAd,kERAI values, which is an
expected result, since the seasons XCESM are statistically more extreme
than the seasons XERAI.
Considering now the grid point 39∘ N, 116∘ W, in Nevada,
US, we find a substantially different ERA-Interim extreme-summer
substructure compared to eastern India (Fig. 3b, c), with largest extreme-summer RDAd,kERAI values in the coldest third of the summer days
and XFcoldERAI=49 %, XFmiddleERAI=31 % and XFhotERAI=20 %. Also for this grid point, the mean
substructure of CESM extreme summers is similar to that of ERA-Interim
extreme summers, with XFcoldCESM=42 %, XFmiddleCESM=33 % and XFhotCESM=25 % (Fig. 4c). Thus, at this grid point, all thirds of the T2m distribution contribute
to extreme summers, but the contribution from the coldest third is overproportionately large (i.e. considerably larger than 33 %). Hence, the
re-analysis and the climate model data both suggest that the suppression of
cool summer days (leading to coldest days of the summer that are milder than
usual) is a key ingredient for extreme summers at 39∘ N, 116∘ W.
A further extreme-summer substructure is apparent at the grid point
closest to Paris, France (49∘ N, 2∘ E; Figs. 3d, 4d). At
this grid point, the ERA-Interim extreme summer of 2018 was characterised by
RDAd,kERAI values of 1.5–2 K for almost all ranks; i.e. this
summer resulted from an almost uniform shift in the entire T2m distribution.
Moreover, this grid point also illustrates that clearly distinct extreme-summer substructures can occur at the same grid point. While the extreme
summer of 2003 exhibited particularly large anomalies in the coldest and the
hottest third (SFcold,2003ERAI=34 %, SFmiddle,2003ERAI=28 % and SFhot,2003ERAI=38 %), the contribution from the coldest third
to the extreme summer 1995 was negative, and the middle and top third were
responsible for the entire seasonal anomaly
(SFcold,1995ERAI=-15 %, SFmiddle,1995ERAI=49 % and SFhot,1995ERAI=66 %; Fig. 3d).
Finally, the grid point 58∘ N, 35∘ E, in western Russia
(Fig. 3e) illustrates that, occasionally, the temperature variability during
individual seasons can be fundamentally different from all other seasons at
a particular grid point. Such a “regime shift” could be observed during
the extreme summer of 2010, which was characterised by RDAd,2010ERAI
values in excess of 4 K for ranks ∼40–92
(SFcold,2010ERAI=1 %, SFmiddle,2010ERAI=46 %
and SFhot,2010ERAI=53 %). For these ranks, the
RDAd,2010ERAI values were almost twice as large as for the second
hottest summer in these ranks (1981). The truly exceptional nature of the
2010 summer at 58∘ N, 35∘ E (e.g.
Barriopedro et al. 2011; Fig. 3e), becomes even more evident when comparing
its RDAd,kERAI values with those of the CESM extreme summers at
the same grid points (Fig. 4e). For some ranks, none of the 700 CESM JJA
seasons reach RDAd,kCESM values of comparable magnitude to those
observed during the 2010 summer at this grid point. Some implications of
this finding will be discussed in Sect. 4.
In summary, the mean extreme-summer substructure at these four grid points
is qualitatively remarkably similar for the 5 hottest ERA-Interim summers
and the 35 hottest CESM summers. On the one hand, this similarity implies
that the rank day anomaly patterns presented in Fig. 3b–e are not artefacts
of the rather short ERA-Interim period but must instead result from physical
processes that shape the local extreme-summer substructure. On the other
hand, these similarities suggest that the CESM is able to correctly capture
the processes that generate the distinct extreme-summer substructures at
these example grid points. We next compare the mean ERA-Interim and mean
CESM extreme-summer substructures at all grid points in the Northern
Hemisphere by considering the spatial patterns of XFcoldERAI, XFhotERAI, XFcoldCESM and XFhotCESM.
Spatial variability in ERA-Interim and CESM extreme-summer substructure
If extreme summers resulted from a uniform shift in the entire T2m
distribution, all three thirds of the T2m distribution would contribute
equally (i.e. 33 %) to XAERAI. However, the XFhotERAI
field (Fig. 5a) reveals a complex pattern of coherent regions with increased
(>33 %) or decreased (<33 %) contributions from the
hottest third of extreme-summer days to XAERAI. Land areas where
particularly large XFhotERAI values are found include the central
US; the UK; parts of northeastern Europe, India and southeastern Asia; and the southern Sahel region (Fig. 5a). In some of these areas,
SFhot,kERAI exceeded SFmiddle,kERAI and SFcold,kERAI
during at least four out of the five ERA-Interim extreme summers (stippling in Fig. 5a). In these regions, at least four out of the five extreme summers thus exhibited a
similar substructure. However, it is important to bear in mind that in other
regions the substructure of individual extreme seasons (i.e. SFcold,k,
SFmiddle,k and SFhot,k) may differ from the mean extreme season
substructure characterised by XFcold, XFmiddle and
XFhot. Furthermore, also in parts of the northern North Pacific and
northern North Atlantic, XFhotERAI is substantially increased and
reaches up to 60 %. In many regions, however, XFhotERAI is less
than 33 %, indicating that in these regions, extreme summers do not arise
primarily from the hottest 30 d of the summer being hotter than they are climatologically.
Spatial variability in the extreme-summer substructure in
ERA-Interim and CESM. Panels (a) and (b) depict XFhotERAI and
XFhotCESM, respectively, while XFcoldERAI and
XFcoldCESM are shown in panels (c) and (d). Stippled areas in all
panels indicate grid points at which the same third of the distribution
contributes the largest fraction of all thirds to at least 80 % of the
extreme summers (i.e. similar substructure in at least 80 % of the
extreme summers). Black crosses as in Fig. 3a.
In fact, in many regions it is the contribution to XAERAI from the
coldest third of the summer (XFcoldERAI) that is substantially
increased (Fig. 5c), for example in the southwestern US, the northern Sahel
region, Pakistan and parts of Greenland. Moreover, increased
XFcoldERAI values are also found in the southern North Pacific and
the southern North Atlantic as well as over the Arctic Ocean (Fig. 5c).
Overall, Fig. 5c clearly demonstrates that the coldest third of all summer
days contributes a substantial fraction to XAERAI in most regions
(more than 25 % over 83 % of the Northern Hemisphere land area in ERAI).
In fact, in 46 % of the Northern Hemisphere land area,
XFcoldERAI exceeds XFhotERAI; i.e. the coldest third of
extreme summers contributes more to XAERAI than the hottest third.
Consequently, in these regions the mechanisms that suppress unusually cool
summer days must be considered when assessing the physical causes of
extremely hot summers.
Comparing these results, which are derived from ERAI with results based on CESM, i.e.
XFhotERAI and XFhotCESM (Fig. 5a, b) as well as
XFcoldERAI and XFcoldCESM (Fig. 5c, d), unravels
strikingly similar patterns in many regions. For example, both data sets
agree (even quantitatively) that extreme summers in India and southeastern Asia
come about primarily by the hottest summer days being hotter than they are climatologically, while the coldest third of extreme-summer days only
contributes a marginal fraction to the respective XA. Also in the western
and central US, XFcold and XFhot agree very well between the
two data sets, with the cool summer days contributing an overproportionately
large fraction to XA in the western US and the hot summer days in the
central US. Further areas of remarkable agreement between
XFcoldERAI and XFcoldCESM (Fig. 5c, d) are the high
Arctic and the northern Sahel region. Moreover, in 49 % of the Northern
Hemisphere land area, XFcoldCESM exceeds XFhotCESM, which
compares well with the 46 % of the land area in which XFcoldERAI
exceeds XFhotERAI. Figure 5 thus clearly reveals that the CESM
reproduces many features of the observed extreme-summer substructure and its
variability in space to a remarkable degree.
However, there are also some areas of notable differences between
XFhotERAI and XFhotCESM as well as XFcoldERAI
and XFcoldCESM. For example over Greenland, Saudi Arabia and the
northern North Atlantic, there are substantial differences between
XFcoldERAI and XFcoldCESM (Fig. 5c, d). Moreover, over
the northern North Pacific as well as the high Arctic, the
XFhotCESM and XFhotERAI patterns agree only
qualitatively but not quantitatively (Fig. 5a, b). It is important to note,
though, that some differences in the XFcold and XFhot fields
for the two data sets are expected due to the different sample sizes, even
if the model was perfect. In the remainder of this paper we aim to explain
statistical and physical reasons behind selected aspects of the spatial
variability in XFcold and XFhot.
A statistical explanation for the observed extreme-summer substructures
Figures 3b and c and 4b and c clearly illustrate that, at the selected grid points
in India (21∘ N, 81∘ E) and in the US (39∘ N, 116∘ W), some rank days are climatologically much more variable
than others. Importantly, this is the case not just for extreme summers but
is rather a climatological characteristic of the local temperature
variability. For example, at 21∘ N, 81∘ E, the hottest 30 d of the summer are much more variable than the colder days. The 5th-
to 95th-percentile range of the RDA80,kCESM values is roughly
4 times larger than that of the RDA10,kCESM values (Fig. 4b).
At 39∘ N, 116∘ W, the largest rank day variability is
found for lower ranks, and the 5th- to 95th-percentile range of the
RDA80,kCESM values is roughly 2 times smaller than the same
percentile range of the RDA10,kCESM values (Fig. 4c). Similar
ratios are found when comparing the spread of RDA80,kERAI and
RDA10,kERAI for these two grid points (Fig. 3b, c). Moreover, at
both grid points extreme summers occur when the most variable rank days are
particularly hot (Figs. 3b and c and 4b and c). Hence, from a statistical point of
view, the extreme-summer substructure at these two particular grid points
appears to be largely determined by the local “rank day variability
pattern” – that is, the contributions to XA from the distinct rank days
during extreme summers depend on how variable the respective values
Td,k are climatologically.
We next assess whether the local rank day variability pattern also explains
the extreme-summer substructure at other Northern Hemisphere grid points. To
do so, we consider the variance (V) of the RDAd,k values of all
ranks and all JJA seasons at a particular grid point:
V=1K⋅D∑k=1K∑d=1DRDAd,k2.
Here we used the fact that the mean of the RDAd,k values is by
construction equal to zero, and thus their variance reduces to the average of
the squared RDAd,k values of all d and all k. The contribution
from the coldest third of summer days to V is then
VFcold=1K⋅D∑k=1K∑d=1D3RDAd,k2/V,
and the contributions from the middle and hottest third of the summer days to V are computed analogously.
The variance of RDAd,kERAI and its contributions from
the coldest and hottest third of summer days. Panel (a) depicts VERAI,
and panels (b) and (c) show VFhotERAI and VFcoldERAI,
respectively. Green contours in panels (b) and (c) depict CERAI gradient
magnitudes of 6 and 12 K 10-6 m-1. The CERAI gradient
magnitudes have been computed as first-order central differences and are
only plotted over oceans. Black crosses as in Fig. 3a.
The variance of RDAd,kCESM and its contributions from
the coldest and hottest third of summer days. Panel (a) depicts VCESM,
and panels (b) and (c) show VFhotCESM and VFcoldCESM,
respectively. Black crosses as in Fig. 3a.
The fields of VERAI and VCESM (Figs. 6a, 7a) resemble the
XAERAI and XACESM fields (Figs. 3a, 4a), as large rank day
anomalies are a prerequisite for large seasonal T2m anomalies. Furthermore,
comparing XFhotERAI and VFhotERAI (Figs. 5a and 6b)
clearly reveals that wherever the contribution from the hottest third of the
summer days to XAERAI is increased (XFhotERAI>33 %), the
rank day variability in the hottest third (quantified by
VFhotERAI) contributes overproportionately to VERAI. Figures 5c and 6c illustrate that the same relationship also holds for
XFcoldERAI and VFcoldERAI: regions where milder-than-normal cool summer days contribute overproportionately to XAERAI
(i.e. XFcoldERAI>33 %) exhibit increased VFcoldERAI
values. Figures 5b and d and 7b and c confirm this finding also for the CESM data.
We thus conclude that in both data sets, the extreme-summer substructure is
largely determined by the local rank day variability pattern.
Furthermore, comparing the patterns of VFhotERAI and
VFhotCESM (Figs. 6b, 7b) reveals agreement in the same regions
where also the patterns of XFhotERAI and XFhotCESM (Fig. 5a, b) agree, and, conversely, disagreement between VFhotERAI and
VFhotCESM also results in disagreement between XFhotERAI
and XFhotCESM. For example, the VFhotERAI and
VFhotCESM fields (and the XFhotERAI and
XFhotCESM fields) are almost identical in India and southeastern
Asia, the northern Sahel, the western US or eastern Europe (cf. Fig. 6b with
Fig. 7b and Fig. 5a with b). Over Saudi Arabia or the northern North Atlantic,
however, the patterns of VFhotERAI and VFhotCESM (and of
XFhotERAI and XFhotCESM) do not agree particularly well.
In summary, while the CESM correctly reproduces the local rank day
variability pattern in most regions, differences in the local rank day
variability patterns between the two data sets also lead to differences in
the extreme-summer substructures.
It is interesting to compare the VFcold and VFhot patterns
presented in Figs. 6 and 7 with the skewness of the local daily temperature
distributions, which has been studied extensively in the past (Donat and Alexander,
2012; Garfinkel and Harnik, 2017; Linz et al., 2018; Loikith et al., 2018;
Loikith and Neelin, 2015; Ruff and Neelin, 2012). The upper tail of a
positively skewed JJA T2m distribution, for example, is longer than the lower tail, which
is the case if the hottest summer days are more variable than the coldest
summer days (cf. Figs. 5b and c with Fig. S1 in the Supplement). Hence, explanations of distinct
skewness in daily T2m distributions also help to understand differences in
the rank day variability patterns and, subsequently, extreme-summer
substructures. Garfinkel and Harnik (2017) showed that the
winter low-level temperature distributions are positively skewed on the cold
side of the Northern Hemisphere storm tracks, primarily because there the
magnitude of warm-air advection exceeds that of cold-air advection. And,
vice versa, the winter low-level temperature distributions are negatively
skewed on the warm side of the Northern Hemisphere storm tracks, where the
magnitude of cold-air advection exceeds that of warm-air advection.
Consistent with their results, Figs. 6 and 7 depict more variable hot summer
days to the north and more variable cold summer days to the south of the
Northern Hemisphere storm tracks, where the horizontal gradients of T2m are
particularly large (see in particular green contours in Fig. 6b, c).
While this argument explains differences in the rank day variability and the
extreme-summer substructures in regions of strong surface temperature
gradients, Figs. 5–7 also reveal numerous rather small-scale features that
do not necessarily occur in regions of strong surface temperature gradients.
We therefore next analyse the extreme-summer substructure and its causes in
three example regions in more detail. Due to the similarity between the
ERA-Interim and CESM extreme-summer substructures, we restrict this analysis
to ERA-Interim data (except where mentioned otherwise).
(Examples of) physical causes of extreme-summer substructures
A particularly striking feature of Fig. 5 is the large contribution from the
hottest third of the summer days to XAERAI in India, illustrated
exemplarily for the grid point at 21∘ N, 81∘ E, in Fig. 3b. The general temperature evolution in JJA (i.e. considering all JJA
seasons) at this grid point follows a particular sub-seasonal pattern (Fig. 8a). In early June, ERA-Interim T2m values are highly variable and range
from 27 to almost 40∘ C, with a mean of 35∘ C on 1 June. Throughout June and the first half of July the climatological
T2m drops to approximately 26∘ C and remains at this level until
the end of August. Moreover, during that period, the variability in T2m is
much smaller than in early June. The extreme summers exhibit comparatively
high temperatures primarily in June, while in July and August their T2m
evolution does not differ substantially from other JJA seasons (Fig. 8a).
The drop of T2m in June is associated with the onset of the Indian summer
monsoon (Fig. 8b; e.g. Slingo, 1999). During most JJA
seasons, precipitation starts to fall already during the first half of June.
However, the extreme summers each featured very little precipitation for at
least the first 20 d of June, which suggests that extreme summers at this
grid point occur when there is an unusually late onset of the Indian summer
monsoon at this particular location. Moreover, the rank day variability
pattern at 21∘ N, 81∘ E, is easily understood from Fig. 8:
the hottest days of the season mostly occur in June and are associated with
dry conditions. The onset date of the monsoon determines how many dry (and
thus very hot) days occur in a JJA season; i.e. an early onset of the
Indian monsoon suppresses a large number of very hot days and a late onset
increases this number, which leads to the large temperature variability seen
in the warmest 30 d of the JJA season.
The JJA temperature and precipitation evolution at 21∘ N, 81∘ E. Panels (a) and (b) depict non-detrended ERA-Interim T2m
and accumulated precipitation at 21∘ N, 81∘ E, for all JJA
seasons, respectively. The extreme summers are highlighted in colours. The
dashed black line in panel (a) depicts the climatological calendar day mean T2m at
21∘ N, 81∘ E.
Arctic sea ice and local summer temperature variability. (a)XFcoldERAI (shading; only 70∘ N–90∘ N is
shown) and mean 1979–2018 JJA ERA-Interim sea ice concentration (green
contours indicate sea ice concentrations of 0.3, 0.5 and 0.7). (b) Empirical probability density function of non-detrended ERA-Interim T2m at
79∘ N, 42∘ E (red); 81∘ N, 42∘ E
(grey); and 83∘ N, 42∘ E (blue). Crosses in panel (a) locate
these three grid points.
A further noteworthy feature in Fig. 5 is the sharp boundary in the extreme-summer substructure around 75–80∘ N, for example in
the North Atlantic sector. North of this boundary, the coldest third of all
extreme-summer days contributes up to 60 % to the extreme-summer anomaly
(Fig. 5c, d). South of it, the contribution from the coldest third of
extreme-summer days is much smaller. (Quantitatively, there is some
disagreement between the CESM and ERAI extreme-summer substructures, but
both data sets agree about the general pattern.) This sharp boundary in the
extreme-summer substructure is co-located with the climatological sea ice
edge in JJA (Fig. 9a). Examining the JJA T2m distributions at three grid
points across this boundary (83∘ N, 42∘ W; 81∘ N, 42∘ W; and 79∘ N, 42∘ W) reveals that for T2m
below -1∘ C, their probability density functions (pdf's) of the
daily T2m values are almost identical, which is not surprising due to their
close spatial proximity. However, large differences in the three pdf's are
found for T2m at about 0∘ C and above. At 83∘ N, i.e.
north of the climatological sea ice edge (Fig. 9a), the pdf exhibits a very
short upper tail with very little probability density exceeding
+2∘ C (i.e. the pdf is strongly negatively skewed), while at
79∘ N (i.e. south of the climatological sea ice edge) the upper
tail is much more variable. The geographical co-location of this extreme-summer substructure boundary and of the climatological sea ice edge is
striking and suggests that the contrasting substructures arise because the
sea ice buffers “warm” temperatures at 0∘ C – that is, air with
T2m >0∘ C is cooled down to close to 0∘ C by
the induced sea ice melting. The same effect has also been shown to shorten
the upper tail of the surface temperature pdf over snow-covered areas (Loikith et al., 2018).
As a third example, we return to the grid point in Nevada, US (at
39∘ N, 116∘ W), where the rank day variability is largest
for the cold summer days and extreme summers occur when the coldest 30 d
exhibit mostly large positive rank day anomalies (Figs. 3c and 4c). Thus, at
this grid point, milder-than-normal coldest days of the summer (or,
equivalently, suppressed cool summer days) are a key ingredient for extreme
summers. We therefore briefly explore why, at this grid point, the coldest
summer days during extreme summers are warmer than normal.
(a) T2m difference between the 100 climatologically coldest JJA
days and the 100 coldest extreme-summer days (shading). Contours depict the
composite PV field at 335 K (contours of 2, 3.5 and 5 PVU) for the 100
climatologically coldest JJA days (blue) and for the 100 coldest extreme-summer days (red). The yellow cross indicates 39∘ N, 116∘ W. Panels (b) and (c) depict composite Hovmöller diagrams of the
anomalous 250 hPa meridional wind, averaged between 35 and
65∘ N, and temporally centred on the 100 climatologically coldest
JJA days (b) and on the 100 coldest extreme-summer days (c). Meridional wind
anomalies are calculated relative to the 1979–2018 mean JJA meridional
wind. The vertical line in panel (b) and (c) indicates 116∘ W.
We first investigate what makes the climatologically coldest summer days at
39∘ N, 116∘ W, particularly cold and then contrast them
with the coldest summer days during extreme summers at 39∘ N, 116∘ W. A composite analysis of the upper-level flow during the
100 climatologically coldest ERA-Interim days of all 1979–2018 summers
unravels a characteristic upper-level flow pattern: a highly amplified
Rossby wave pattern over the eastern North Pacific and North America, with a
breaking synoptic-scale trough covering 39∘ N, 116∘ W
(Fig. 10a). The breaking Rossby wave causing the trough is part of a
synoptic-scale and transient wave packet (Fig. 10b) which has just the right
phasing such that the trough axis crosses 39∘ N, 116∘ W,
when the amplitude of the trough is largest (Fig. 10b). This type of
relatively small-scale trough, shown here with contours of potential
vorticity on an isentrope in the upper troposphere (Fig. 10a), is relatively
slow-moving (Fig. 10b), such that the induced northwesterly low-level flow
along its western flank can lead to strong and persistent cold-air advection
to the western US. Additionally, the low-level flow induced by the trough
impinges on the topography at the US West Coast. Consequently, low-level air
masses that are advected into the western US are most likely forced to
ascend, which leads to adiabatic cooling of these already cool air masses and
finally results in the climatologically coldest summer days at
39∘ N, 116∘ W.
The composites for the 100 coldest days during extreme summers, in contrast,
do not reveal such a wave pattern (Fig. 10a and c). This indicates that
the flow pattern characteristic of the climatologically coldest days at this
grid point, i.e. the Rossby wave breaking and trough formation with the
phasing discussed above, simply did not occur very often during extreme
summers. Furthermore, a synoptic analysis of these 100 coldest extreme-summer days (not shown) reveals that the associated upper-level flow
configurations are rather variable, some featuring troughs while others even
exhibited low-amplitude ridges, resulting in the rather zonal composite
upper-level flow apparent in Fig. 10a and c.
The reason why such highly
amplified troughs with the right phasing did not occur during extreme summers at 39∘ N, 116∘ W, is currently unclear
and at the same time challenging to assess. Possibly, the exact longitude
where the synoptic-scale waves have been triggered (Röthlisberger et al., 2018) as well as the
strength and longitudinal extent of the North Pacific jet, which modulates
the waves' downstream propagation and breaking behaviour (e.g. Drouard et al. 2015),
might have played a role. However, both the jet strength and the
characteristics of the transient waves propagating along the jet are
strongly modulated by lower-frequency processes such as the Madden–Julian
Oscillation (Moore et al., 2010) and the
El Niño–Southern Oscillation (Drouard et al., 2015;
Shapiro et al., 2001). This example thus illustrates that a seamless
approach, combining processes on different timescales, is most likely
required to fully reveal the physical causes of extreme summers.
Summary and concluding remarks
In this study, extreme summers are defined in the upper tail of the JJA
seasonal mean T2m distribution at each grid point in the Northern Hemisphere
and then analysed with regard to their substructure. Hereby, the extreme-summer T2m anomaly is decomposed into its contribution from each rank day.
First, all days are ranked within their respective season (i.e. from rank 1
to 92 for JJA) and then compared to the climatological T2m of all days with
the same rank. The resulting rank day anomalies exactly quantify how much
each (rank) day contributes to the T2m anomaly of the respective season and
therefore allow for very intuitive statements about the characteristics of
extreme summers. For example, we show that during the 2010 summer at the
ERAI grid point at 58∘ N, 35∘ E, the 31 hottest days
contributed 53 % to the seasonal anomaly of 3.13 K and were each at least
4 K warmer than they are climatologically. This decomposition is applied to T2m data
from ERA-Interim as well as data from 700 simulated years with CESM for
present-day climate conditions. Thereby, the contributions from the coldest,
middle and hottest third of extreme summers to the extreme-summer T2m
anomalies are quantified at each Northern Hemisphere grid point
(XFcold, XFmiddle and XFhot).
This analysis reveals clearly distinct extreme-summer substructures,
occurring in coherent geographical regions. Despite the relatively small
scale of the structures in the XFcoldERAI and XFhotERAI
fields as well as different numbers of extreme summers in the two data sets,
CESM is able to reproduce these fields to a remarkable degree. This result
firstly underlines that the ERA-Interim extreme-summer substructures and
their spatial variability result from physical processes rather than too
short a data record and, secondly, testifies to the model's ability to
reproduce the physical processes responsible for the occurrence of extreme
summers in most regions in the Northern Hemisphere. Areas where CESM and
ERA-Interim extreme-summer substructures differ include Greenland, the
northern North Atlantic and the Arabian Peninsula.
Furthermore, a key finding of this study is that the mean extreme-summer
substructure is consistent with the shape of the underlying local T2m
distribution. The extreme-summer substructure is largely determined by which
of the 92 JJA rank days are most variable (i.e. the rank day variability
pattern), which is qualitatively related to the skewness of the T2m
distribution. Simply speaking, in regions where the coldest days of the
summer are most variable (i.e. negatively skewed T2m distribution), extreme
summers occur when the coldest days of the summer are unusually hot and,
analogously, for the case where hottest days vary the most (i.e. positively
skewed T2m distribution). This finding is relevant for two reasons. Firstly,
it constrains what kind of extreme-summer substructures can locally be
expected, in particular in regions with strongly skewed daily temperature
distributions. For example, extreme summers arising primarily from extremely
hot summer days (i.e. heat waves) are unlikely to occur in regions with
strongly negatively skewed temperature distributions. Secondly, some
individual extreme summers such as the 2010 summer at the grid point at
58∘ N, 35∘ E, featured clear temperature regime shifts,
with rank day anomalies far outside of what could be expected from their
climatological variability (e.g. almost twice as large as the second large
anomalies for the same ranks during the 2010 summer at 58∘ N, 35∘ E). The general consistency between the mean extreme-summer
substructure and the skewness of the underlying T2m distribution illustrates
that such regime shifts in the temperature variability during extreme
summers are the exception rather than the norm.
This consistency furthermore allows us to rely on previous work on physical
causes of skewed surface temperature distributions for interpreting our
results. Consistent with the findings of Garfinkel and
Harnik (2017), we find distinct extreme-summer substructures relative to the
location of large surface temperature gradients, in particular in the
Northern Hemisphere storm track regions. Extreme summers occurring north of
the Northern Hemisphere storm tracks have large contributions from the
hottest third of summer days, and south of the storm tracks the
contributions from the coldest days are largest. This is primarily because
on the cold side of a temperature gradient, warm-air advection can reach
much larger magnitudes than cold-air advection, and vice versa on the warm
side (e.g. Garfinkel and
Harnik, 2017; Linz et al., 2018; Tamarin-Brodsky et al., 2019). Moreover,
the few areas where the ERA-Interim and CESM extreme-summer substructures
differ also have distinct rank day variability patterns in ERA-Interim and
CESM. Thus, the climate model's ability to reproduce the ERA-Interim extreme-summer substructures in most places results largely from the model's ability
to produce local rank day variability patterns that agree with ERA-Interim.
However, three case studies illustrate that the extreme-summer substructure
cannot always be explained by temperature advection alone. In eastern India,
more than 65 % of the extreme-summer T2m anomaly results from the hottest
30 d of JJA being hotter than they are climatologically. At the considered grid
point, T2m exhibits a distinct sub-seasonal pattern, as it typically drops
by almost 10 K with the onset of the Indian summer monsoon. Thus, the
hottest days of the season (occurring in June) are highly variable, and
extreme summers occur in seasons with particularly late monsoon onsets.
In the high Arctic the highest surface temperatures are buffered around
0∘ C, as excess heat would result in sea ice melting and
subsequent latent cooling. Hence, the cold part of the T2m distribution
accounts for most of the rank day anomaly variance, and, consequently,
extreme summers occur when the coldest summer days are warmer than normal.
This buffering effect of the Arctic sea ice leads to a strong boundary in
the extreme-summer substructure around 75–80∘ N,
i.e. near the climatological JJA sea ice edge.
At a grid point in the western United States, all parts of the T2m
distribution contribute significantly to extreme summers; however, an overproportionately large fraction comes from the coldest third of the extreme-summer days (i.e. the coldest extreme-summer days are warmer than their
rank day mean). Composites of the upper-level flow during the 100
climatologically coldest summer days reveal that an amplified upper-level
flow pattern with a particular phasing of a prominent trough and its
associated cold-air advection is characteristic of the climatologically
coldest summer days at this grid point. This particular flow pattern did not
occur frequently during the extreme summers, leading to milder-than-normal cool summer days. This result is consistent with previous work on physical
causes of non-Gaussian temperature distributions (Garfinkel and Harnik, 2017; Linz et
al., 2018; Tamarin-Brodsky et al., 2019), as it highlights the role of
temperature advection by transient waves in generating a non-uniform rank
day variability pattern, or similarly, a skewed T2m distribution.
Overall, the case studies illustrate that for understanding the physical
causes of extreme summers, a seamless approach is necessary, which combines
weather system dynamics, local thermodynamics and surface–atmosphere
interactions as well as lower frequency variability in the atmosphere and
the ocean. Clearly, distinct physical causes might lead to similar extreme-summer substructures, in particular when comparing regions that are far
apart (e.g. the northern Sahel region and the high Arctic; Fig. 5).
However, similar extreme-summer substructures in neighbouring regions
conceivably also point to similar physical causes of extreme summers (e.g.
the Asian Monsoon region). Therefore, the extreme-summer substructure is a
helpful tool for discriminating between neighbouring regions with distinct
physical causes of extreme summers and might also be helpful for identifying
coherent regions with similar physical causes of extreme summers.
A further key result of this study is that in most places, the cool summer
days contribute substantially to extreme-summer T2m anomalies (more than
25 % over 83 % of the Northern Hemisphere land area in ERAI). In fact, Fig. 5 reveals that for ERA-Interim (CESM) in 46 %
(49 %) of the Northern Hemisphere land area, the coldest third of the
summer contributes more to the extreme-summer anomaly (XA) than the
hottest third. Thus, large positive seasonal temperature anomalies (i.e.
extreme summers as opposed to individual heat waves) cannot be understood
and explained by only considering the physical drivers of heat waves.
Rather, the processes which suppress the occurrence of cold summer days must
also be considered. These processes, though, are so far virtually unexplored and
thus possibly yield an untapped potential for improving our understanding of
extreme summers. However, as illustrated by the example of extreme summers
in the western US, the processes that suppress the occurrence of cold summer
days sometimes seem rather intangible, as they do not necessarily manifest
themselves in the occurrence of an unusual flow pattern but rather in the
non-occurrence of the particular flow pattern that typically produces the coldest
summer days.
This study has illustrated that extreme summers across the Northern
Hemisphere have distinct substructures, which result directly from the
physical causes of the extreme summers. However, the concept of the extreme
season substructure has applications beyond what has been presented in this
study and thus calls for subsequent studies. Firstly, the presented analyses
could be extended to the Southern Hemisphere and other seasons and
variables. (The application of the technique is most promising for variables
that are potentially unbound and variable on both ends, i.e. not for a
positive definite variable like precipitation.) Secondly, the concept of a
“season substructure” can be relevant for field campaigns, as the
representativeness of the campaigns' measurements depends on how
representative the time period of the campaign was (Wernli et al., 2010). Thirdly,
extreme summers with distinct substructures conceivably have different
societal effects, and thus future research should assess whether or not and
where the extreme-summer substructure is affected by climate change. The
results of this study suggest that the CESM is a suitable tool for this
task, as it is largely able to reproduce the observed (ERA-Interim) extreme-summer substructure in the current climate. However, some of the extreme
summers observed within the last 40 years appear to be outside of the
spectrum of 700 years of CESM. Hence, while CESM is able to reproduce the
local extreme-summer substructures, it may not be able to reproduce the most
extreme summers that are physically possible in some regions. Clearly, this
finding requires detailed and critical further investigation. Finally,
changes in the extreme-summer substructure with climate change must be
related to changes in the physical causes of extreme summers, as a uniform
warming would not affect the local rank day variability pattern. Therefore,
contrasting extreme-summer substructures in present and future climate
simulations might also help to identify regions where the physical causes of
extreme summers are altered by climate change.
Data availability
ERA-Interim data can be downloaded from the ECMWF web page
at: https://apps.ecmwf.int/datasets/data/interim-full-daily/levtype=sfc/ (European Centre for Medium-Range Weather Forecasts, 2020).
The CESM T2m data used here are available upon request from the authors.
The supplement related to this article is available online at: https://doi.org/10.5194/wcd-1-45-2020-supplement.
Author contributions
MR and HW conceived the study, MS provided technical support, UB performed
the CESM simulations, and MR analysed the data and wrote the major part of the
paper. HW, EF, MS and UB also contributed to writing the paper
and commented on earlier versions of this paper.
Competing interests
The authors declare that they have no conflict of interest.
Acknowledgements
Maxi Boettcher (ETH Zürich) and Lukas Papritz (ETH Zürich) are
acknowledged for helpful discussions during different stages of this work;
Gary Strand (NCAR) and Clara Deser (NCAR) are acknowledged for providing the CESM restart
files; and two anonymous reviewers are acknowledged for providing thoughtful, challenging
yet encouraging reviews.
Financial support
This research has been supported by the H2020 European Research Council (INTEXseas (grant no. 787652)).
Review statement
This paper was edited by Peter Knippertz and reviewed by two anonymous referees.
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