Historical Trends and Variability in Heat Waves in the United Kingdom

Abstract

Increases in numbers and lengths of heat waves have previously been identified in global temperature records, including locations within Europe. However, studies of changes in UK heat wave characteristics are limited. Historic daily maximum temperatures from 29 weather stations with records exceeding 85 years in length across the country were examined. Heat waves were defined as periods with unusually high temperatures for each station, even if the temperatures would not be considered warm in an absolute sense. Positive trends in numbers and lengths of heat waves were identified at some stations. However, for some stations in the south east of England, lengths of very long heat waves (over 10 days) had declined since the 1970s, whereas the lengths of shorter heat waves had increased slightly. Considerable multidecadal variability in heat wave numbers and lengths was apparent at all stations. Logistic regression, using a subset of eight stations with records beginning in the nineteenth century, suggested an association between the Atlantic Multidecadal Oscillation and the variability in heat wave numbers and lengths, with the summertime North Atlantic Oscillation playing a smaller role. The results were robust against different temperature thresholds.

Full text

atmosphere
Article
Historical Trends and Variability in Heat Waves in the
United Kingdom
Michael G. Sanderson 1, *ID , Theo Economou 1,2 ID , Kate H. Salmon 1and Sarah E. O. Jones 1,3
1Met Office, Exeter EX1 3PB, UK; t.economou@exeter.ac.uk (T.E.); kate.salmon@metoffice.gov.uk (K.H.S.);
saraheojones@gmail.com (S.E.O.J.)
2College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter EX4 4QF, UK
3JBA Consulting, Skipton BD23 1FJ, UK
*Correspondence: michael.sanderson@metoffice.gov.uk; Tel.: +44-1392-885680
Received: 9 August 2017; Accepted: 25 September 2017; Published: 30 September 2017
Abstract:
Increases in numbers and lengths of heat waves have previously been identified in global
temperature records, including locations within Europe. However, studies of changes in UK heat
wave characteristics are limited. Historic daily maximum temperatures from 29 weather stations with
records exceeding 85 years in length across the country were examined. Heat waves were defined as
periods with unusually high temperatures for each station, even if the temperatures would not be
considered warm in an absolute sense. Positive trends in numbers and lengths of heat waves were
identified at some stations. However, for some stations in the south east of England, lengths of very
long heat waves (over 10 days) had declined since the 1970s, whereas the lengths of shorter heat waves
had increased slightly. Considerable multidecadal variability in heat wave numbers and lengths was
apparent at all stations. Logistic regression, using a subset of eight stations with records beginning in
the nineteenth century, suggested an association between the Atlantic Multidecadal Oscillation and
the variability in heat wave numbers and lengths, with the summertime North Atlantic Oscillation
playing a smaller role. The results were robust against different temperature thresholds.
Keywords: heat waves; UK; climate variability; logistic regression; temperature; AMO; NAO
1. Introduction
Heat waves, a period of consecutive days with unusually warm temperatures, have a diverse
range of impacts on society. Mortality is often elevated, especially in people over 65 years old [
1
].
Sustained high temperatures during heat waves increase the likelihood of railway tracks buckling,
leading to speed restrictions, longer journey times or even closure of the line in extreme cases [
2
]. In
addition, heat waves are often accompanied by droughts, leading to reduced water availability for
irrigation and drinking water supplies. River temperatures are often raised during heat waves [
3
],
which can cause serious problems for cooling of power stations. Lower river and lake levels during
heat waves can lead to algal blooms, causing mass mortality of fish and birds and posing a serious
health threat to both animals and humans [4].
Positive trends in numbers and lengths of heat waves have been found over much of Europe.
One study [
5
] found that average summer heat wave lengths in western Europe had increased by
about 1.3 days per century between 1880 and 2005. Another [
6
] identified an increase in the frequency
of heat waves of 0.6 per decade in the Spanish central plateau between 1961 and 2010. In the Southern
Alpine region, the lengths of the longest heat waves had increased by 2.7 days per century over the
period 1874–2015 [
7
]. A study of heat waves in Lublin, south east Poland [
8
], used data recorded over
1951–2015. The number of heat waves over this period had not changed, but heat waves after about
1990 had higher maximum temperatures and longer durations. Significant positive trends in numbers
Atmosphere 2017,8, 191; doi:10.3390/atmos8100191 www.mdpi.com/journal/atmosphere

Atmosphere 2017,8, 191 2 of 17
of heat wave days and heat wave lengths were identified in many south eastern European cities [
9
],
although the period of data used was fairly short (1980–2015). In a study of heat waves in Ukraine
using temperatures recorded over 1951–2011, the largest numbers of heat waves were found in the
most recent decade (2001–2010), and the fewest in 1961–1970 and 1971–1980 [
10
]. In contrast, large
variations in numbers of hot days and lengths of heat waves between 1901 and 2003 were found for
Basel, Switzerland, but no long-term trends [11].
Only two studies have investigated heat wave trends in the UK, both of which used daily
maximum temperatures from the Central England Temperature (CET) record [
12
]. One study [
13
]
stated that heat waves had become more frequent in May and June over the period 1878–2001, although
it was unclear how this conclusion was reached. Another study [
5
] detected increases in the lengths of
the longest heat waves in the CET over a similar period (1880–2005). It is clear from these studies that
the full extent of trends in heat wave characteristics and their variations in the UK is not apparent and
more investigation is needed. This study aims to understand long-term trends and regional variability
in UK heat waves via analysis of heat wave characteristics in the observational record. One issue is the
lack of consistent definitions of heat waves which makes comparisons of different studies difficult.
A wide variety of heat wave definitions based on single, dual or daily thresholds have been used [
14
].
In the present study, a simple definition based around a single temperature threshold will be used
(Section 2.3).
Previous research has shown that there is a relationship between the Atlantic Multidecadal
Oscillation (AMO) and mean summer temperatures in the UK [
15
]. The AMO is a large-scale pattern of
multidecadal variability in sea surface temperatures in the north Atlantic which exerts a considerable
influence on global and regional climate [
16
], with intervals between successive peaks and troughs of
several decades [
15
]. One study [
17
] suggested that the AMO moderated the lengths of heat waves in
western Europe, with longer heat waves corresponding to positive phases of the AMO. In contrast,
little effect of the AMO on several extreme high temperature indices was found using data recorded at
Sheffield [
18
]. However, this latter study [
18
] used a relatively short period of data (1979–2015) and a
simple linear correlation, whereas the relationship between the AMO and heat waves or other indices
could be non-linear.
Another large scale index which affects summer temperatures in northwest Europe and the UK is
the summertime North Atlantic Oscillation (NAO) [
19
], which may also moderate heat wave numbers
and lengths. A significant positive correlation was found between the summertime NAO index and
July-August mean temperatures over the UK for the period 1900–2007 [
19
]. In a study of the effects of
many different large-scale atmospheric indices on European climate, the summertime NAO had the
highest correlation coefficients with temperatures in July in the UK [
20
]. The Arctic oscillation had
smaller correlation coefficients with July temperatures, and the Polar/Eurasian (POLEUR) and East
Asia/Western Russian (EAWR) indices had weaker effects [
20
]. Other indices studied in [
20
] had little
or no effect on summer temperatures in the UK. The El Niño-Southern Oscillation (ENSO) appeared to
have no clear effect on the numbers of warm days between April and October in the UK [
21
]. However,
a more recent analysis [
22
] of the AMO and ENSO suggested that the ENSO does modulate the number
of heat wave days in the UK, although the effect was smaller than that of the AMO.
In addition to analysing the long-term trends and regional variability in numbers and lengths of
UK heat waves in the observation records, this study also aims to assess the role that the AMO and
summertime NAO may have in moderating these heat wave characteristics.
2. Experiments
2.1. Selection of Stations
For this study, daily maximum surface air temperatures from weather stations in the UK
observation network, which have been continuously operational over the same period for many
decades, were required. Any trends in heat wave characteristics in data series of relatively short

Atmosphere 2017,8, 191 3 of 17
lengths (e.g., a few decades) could be caused by longer-term variations of the climate system. The Met
Office Integrated Data Archive System (MIDAS) [
23
] contains historical and current observations from
weather stations around the UK, including data from stations which are no longer operational. MIDAS
was initially searched to identify weather stations which were operational at the end of 2016. Some of
these stations were active from 1931 or earlier, in theory allowing a period of more than 85 years to be
studied. However, records from some stations were shorter than expected as not all the data had been
digitised. Some stations were found to have missing data during the warm season (May to September)
in multiple years. For example, the record for Bude begins in 1913, but no data are available for
1926–1930 and 1936–1958. Overall, 29 inland and coastal weather stations with near-complete records
were selected (Figure 1, Table A1).
Atmosphere 2017, 8, 191 3 of 17
The Met Office Integrated Data Archive System (MIDAS) [23] contains historical and current
observations from weather stations around the UK, including data from stations which are no longer
operational. MIDAS was initially searched to identify weather stations which were operational at the
end of 2016. Some of these stations were active from 1931 or earlier, in theory allowing a period of
more than 85 years to be studied. However, records from some stations were shorter than expected
as not all the data had been digitised. Some stations were found to have missing data during the
warm season (May to September) in multiple years. For example, the record for Bude begins in 1913,
but no data are available for 1926–1930 and 1936–1958. Overall, 29 inland and coastal weather stations
with near-complete records were selected (Figure 1, Table A1).
Figure 1. Locations of the 29 weather stations analysed. JP—London, St James’s Park; MC—
Morecambe; SK—Skegness.
2.2. Pre-Processing of Station Data
Some pre-processing was performed to account for changes in reporting types and periods
(described in more detail in Supplementary S1 and S2). For example, data at some stations were
initially reported every 24 h, but were archived every 12 h after 1999. In some cases, this modification
may have coincided with a change in instrumentation. Data recorded under different types at the
same station were joined into a single series (Supplementary S2). For two locations (Plymouth
Mountbatten and Shoeburyness), a long series of daily temperatures was created by adjusting and
joining records from nearby stations (Supplementary S3). No attempt was made to infill any gaps in
the temperature series from any of the stations.
2.3. Definitions of Hot Days and Heat Waves
There is no universal definition of a heat wave, and previous studies have used many different
thresholds and metrics [14]. Most heat waves are defined as a consecutive number of hot days, where
daily mean or maximum temperatures exceed a predetermined threshold. The numbers and lengths
of heat waves identified will therefore be dependent on the hot day temperature threshold and
minimum number of consecutive days; the higher the threshold and/or number of consecutive hot
days, the fewer heat waves will be identified [14]. Here, a “hot day” means a day with an unusually
Figure 1.
Locations of the 29 weather stations analysed. JP—London, St James’s Park;
MC—Morecambe; SK—Skegness.
2.2. Pre-Processing of Station Data
Some pre-processing was performed to account for changes in reporting types and periods
(described in more detail in Supplementary S1 and S2). For example, data at some stations were
initially reported every 24 h, but were archived every 12 h after 1999. In some cases, this modification
may have coincided with a change in instrumentation. Data recorded under different types at the same
station were joined into a single series (Supplementary S2). For two locations (Plymouth Mountbatten
and Shoeburyness), a long series of daily temperatures was created by adjusting and joining records
from nearby stations (Supplementary S3). No attempt was made to infill any gaps in the temperature
series from any of the stations.
2.3. Definitions of Hot Days and Heat Waves
There is no universal definition of a heat wave, and previous studies have used many different
thresholds and metrics [
14
]. Most heat waves are defined as a consecutive number of hot days,
where daily mean or maximum temperatures exceed a predetermined threshold. The numbers and

Atmosphere 2017,8, 191 4 of 17
lengths of heat waves identified will therefore be dependent on the hot day temperature threshold and
minimum number of consecutive days; the higher the threshold and/or number of consecutive hot
days, the fewer heat waves will be identified [
14
]. Here, a “hot day” means a day with an unusually
high temperature for a given location, even if that temperature would not be considered high in an
absolute sense.
In the present study, a hot day threshold was calculated for each station as a percentile of
year-round daily maximum temperatures recorded between 1971 and 2000, where any daily maximum
temperature reaching or exceeding the threshold is defined as a hot day. Thresholds corresponding
to the 90th, 93rd, 95th and 98th percentiles of daily maximum temperatures were calculated for each
station. The 90th percentile temperatures were mostly less than 21
◦
C, which is not exceptionally
warm in the UK. This study therefore focuses on heat waves derived from the 93rd, 95th and 98th
percentiles, so that the sensitivity of the results to the threshold choice can be assessed. The 93rd and
95th percentiles are considered to be thresholds for moderate heat waves, and the 98th percentile more
extreme heat waves. As a result of being station-specific, the 98th percentile thresholds vary across
the UK, from 16
◦
C at Lerwick in Shetland to 28
◦
C in southeast England. The thresholds for most of
the stations were above 23
◦
C. A heat wave was defined as a period with 3 or more consecutive hot
days [
14
]. Although a daily maximum temperature of 16
◦
C is not exceptionally warm in an absolute
sense, it is for the climate of Lerwick. The occurrence of such temperatures would be expected to be
linked with heat waves in other parts of the UK.
Four heat wave metrics were calculated for each year of the temperature records to understand
how the climate signal could be manifested: HWN—the number of heat waves; HWD—the length of
the longest heat wave; HWF—the total number of heat wave days (or sum of lengths of all heat waves
in a year); and HWA—the highest temperature within a heat wave [14].
2.4. Analysis of Trends
A robust method for fitting linear models to the various heat wave characteristics was used to
reduce the effects of outliers. The particular method used is based on M-estimators [
24
]. Briefly,
maximum likelihood estimation (MLE) is used to estimate the slope of the fitted line based on a
minimising function of the residuals. The fitting was carried out using the Robust Linear Model
module which is part of the Python “statsmodels” package. The minimising function was Huber ’s t.
Statistical significance was calculated at the 5% level.
2.5. Ocean and Atmospheric Indices
AMO and NAO indices have been derived from multiple datasets. In this study, four different
series of the AMO and two of the summertime NAO are selected. The statistical modelling (described
in Section 2.6) used to assess any influence of the AMO and NAO on heat wave numbers and lengths
will be repeated using different combinations of the AMO and NAO datasets. If similar results are
obtained regardless of the source of the AMO and NAO, the results would be considered robust.
Time series of the AMO index have been derived from four different global sea surface
temperature (SST) datasets (Table S4). Two series were derived from different SST datasets as
described in [
25
], and were downloaded from the KNMI Climate Explorer (available online:
https://climexp.knmi.nl/). The AMO has been derived from another SST dataset [
26
] and
was obtained from the NOAA/OAR/ESRL PSD, Boulder, Colorado, USA (available online:
https://www.esrl.noaa.gov/psd/data/timeseries/AMO/
). A fourth AMO time series for 1870–2016
was calculated from the HadSST3 dataset [
27
] using data for the Atlantic between 20
◦
N–60
◦
N. Before
use, all the AMO data were smoothed with a Chebyshev filter of order 2 and a cut off frequency of
12 years to emphasise the multidecadal variability [28].
Two series of the summertime NAO indices, derived from a sea level pressure reconstruction [
29
]
and the twentieth century reanalysis [
30
] were obtained from the KNMI Climate Explorer. In both
cases, the NAO was the principle component of the first empirical orthogonal function of sea level

Atmosphere 2017,8, 191 5 of 17
pressure over the region 40
◦
N–70
◦
N and 90
◦
W–30
◦
E (Table S4). The two NAO datasets contain
monthly values. The summertime NAO used in the present study was the mean of the values for July
and August. The summertime NAO data were smoothed using a binomial filter with a half period of
25 years [19]. The smoothed AMO and summertime NAO series are shown in Figure A1.
2.6. Logistic Regression across Multiple Stations
Logistic regression will be used to quantify any possible effect of the AMO and summertime NAO
on the numbers and lengths of heat waves in the UK. When considering numbers of heat waves, for
example, a variable of interest, y(t), is defined as an event with more than a prescribed number nof
heat waves in a year. y(t) is binary with y(t) = 1 if nor more heat waves occurred in year t, and y(t) = 0
otherwise. Years with no heat waves are included and y(t) = 0 in those years. In the equations below,
AMO(t) and NAO(t) are the smoothed annual mean AMO and summertime NAO indices for year t.
The baseline model used to explain the probability that nor more heat waves would occur in a
given year is a Bernoulli Generalised Linear Model (GLM), where:
p(t)=probability that yj(t)=1 at station j=1, · · · , 8 (1)
log pj
1−pj!=α+βAMO(t)+γNAO(t)(2)
This approach is the conventional way of modelling binary data, where the logarithm of the
odds ratio p(t)/(1
−
p(t)) (called the log-odds ratio) is modelled as a linear function of the explanatory
variables. Positive values of the log-odds ratio correspond to probabilities greater than one half,
and negative values to probabilities below one half. Hence both positive and negative values of the
parameters βjand γjare possible.
In order to pool all the data together across multiple stations, but at the same time allow each
station to have a potentially different AMO and NAO effect, the model is extended so that
α
,
β
and
γ
are treated as random variables:
pj(t)=probability that yj(t)=1 at station j=1, · · · , 8 (3)
log pj(t)
1−pj(t)!=αj+βjAMO(t)+γjNAO(t)(4)
αj∼Normal0, σ2
α(5)
βj∼Normalµβ,σ2
β(6)
γj∼Normalµγ,σ2
γ(7)
where
µβ
and
µγ
are the average effects of the AMO and summertime NAO respectively across the
stations. The individual effects
βj
and
γj
are deviations from those means, but it should be noted that
they are constrained by the common variances
σβ2
and
σγ2
. Constraining the individual responses in
this way allows information across the stations to be pooled, whilst maintaining enough flexibility
for each station to have a unique AMO and NAO effect due to measurement discrepancies or the two
drivers having a different effect across the UK.
The model parameters are estimated in a Bayesian framework using a Markov Chain Monte
Carlo (MCMC) method, using the statistical software R [
31
], and specifically the package “rjags” [
32
].
Inference in the Bayesian framework is based on the posterior distribution of each model parameter,
from which one obtains samples when fitting the model using MCMC. The posterior distributions
express uncertainty in the model parameters and direct probabilistic statements can be made to assess
significance. For instance, noticing that zero is not included in the 95% Credible Interval (CrI) of

Atmosphere 2017,8, 191 6 of 17
a parameter, it may be concluded that the parameter is “significantly different from zero” in the
classical sense.
3. Results
3.1. Analysis of First and Last Heat Wave Days
The dates of the first and last heat wave days at the stations shown in Figure 1were recorded.
Most of the heat wave days occurred between May and September. However, heat waves were also
identified in April and October at some of the stations during a few years. Hence, temperatures within
an extended warm season, April to October, were used to identify heat waves at all stations.
Heat waves might appear earlier and end later in the year as the climate warms. Trends in the
first and last days of year belonging to a heat wave were calculated for each weather station and
temperature threshold for the period 1961–2016. Most of the trends in the first days were negative
when the 93rd or 95th percentile thresholds were used (suggesting that moderate heat waves were
appearing earlier in the year), but, with the exceptions of Eastbourne and Teignmouth, none were
significant at the 5% level (data not shown). Most of the trends using the 98th percentile threshold
were positive (at 22 out of 29 stations) but none (positive or negative trends) were significant, except at
Cromer, where a positive trend was found.
In contrast, significant positive trends in the last days of year belonging to heat waves were found
at nine stations for the 93rd and at eight stations for the 95th percentile thresholds (Table S5.1). This
result suggests heat waves have occurred later in the year in south east England over last five decades.
Negative trends were found at a small number of stations but none were significant. When the 98th
percentile threshold (representing extreme heat waves) was used, twelve of the trends were positive
and the rest were negative (Table S5.1). Only the trends at Cromer (positive) and Wisley (negative)
were significant.
3.2. Heat Wave Characteristics
The median and interquartile ranges of numbers of heat waves (HWN), longest heat waves
(HWD), annual total of heat wave days (HWF) and hottest day during a heat wave (HWA) are shown
in Table 1using the 95th percentile thresholds. The median numbers of heat waves are similar across the
stations, 2 or 3. The medians of the longest heat waves (HWD) are also similar. Greater variation is seen
in sums of lengths of heat waves (HWF) and the maximum temperatures in the heat waves (HWA).
Table 1.
Median and interquartile ranges of numbers of heat waves (HWN), longest heat waves (HWD),
annual numbers of heat wave days (HWF) and highest temperatures in the heat waves (HWA) using
data for 1931–2016. The temperature thresholds used to identify heat waves were the 95th percentiles.
Station HWN HWD HWF HWA
Aldergrove 2 [1–3] 5 [4–7] 10 [6–14] 25.2 [24.0–27.2]
Armagh 2 [1–3] 5 [4–8] 10 [7–16] 26.0 [25.0–27.6]
Balmoral 2 [1–3] 5 [4–7] 9 [6–14] 25.6 [24.7–27.5]
Bradford 2 [1–3] 5 [4–7] 8 [6–16] 27.2 [26.1–28.3]
Cambridge, Botanical Gardens
2 [1–3] 6 [4–7] 10 [5–15] 30.6 [29.4–32.4]
Craibstone 2 [1–3] 5 [3–6] 9 [4–14] 24.9 [23.3–25.6]
Cranwell 2 [1–4] 5 [4–8] 10 [6–18] 30.0 [28.6–31.7]
Cromer 2 [2–3] 4 [3–6] 10 [6–14] 29.0 [27.1–30.9]
Douglas 2 [1–4] 5 [4–8] 12 [6–18] 24.4 [22.8–25.5]
Durham 2 [1–4] 5 [4–7] 10 [5–17] 27.2 [25.6–29.0]
Eastbourne 2 [1–4] 6 [4–8] 11 [6–18] 26.5 [25.6–27.8]
Lerwick 2 [2–4] 6 [4–9] 12 [7–20] 18.9 [17.5–20.6]
Leuchars 2 [1–3] 4 [3–6] 7 [4–14] 25.4 [24.4–27.2]
London, St James’s Park 2 [1–4] 6 [4–8] 11 [6–17] 30.9 [29.4–32.8]
Morecambe 2 [2–3] 5 [4–8] 10 [6–16] 27.6 [25.6–28.9]
Morpeth 2 [1–4] 5 [3–7] 9 [6–17] 25.3 [24.4–27.2]
Newton Rigg 2 [1–34] 6 [4–8] 11 [7–16] 27.0 [25.4–28.3]

Atmosphere 2017,8, 191 7 of 17
Table 1. Cont.
Station HWN HWD HWF HWA
Oxford 2 [1–3] 5 [4–8] 10 [6–16] 30.0 [28.7–31.6]
Plymouth Mountbatten 2 [1–3] 5 [4–7] 9 [5–14] 25.8 [24.8–27.4]
Rothamstead 2 [1–3] 5 [4–7] 10 [6–14] 29.4 [27.8–30.7]
Sheffield 2 [1–3] 5 [4–6] 8 [5–13] 28.6 [27.7–30.2]
Shoeburyness 3 [2–4] 5 [4–8] 12 [6–19] 28.0 [27.1–29.5]
Skegness 2 [1–3] 4 [3–6] 8 [5–13] 27.2 [25.8–28.4]
Stornoway Airport 3 [1–4] 6 [4–8] 14 [7–20] 22.2 [20.6–23.3]
Teignmouth 2 [1–4] 5 [3–8] 10 [6–19] 25.6 [24.6–27.2]
Tiree 2 [1–3] 5 [4–9] 9 [5–17] 22.4 [20.5–23.8]
Valley 2 [1–3] 4 [3–8]
8 [4–7,16]
27.1 [25.2–28.2]
Wick Airport 2 [1–3] 4 [3–6] 7 [4–14] 21.7 [20.5–22.9]
Wisley 2 [1–4] 6 [4–8] 10 [6–17] 30.6 [29.0–32.2]
3.3. Trends in Heat Waves
Trends in heat wave numbers (HWN), longest lengths (HWD) and sums of lengths (HWF) for
all three thresholds are illustrated in Figure 2a–c for 1961–2016. None of the trends in the heat wave
metrics based on the 98th percentile were significant, whereas many trends based on the 93rd and
95th percentiles were significant. These findings suggest that moderate heat waves have increased
in number and length from 1960, but any changes in the most extreme heat waves are unclear.
These results are in qualitative agreement with other studies [
5
,
7
,
13
]. The stations with significant
trends in heat wave numbers (Figure 2a) are spread around the UK. In contrast, the stations with
significant trends in heat wave lengths (Figure 2b,c) are mostly located in south east England and the
islands around Scotland.
Atmosphere 2017, 8, 191 7 of 17
Plymouth Mountbatten 2 [1–3] 5 [4–7] 9 [5–14] 25.8 [24.8–27.4]
Rothamstead 2 [1–3] 5 [4–7] 10 [6–14] 29.4 [27.8–30.7]
Sheffield 2 [1–3] 5 [4–6] 8 [5–13] 28.6 [27.7–30.2]
Shoeburyness 3 [2–4] 5 [4–8] 12 [6–19] 28.0 [27.1–29.5]
Skegness 2 [1–3] 4 [3–6] 8 [5–13] 27.2 [25.8–28.4]
Stornoway Airport 3 [1–4] 6 [4–8] 14 [7–20] 22.2 [20.6–23.3]
Teignmouth 2 [1–4] 5 [3–8] 10 [6–19] 25.6 [24.6–27.2]
Tiree 2 [1–3] 5 [4–9] 9 [5–17] 22.4 [20.5–23.8]
Valley 2 [1–3] 4 [3–8] 8 [4–16] 27.1 [25.2–28.2]
Wick Airport 2 [1–3] 4 [3–6] 7 [4–14] 21.7 [20.5–22.9]
Wisley 2 [1–4] 6 [4–8] 10 [6–17] 30.6 [29.0–32.2]
3.3. Trends in Heat Waves
Trends in heat wave numbers (HWN), longest lengths (HWD) and sums of lengths (HWF) for
all three thresholds are illustrated in Figure 2a–c for 1961–2016. None of the trends in the heat wave
metrics based on the 98th percentile were significant, whereas many trends based on the 93rd and
95th percentiles were significant. These findings suggest that moderate heat waves have increased in
number and length from 1960, but any changes in the most extreme heat waves are unclear. These
results are in qualitative agreement with other studies [5,7,13]. The stations with significant trends in
heat wave numbers (Figure 2a) are spread around the UK. In contrast, the stations with significant
trends in heat wave lengths (Figure 2b,c) are mostly located in south east England and the islands
around Scotland.
(a) (b)
(c)
Figure 2. (a) Trends in numbers of heat waves (HWN) per decade over 1961–2016. The three symbols
for each station are (from left to right) the trends using the 93rd, 95th and 98th percentile thresholds.
Upward and downward-pointing triangles indicate positive and negative trends respectively. Large
symbols with a border indicate trends significant at the 5% level; non-significant trends are shown by
small symbols without a border. The trend values are indicated by the colour bar. The ‘×’ at Leuchars
indicates a trend could not be calculated; (b) As (a), but trends in lengths of longest heat waves (HWD)
per decade over 1961–2016; (c) As (a), but trends in total numbers of heat wave days (HWF) per decade
over 1961–2016.
Figure 2.
(
a
) Trends in numbers of heat waves (HWN) per decade over 1961–2016. The three
symbols for each station are (from left to right) the trends using the 93rd, 95th and 98th percentile
thresholds. Upward and downward-pointing triangles indicate positive and negative trends
respectively. Large symbols with a border indicate trends significant at the 5% level; non-significant
trends are shown by small symbols without a border. The trend values are indicated by the colour bar.
The ‘
×
’ at Leuchars indicates a trend could not be calculated; (
b
) As (
a
), but trends in lengths of longest
heat waves (HWD) per decade over 1961–2016; (
c
) As (
a
), but trends in total numbers of heat wave
days (HWF) per decade over 1961–2016.

Atmosphere 2017,8, 191 8 of 17
The trend values for the three heat wave metrics are listed in Tables S5.2–S5.4 for each threshold
over two time periods, 1931–2016 and 1961–2016. Generally, few of the trends are significant at the 5%
level for 1931–2016, whereas more are significant for 1961–2016.
However, the changes in lengths of longest heat waves (HWD) are more complex than suggested
by a simple analysis of trends. Heat waves longer than 8–12 days (depending on the station) were
very rare before the 1970s, and only occurred in 1911, 1921 and 1947. From 1976, these longer heat
waves were present in most or all of the years 1976, 1983, 1990, 1995, 1997, 2003, 2006, 2011 and 2013
(Figure 3).
There is a marked difference in the changes in lengths of heat waves up to 11 days in length and
those with longer lengths when the 93rd and 95th percentile thresholds are used for some stations in
southern and eastern England (Cambridge, Durham, Eastbourne, Morecambe, London St James’ Park
and Wisley). As an example, the longest heat waves in each year (HWD) are shown in Figure 3for
London St James’s Park. Heat waves with lengths of 11 days or less (below the dotted line) declined in
range between the 1930 and 1970 from 3–10 days to 3–7 days, after which the range increased slightly
to 3–9 days. In contrast, the lengths of very long heat waves (those above the dotted line) declined
from a high point in the mid-1970s (about 22 days) to 12–13 days in the 2010s. This decline is shown by
the solid grey line. The reasons for the decline in lengths of very long heat waves are unclear.
Atmosphere 2017, 8, 191 8 of 17
The trend values for the three heat wave metrics are listed in Tables S5.2–S5.4 for each threshold
over two time periods, 1931–2016 and 1961–2016. Generally, few of the trends are significant at the
5% level for 1931–2016, whereas more are significant for 1961–2016.
However, the changes in lengths of longest heat waves (HWD) are more complex than suggested
by a simple analysis of trends. Heat waves longer than 8–12 days (depending on the station) were
very rare before the 1970s, and only occurred in 1911, 1921 and 1947. From 1976, these longer heat
waves were present in most or all of the years 1976, 1983, 1990, 1995, 1997, 2003, 2006, 2011 and 2013
(Figure 3).
There is a marked difference in the changes in lengths of heat waves up to 11 days in length and
those with longer lengths when the 93rd and 95th percentile thresholds are used for some stations in
southern and eastern England (Cambridge, Durham, Eastbourne, Morecambe, London St James’ Park
and Wisley). As an example, the longest heat waves in each year (HWD) are shown in Figure 3 for
London St James’s Park. Heat waves with lengths of 11 days or less (below the dotted line) declined
in range between the 1930 and 1970 from 3–10 days to 3–7 days, after which the range increased
slightly to 3–9 days. In contrast, the lengths of very long heat waves (those above the dotted line)
declined from a high point in the mid-1970s (about 22 days) to 12–13 days in the 2010s. This decline
is shown by the solid grey line. The reasons for the decline in lengths of very long heat waves are
unclear.
Figure 3. Lengths of longest heat waves (days) for St James’s Park, London. Heat waves are defined
as 3 or more consecutive days when daily maximum temperatures reach or exceed the 93rd (red
circles) or 95th (green triangles) percentile of year-round temperatures over 1971–2000. The red and
green dashed lines indicate linear trends fitted to the whole data. The boundary defining very long
heat waves (12 days or more) is shown by the horizontal dotted line. The solid grey line illustrates the
downward trend in lengths of very long heat waves from 1975.
The directions of change in lengths of very long heat waves (i.e., those above the dotted line in
Figure 3) are shown in Figure 4 using heat waves associated with the 93rd percentile threshold.
A decline in the length of the very long heat waves is seen for stations in south east England. When
the 95th percentile threshold is used, any changes in the lengths of the very long heat waves were
less clear, but those showing the clearest decreases were also located in the south east of England.
Figure 3.
Lengths of longest heat waves (days) for St James’s Park, London. Heat waves are defined as
3 or more consecutive days when daily maximum temperatures reach or exceed the 93rd (red circles)
or 95th (green triangles) percentile of year-round temperatures over 1971–2000. The red and green
dashed lines indicate linear trends fitted to the whole data. The boundary defining very long heat
waves (12 days or more) is shown by the horizontal dotted line. The solid grey line illustrates the
downward trend in lengths of very long heat waves from 1975.
The directions of change in lengths of very long heat waves (i.e., those above the dotted line
in Figure 3) are shown in Figure 4using heat waves associated with the 93rd percentile threshold.
A decline in the length of the very long heat waves is seen for stations in south east England. When
the 95th percentile threshold is used, any changes in the lengths of the very long heat waves were less
clear, but those showing the clearest decreases were also located in the south east of England.

Atmosphere 2017,8, 191 9 of 17
Atmosphere 2017, 8, 191 9 of 17
Figure 4. Direction of change in lengths of very long heat waves (longer than 8–12 days, depending
on the station) at each station using the 93rd percentile thresholds. Upward- and downward-pointing
triangles indicate an increase and decrease in the lengths respectively. Large symbols indicate a clear
change, whereas small symbols show a small change. A solid circle indicates no clear direction of
change in the lengths.
3.4. Variations in the AMO, Summertime NAO and Heat Wave Characteristics
Positive trends in heat wave numbers and lengths have been identified for many of the stations
in Figure 1 (Section 3.3). However, considerable multidecadal variability is evident in the numbers
and lengths of heat waves (Figure A2). Variations in the sign and magnitude of the AMO could be
responsible for modulating heat wave lengths [5].
A comparison by eye of the smoothed annual mean AMO and NAO anomalies and time series
of numbers of heat waves (Figure A2) suggests that when the AMO or NAO is in a positive phase,
there are generally greater numbers of heat waves. In contrast, when the AMO or NAO is in a
negative phase, there are generally fewer heat waves. In Figure A2, years with 1 or 2 heat waves are
reasonably common, but years with 3 or more heat waves are notably smaller in number, with these
events typically occurring during a positive phase of the AMO and/or NAO.
3.4.1. Effects on Numbers of Heat Waves
Logistic regression was used to quantify the possible effect of the AMO and summertime NAO
on the numbers of heat waves in the UK. The AMO and summertime NAO records are available from
the mid-19th century (Table S4). Eight weather stations with records beginning in the 19th century
(Armagh, Douglas, Durham, Morpeth, Oxford, Plymouth, Sheffield and Stornoway Airport; Table
A1) were therefore selected to maximise the overlap with the AMO and NAO datasets and hence
numbers of years for study. The logistic regression used all available data, so that the periods differed
slightly depending on the combination of AMO and summertime NAO datasets (Table S4).
Results using the AMO from HadSST3 [27] and summertime NAO derived from the sea level
pressure (SLP) data of Trenberth and Paolino [29] are shown in Figure 5, using heat wave numbers
derived using the 95th percentile threshold. The individual effects for each station β
j
and γ
j
(defined
in Equations (6) and (7)) and their 95% CrIs are indicated by the solid circles and horizontal lines
respectively. The average effects across all stations (μ
β
and μ
γ
in Equations (6) and (7)) and their
respective 95% CrIs are illustrated by the vertical solid and dashed lines. The results shown in Figure
5a suggest that there is a positive effect of the AMO on the log-odds ratio of three or more heat waves
with some small variability between stations, although the effect at Stornoway is weaker than the
other stations. The mean AMO effect across all stations is 1.41 with CrI [0.53, 2.26]. The overall effect
of the summertime NAO is also positive (Figure 5b) but smaller than the AMO effect, and appears to
Figure 4.
Direction of change in lengths of very long heat waves (longer than 8–12 days, depending
on the station) at each station using the 93rd percentile thresholds. Upward- and downward-pointing
triangles indicate an increase and decrease in the lengths respectively. Large symbols indicate a clear
change, whereas small symbols show a small change. A solid circle indicates no clear direction of
change in the lengths.
3.4. Variations in the AMO, Summertime NAO and Heat Wave Characteristics
Positive trends in heat wave numbers and lengths have been identified for many of the stations
in Figure 1(Section 3.3). However, considerable multidecadal variability is evident in the numbers
and lengths of heat waves (Figure A2). Variations in the sign and magnitude of the AMO could be
responsible for modulating heat wave lengths [5].
A comparison by eye of the smoothed annual mean AMO and NAO anomalies and time series of
numbers of heat waves (Figure A2) suggests that when the AMO or NAO is in a positive phase, there
are generally greater numbers of heat waves. In contrast, when the AMO or NAO is in a negative
phase, there are generally fewer heat waves. In Figure A2, years with 1 or 2 heat waves are reasonably
common, but years with 3 or more heat waves are notably smaller in number, with these events
typically occurring during a positive phase of the AMO and/or NAO.
3.4.1. Effects on Numbers of Heat Waves
Logistic regression was used to quantify the possible effect of the AMO and summertime NAO
on the numbers of heat waves in the UK. The AMO and summertime NAO records are available from
the mid-19th century (Table S4). Eight weather stations with records beginning in the 19th century
(Armagh, Douglas, Durham, Morpeth, Oxford, Plymouth, Sheffield and Stornoway Airport; Table A1)
were therefore selected to maximise the overlap with the AMO and NAO datasets and hence numbers
of years for study. The logistic regression used all available data, so that the periods differed slightly
depending on the combination of AMO and summertime NAO datasets (Table S4).
Results using the AMO from HadSST3 [
27
] and summertime NAO derived from the sea level
pressure (SLP) data of Trenberth and Paolino [
29
] are shown in Figure 5, using heat wave numbers
derived using the 95th percentile threshold. The individual effects for each station
βj
and
γj
(defined
in Equations (6) and (7)) and their 95% CrIs are indicated by the solid circles and horizontal lines
respectively. The average effects across all stations (
µβ
and
µγ
in Equations (6) and (7)) and their
respective 95% CrIs are illustrated by the vertical solid and dashed lines. The results shown in Figure 5a
suggest that there is a positive effect of the AMO on the log-odds ratio of three or more heat waves
with some small variability between stations, although the effect at Stornoway is weaker than the other

Atmosphere 2017,8, 191 10 of 17
stations. The mean AMO effect across all stations is 1.41 with CrI [0.53, 2.26]. The overall effect of
the summertime NAO is also positive (Figure 5b) but smaller than the AMO effect, and appears to be
weaker at Oxford and Stornoway than the other locations. Overall, the results in Figure 4suggest that
variations in the AMO and summertime NAO moderate the numbers of heat waves, with a higher
probability of larger numbers during positive phases of both indices.
Atmosphere 2017, 8, 191 10 of 17
be weaker at Oxford and Stornoway than the other locations. Overall, the results in Figure 4 suggest
that variations in the AMO and summertime NAO moderate the numbers of heat waves, with a
higher probability of larger numbers during positive phases of both indices.
Figure 5. Modelled effects of (a) the Atlantic Multidecadal Oscillation (AMO) and (b) summertime
North Atlantic Oscillation (NAO) on the probability of 3 or more heat waves in a year, using the 95th
percentile threshold to define heat waves. The individual effects (corresponding to the parameters βj
(panel a) and γj (panel b) in Equations (6) and (7) above) and their 95% confidence intervals are shown
by the solid grey circles and lines respectively. The mean effects across all eight stations (parameters
μβ (panel a) and μγ (panel b) in Equations (6) and (7)) and associated 95% confidence intervals are
shown by the vertical solid and dashed lines respectively. Note that ranges of the effects in the two
panels (values along the x-axis) are different.
The analysis above was repeated using heat waves derived using the 93rd and 98th percentile
thresholds. The mean effects of the AMO and summertime NAO across all eight stations are shown
in Figure 6 for all combinations of the AMO and NAO datasets and the three percentile thresholds.
Overall, the results are consistent across the percentile choice. Any changes in the magnitudes of the
effects between thresholds are small and none have changed sign. The size of the AMO effect remains
greater than the summer NAO effect. The CrIs using the 98th percentile thresholds are larger than
the CrIs for the lower thresholds, and some include zero, although most of the masses of the
Figure 5.
Modelled effects of (
a
) the Atlantic Multidecadal Oscillation (AMO) and (
b
) summertime
North Atlantic Oscillation (NAO) on the probability of 3 or more heat waves in a year, using the 95th
percentile threshold to define heat waves. The individual effects (corresponding to the parameters
βj
(panel a) and
γj
(panel b) in Equations (6) and (7) above) and their 95% confidence intervals are shown
by the solid grey circles and lines respectively. The mean effects across all eight stations (parameters
µβ
(panel a) and
µγ
(panel b) in Equations (6) and (7)) and associated 95% confidence intervals are shown
by the vertical solid and dashed lines respectively. Note that ranges of the effects in the two panels
(values along the x-axis) are different.
The analysis above was repeated using heat waves derived using the 93rd and 98th percentile
thresholds. The mean effects of the AMO and summertime NAO across all eight stations are shown
in Figure 6for all combinations of the AMO and NAO datasets and the three percentile thresholds.
Overall, the results are consistent across the percentile choice. Any changes in the magnitudes of the
effects between thresholds are small and none have changed sign. The size of the AMO effect remains

Atmosphere 2017,8, 191 11 of 17
greater than the summer NAO effect. The CrIs using the 98th percentile thresholds are larger than the
CrIs for the lower thresholds, and some include zero, although most of the masses of the distributions
lie above zero. The deviations between the percentile thresholds are probably caused by randomness
in sampling the data.
Atmosphere 2017, 8, 191 11 of 17
distributions lie above zero. The deviations between the percentile thresholds are probably caused
by randomness in sampling the data.
Figure 6. Mean effects of (a) the AMO and (b) summertime NAO (corresponding to parameters μβ
and μγ in Equations (6) and (7) respectively) on the probabilities of 3 or more heat waves in a year
across eight stations using three different percentile-based thresholds. Four AMO and two NAO
datasets were used, giving eight combinations (Table S4). The solid circles show the mean effects and
the horizontal lines the 95% confidence intervals.
3.4.2. Logistic Modelling of Heat Wave Lengths
The logistic model was fitted to the longest heat waves (HWD) for each station. Threshold
lengths of 8 and 10 days were used based on an inspection of the lengths identified for the weather
stations. The mean effects across all eight stations are shown in Figures S6.1 and S6.2. For the
threshold of 8 days (Figure S6.1), the AMO effects were mostly in the range 1.0–2.0 and were
consistent across the different combinations of AMO and summer NAO datasets and heat wave
temperature thresholds. The CrIs of the effects for the 98th percentile thresholds were broader and
included zero but were consistent with the results using the lower percentile thresholds. This result
suggests that the AMO may also moderate heat wave lengths.
The summer NAO effects were smaller (range 0.5–1.0) and had similar magnitudes when the
93rd and 95th percentile thresholds were used, but some of the CrIs included zero. The effects using
the 98th percentile threshold were notably larger (2.0–3.5) and none of the CrIs included zero,
although the CrIs were also wider. The estimated effects using the summer NAO derived from the
SLP data of Trenberth and Paolino (Table S4) were smaller than when the NAO derived from the 20
Figure 6.
Mean effects of (
a
) the AMO and (
b
) summertime NAO (corresponding to parameters
µβ
and
µγ
in Equations (6) and (7) respectively) on the probabilities of 3 or more heat waves in a year across
eight stations using three different percentile-based thresholds. Four AMO and two NAO datasets were
used, giving eight combinations (Table S4). The solid circles show the mean effects and the horizontal
lines the 95% confidence intervals.
3.4.2. Logistic Modelling of Heat Wave Lengths
The logistic model was fitted to the longest heat waves (HWD) for each station. Threshold lengths
of 8 and 10 days were used based on an inspection of the lengths identified for the weather stations.
The mean effects across all eight stations are shown in Figures S6.1 and S6.2. For the threshold of
8 days (Figure S6.1), the AMO effects were mostly in the range 1.0–2.0 and were consistent across the
different combinations of AMO and summer NAO datasets and heat wave temperature thresholds.
The CrIs of the effects for the 98th percentile thresholds were broader and included zero but were
consistent with the results using the lower percentile thresholds. This result suggests that the AMO
may also moderate heat wave lengths.

Atmosphere 2017,8, 191 12 of 17
The summer NAO effects were smaller (range 0.5–1.0) and had similar magnitudes when the 93rd
and 95th percentile thresholds were used, but some of the CrIs included zero. The effects using the
98th percentile threshold were notably larger (2.0–3.5) and none of the CrIs included zero, although
the CrIs were also wider. The estimated effects using the summer NAO derived from the SLP data of
Trenberth and Paolino (Table S4) were smaller than when the NAO derived from the 20 CR data were
used, which may be related to the differing lengths of the two sea level pressure datasets (Table S4).
It is tentatively concluded that the summer NAO might moderate the lengths of extreme heat waves,
but possibly has less effect on moderate heat waves. When a threshold length of 10 days was used, the
results were similar, but more of the CrIs included zero (Figure S6.2).
4. Discussion
4.1. Heat Wave Metrics
Numbers and lengths of heat waves calculated from weather station records in the UK were
found to be highly variable over time. The median numbers and lengths (Table 1) for stations in or
close to London and in Northern Ireland were similar to those calculated for London and Dublin
using a different heat wave definition [
9
]. Positive trends in numbers and lengths of longest heat
waves were identified at many stations using data from 1961. These results are consistent with the
anthropogenic climate warming signal [
33
]. Studies of heat waves using temperatures recorded in
continental Europe identified positive trends in numbers and lengths of heat waves since the end of
the nineteenth century [5,7].
However, the lengths of heat waves at some stations in the UK were found to fall into two groups.
Heat waves with lengths less than about 11 days occur throughout the data series, and the range of
longest lengths fell from 3–10 to about 3–7 days between 1931 and 1970 before increasing slightly
to 3–9 days by 2016. In contrast, very long heat waves (longer than 11 days) were very rare at most
stations until the mid-1970s. Since this time, these very long heat waves have been more common,
but their lengths at stations in central and south east England have declined, from around 20 days to
12 days. The reasons for the different directions of changes in these two groups of heat wave lengths
is unclear.
4.2. Circulation and SST Influences
Considerable multidecadal variability in both the numbers and lengths of heat waves was
apparent at all stations. Logistic regression was used to quantify the possible effect of the AMO
and summertime NAO on heat wave numbers and lengths. The results suggested that higher numbers
and lengths of heat waves in the UK are associated with the positive phase of the AMO. Smaller
numbers and lengths of heat waves tend to occur when the AMO is in a negative phase. The exceptions
were the long heat waves of 1975 and 1976, which were probably exacerbated by an accompanying
drought. The logistic regression also suggested that the summertime NAO moderates numbers and
lengths of heat waves, although its influence was smaller than that of the AMO. These results were
robust across three different temperature thresholds used to define heat waves. The exact magnitudes
of the effects of the AMO and summertime NAO on heat wave numbers were dependent on the
particular datasets chosen. Overall, the conclusions are not sensitive to the choice of threshold, or the
particular AMO and NAO datasets employed.
4.3. Limitations and Further Work
Only two cycles of the AMO have been observed directly, so the results in the present study
should be regarded as preliminary. The AMO and NAO were treated as independent variables in
the logistic regression. The exact cause of the AMO and the possible role of the NAO in controlling
the AMO is not fully understood, with both internal variability of the ocean circulation and external
forcing playing a role [
34
]. It is noted that another study [
17
] suggested that global mean temperature

Atmosphere 2017,8, 191 13 of 17
changes might be driving the variability in heat wave numbers and lengths instead of the AMO and
NAO. Identifying whether the AMO/NAO or global mean temperatures are the cause of heat wave
variability would require the analysis of appropriate climate model experiments [
17
] and is beyond the
scope of the present study. Other large-scale indices moderate summer temperatures in Europe [
20
],
but their effects appear to be weaker than those of the AMO and summertime NAO. Nevertheless, the
statistical model could be extended to incorporate other indices and quantify their possible effects on
UK heat wave numbers and lengths.
The patterns of SSTs in the North Atlantic have changed in recent years, with a cold anomaly
in the subpolar gyre and a warm anomaly in the subtropics [
35
]. A similar cold anomaly was last
present during the 1990s when the AMO index was negative and the subtropical SSTs were also
cooler than average [
36
]. The AMO index is typically calculated using SSTs over 20
◦
N to 70
◦
N, and
so does not represent these strong meridional gradients in SSTs well. Such gradients may lead to
increased storminess over Europe [
36
]. The impact of these SST gradients on UK heat waves is unclear.
In 2015, much of central Europe experienced prolonged periods of very high temperatures which have
been partly attributed to the strong SST gradient in the north Atlantic [
35
]. In contrast, the UK only
experienced a single very warm day (1 July 2015) when temperatures over 30
◦
C were recorded much
of England. Heat waves in the UK in 2015 were shorter in length than those in other years between
2010 and 2016 and were confined to south east England. Nevertheless, the statistical model could
be extended to include these cold SST anomalies, either as a simple binary flag or by the meridional
SST gradient, as another possible indicator of a summer heat wave. Another study [
22
] showed that
both the mega-El Niño/Southern Oscillation (mega-ENSO) and the AMO modulated the number of
heat wave days (HWF) over Europe on decadal timescales, although the effect of the AMO was larger.
The statistical model could be extended to include the mega-ENSO.
5. Conclusions
Increasing numbers and lengths of heat waves have been inferred from temperatures recorded at
weather stations the UK. These results are consistent with similar studies of heat waves in continental
Europe. Changes in heat wave lengths at some stations were found to be more complex than suggested
by a simple linear trend. The lengths of very long heat waves (over 10 days in length) declined from
the mid-1970s to the present day, whereas the lengths of shorter heat waves (up to 10 days) have
increased slightly over a similar period.
High multi-decadal variability in numbers and lengths of UK heat waves were identified at all
stations. A logistic regression model was constructed which suggested an association between the
sign and magnitude of the AMO and summertime NAO indices and numbers and lengths of heat
waves. The AMO had a larger effect than the NAO. These results were robust to different temperature
thresholds used to define heat waves and combinations of datasets of the AMO and summertime NAO.
Variations in the AMO and summertime NAO therefore appear to moderate the numbers and
lengths of heat waves in the UK. The AMO is currently in marginally negative phase, but could become
more negative. Any effects of a warming climate on heat waves in the UK in the near future could be
moderated by changes in the AMO.
Supplementary Materials: Supplementary materials can be found at www.mdpi.com/2073-4433/8/10/191/s1.
Acknowledgments:
This work was funded under the National Institute for Health Research Health Protection
Research Unit (NIHR HPRU) in environmental change and health, led by the London School of Hygiene and
Tropical Medicine in partnership with Public Health England (PHE), the University of Exeter and the Met Office.
The authors would like to thank KNMI and NOAA for enabling access to the climate indices and John Kennedy
for calculating one of the series of the Atlantic Meridional Oscillation used in this study.
Author Contributions:
M.G.S. conceived the study and designed the experiments. S.E.O.J. identified the weather
stations. M.G.S., K.H.S. and S.E.O.J. analysed the data. T.E. designed the logistic regression model and guided the
interpretation of the results. M.G.S. wrote the paper with substantial input from T.E., K.H.S. and S.E.O.J.

Atmosphere 2017,8, 191 14 of 17
Conflicts of Interest:
The authors declare no conflict of interest. The funding sponsors had no role in the design
of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, and in the
decision to publish the results.
Appendix A
Locations and Data Periods of the 29 Weather Stations Selected for Study
Table A1.
The 29 weather stations selected for study. All stations were operational up to and including
2016 and had near-continuous daily temperature data available from 1931 or earlier.
Station Name Latitude Longitude Country aData From
Aldergrove 54.6636 −6.22436 NI 1930
Armagh 54.3523 −6.64866 NI 1865
Balmoral 57.0375 −3.21897 SCO 1918
Bradford 53.8134 −1.77234 ENG 1908
Cambridge, Botanic
Gardens 52.1935 0.13113 ENG 1911
Craibstone 57.1868 −2.21323 SCO 1931
Cranwell 53.0309 −0.50194 ENG 1930
Cromer 52.9332 1.29273 ENG 1902
Douglas 54.168 −4.48022 IOM 1878
Durham 54.7679 −1.58455 ENG 1880
Eastbourne 50.7617 0.28543 ENG 1911
Lerwick 60.1395 −1.18299 SCO 1930
Leuchars 56.3775 −2.86051 SCO 1921
London, St James’s Park 51.5043 −0.12948 ENG 1903
Morecambe No 2 54.0762 −2.85825 ENG 1930
Morpeth, Cockle Park 55.2129 −1.68615 ENG 1897
Newton Rigg 54.6699 −2.78644 ENG 1906
Oxford 51.7607 −1.2625 ENG 1853
Plymouth Mountbatten
b50.3544 −4.11986 ENG 1874
Rothamsted 51.8062 −0.35858 ENG 1916
Sheffield 53.38128 −1.48986 ENG 1882
Shoeburyness b51.53606 0.80914 ENG 1930
Skegness 53.1476 0.34797 ENG 1904
Stornoway Airport 58.2138 −6.31772 SCO 1873
Teignmouth 50.5451 −3.49487 ENG 1931
Tiree 56.49982 −6.8796 SCO 1930
Valley 53.2524 −4.53524 WAL 1930
Wick Airport 58.4541 −3.0884 SCO 1930
Wisley 51.3103 −0.47478 ENG 1904
a
NI—Northern Ireland; SCO—Scotland; ENG—England; WAL—Wales; IOM—Isle of Man.
b
Data from two or
more stations were combined into a single series; see Section S2 for further details.

Atmosphere 2017,8, 191 15 of 17
Atmosphere 2017, 8, 191 15 of 17
Figure A1. Smoothed time series of the AMO (upper panel) and summertime NAO (lower panel).
The data sources are listed in Table S4.
Figure A2. Smoothed series of the AMO (orange line) and summertime NAO (pink line), together
with the numbers of heat waves per year for Armagh (solid circles) identified using the 98th percentile
threshold temperature. The values of the AMO index have been doubled for clarity.
Figure A1.
Smoothed time series of the AMO (upper panel) and summertime NAO (lower panel).
The data sources are listed in Table S4.
Atmosphere 2017, 8, 191 15 of 17
Figure A1. Smoothed time series of the AMO (upper panel) and summertime NAO (lower panel).
The data sources are listed in Table S4.
Figure A2. Smoothed series of the AMO (orange line) and summertime NAO (pink line), together
with the numbers of heat waves per year for Armagh (solid circles) identified using the 98th percentile
threshold temperature. The values of the AMO index have been doubled for clarity.
Figure A2.
Smoothed series of the AMO (orange line) and summertime NAO (pink line), together
with the numbers of heat waves per year for Armagh (solid circles) identified using the 98th percentile
threshold temperature. The values of the AMO index have been doubled for clarity.

Atmosphere 2017,8, 191 16 of 17
References
1.
D’Ippoliti, D.; Michelozzi, P.; Marino, C.; de’Donato, F.; Menne, B.; Katsouyanni, K.; Kirchmayer, U.;
Analitis, A.; Medina-Ramón, M.; Paldy, A.; et al. The impact of heat waves on mortality in 9 European cities:
Results from the EuroHEAT project. Environ. Health 2010,9, 37. [CrossRef] [PubMed]
2.
Dobney, K.; Baker, C.J.; Quinn, A.D.; Chapman, L. Quantifying the effects of high summer temperatures due
to climate change on buckling and rail related delays in south-east United Kingdom. Meteorol. Appl.
2009
,6,
245–251. [CrossRef]
3.
Van Vliet, M.T.H.; Ludwig, F.; Zwolsman, J.J.G.; Weedon, G.P.; Kabat, P. Global river temperatures and
sensitivity to atmospheric warming and changes in river flow. Water Resour. Res.
2011
,47, W02544. [CrossRef]
4.
Johnk, K.D.; Huisman, J.; Sharples, J.; Sommeijeri, B.; Visser, P.M.; Strooms, J.M. Summer heat-waves promote
blooms of harmful cyanobacteria. Glob. Chang. Biol. 2008,14, 495–512. [CrossRef]
5.
Della-Marta, P.M.; Haylock, M.R.; Luterbacher, J.; Wanner, H. Doubled length of western European summer
heat waves since 1880. J. Geophys. Res. 2007,112. [CrossRef]
6.
Labajo, Á.L.; Egido, M.; Martin, Q.; Labajo, J.; Labajo, J.L. Definition and temporal evolution of the heat and
cold waves over the Spanish Central Plateau from 1961 to 2010. Atmósfera 2014,27, 273–286. [CrossRef]
7.
Brugnara, Y.; Auchmann, R.; Brönnimann, S.; Bozzo, A.; Berro, D.C.; Mercalli, L. Trends of mean and extreme
temperature indices since 1874 at low-elevation sites in the southern Alps. J. Geophys. Res. Atmos.
2016
,121,
3304–3325. [CrossRef]
8.
Bartoszek, K.; Krzy ˙
zewska, A. The atmospheric circulation conditions of the occurrence of heatwaves in
Lublin, southeast Poland. Weather 2016,72, 176–180. [CrossRef]
9.
Morabito, M.; Crisci, A.; Messeri, A.; Messeri, G.; Betti, G.; Orlandini, S.; Raschi, A.; Maracchi, G. Increasing
heatwave hazards in the southeastern European Union capitals. Atmosphere 2017,8, 115. [CrossRef]
10.
Shevchenko, O.; Lee, H.; Snizhko, S.; Mayer, H. Long-term analysis of heat waves in Ukraine. Int. J. Climatol.
2014,34, 1642–1650. [CrossRef]
11.
Beniston, M. The 2003 heat wave in Europe: A shape of things to come? An analysis based on Swiss
climatological data and model simulations. Geophys. Res. Lett. 2004,31, L02202. [CrossRef]
12.
Parker, D.E.; Horton, E.B. Uncertainties in the Central England Temperature series since 1878 and some
changes to the maximum and minimum series. Int. J. Climatol. 2005,25, 1173–1188. [CrossRef]
13.
Hulme, M.; Jenkins, G.J.; Lu, X.; Turnpenny, J.R.; Mitchell, T.D.; Jones, R.G.; Lowe, J.; Murphy, J.M.; Hassell, D.
Climate Change Scenarios for the United Kingdom: The UKCIP02 Scientific Report; Tyndall Centre for Climate
Change Research, School of Environmental Sciences, University of East Anglia: Norwich, UK, 2002; p. 120.
14. Perkins, S.E.; Alexander, L.V. On the measurement of heat waves. J. Clim. 2013,26, 4500–4517. [CrossRef]
15.
Knight, J.R.; Folland, C.K.; Scaife, A.A. Climate impacts of the Atlantic Multidecadal Oscillation. Geophys. Res.
Lett. 2006,33, L17706. [CrossRef]
16.
Chylek, P.; Klett, J.D.; Lesins, G.; Dubey, M.K.; Hengartner, N. The Atlantic Multidecadal Oscillation as a
dominant factor of oceanic influence on climate. Geophys. Res. Lett. 2014,41, 1689–1697. [CrossRef]
17.
Della-Marta, P.M.; Luterbacher, J.; von Weissenfluh, H.; Xoplaki, E.; Brunet, M.; Wanner, H. Summer heat
waves over western Europe 1880–2003, their relationship to large-scale forcings and predictability. Clim. Dyn.
2007,29, 251–275. [CrossRef]
18.
Cropper, T.; Cropper, P.A. 133-year record of climate change and variability from Sheffield, England. Climate
2016,4, 46. [CrossRef]
19.
Folland, C.K.; Knight, J.; Linderholm, H.W.; Fereday, D.; Ineson, S.; Hurrell, J.W. The summer North Atlantic
Oscillation: Past, present, and future. J. Clim. 2009,22, 1082–1103. [CrossRef]
20.
Rust, H.W.; Richling, A.; Bissolli, P.; Ulbrich, U. Linking teleconnection patterns to European temperature—A
multiple linear regression model. Meteorol. Z. 2015,24, 411–423. [CrossRef]
21.
Kenyon, J.; Hegerl, G.C. Influence of modes of climate variability on global temperature extremes. J. Clim.
2008,21, 3872–3889. [CrossRef]
22.
Zhou, Y.; Wu, Z. Possible impacts of mega-El Niño/Southern Oscillation and Atlantic Multidecadal
Oscillation on Eurasian heatwave frequency variability. Q. J. R. Meteorol. Soc.
2016
,142, 1647–1661. [CrossRef]
23.
Met Office Integrated Data Archive System (MIDAS) Land and Marine Surface Stations Data
(1853–Current). NCAS British Atmospheric Data Centre. Available online: http://catalogue.ceda.ac.uk/
uuid/220a65615218d5c9cc9e4785a3234bd0 (accessed on 27 March 2017).

Atmosphere 2017,8, 191 17 of 17
24. Venables, W.N.; Ripley, B.D. Modern Applied Statistics with S, 4th ed.; Springer: New York, NY, USA, 2002.
25.
Van Oldenborgh, G.J.; te Raa, L.A.; Dijkstra, H.A.; Philip, S.Y. Frequency- or amplitude-dependent effects of
the Atlantic meridional overturning on the tropical Pacific Ocean. Ocean Sci. 2009,5, 293–301. [CrossRef]
26.
Enfield, D.B.; Mestas-Nunez, A.M.; Trimble, P.J. The Atlantic Multidecadal Oscillation and its relationship to
rainfall and river flows in the continental U.S. Geophys. Res. Lett. 2001,28, 2077–2080. [CrossRef]
27.
Kennedy, J.J.; Rayner, N.A.; Smith, R.O.; Saunby, M.; Parker, D.E. Reassessing biases and other uncertainties
in sea-surface temperature observations since 1850 part 2: Biases and homogenisation. J. Geophys. Res.
2011
,
116, D14104. [CrossRef]
28.
Knight, J.R.; Allan, R.J.; Folland, C.K.; Vellinga, M.; Mann, M.E. A signature of persistent natural thermohaline
circulation cycles in observed climate. Geophys. Res. Lett. 2005,32, L20708. [CrossRef]
29.
Trenberth, K.E.; Paolino, D.A. The Northern Hemisphere sea level pressure data set: Trends, errors, and
discontinuities. Mon. Weather Rev. 1980,108, 855–872. [CrossRef]
30.
Compo, G.P.; Whitaker, J.S.; Sardeshmukh, P.D. The Twentieth Century Reanalysis Project. Q. J. R.
Meteorol. Soc. 2001,137, 1–28. [CrossRef]
31.
R Core Team. R: A Language and Environment for Statistical Computing; R Foundation for Statistical Computing:
Vienna, Austria, 2016; Available online: https://www.R-project.org/ (accessed on 8 August 2017).
32.
Plummer, M. Rjags: Bayesian Graphical Models Using MCMC, R Package Version 4-4, 2015. Available online:
https://cran.r-project.org/package=rjags (accessed on 30 August 2016).
33.
IPCC. Summary for Policymakers. In Climate Change 2013: The Physical Science Basis. Contribution of Working
Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change; Stocker, T.F., Qin, D.,
Plattner, G., Tignor, M., Allen, S.K., Boschung, J., Nauels, A., Xia, Y., Bex, V., Midgley, P.M., Eds.; Cambridge
University Press: Cambridge, UK; New York, NY, USA, 2013; pp. 1–30.
34.
Vecchi, G.A.; Delworth, T.L.; Booth, B. Climate science: Origins of Atlantic decadal swings. Nature
2017
,548,
284–285. [CrossRef] [PubMed]
35.
Duchez, A.; Frajka-Williams, E.; Josey, S.A.; Evans, D.G.; Grist, J.P.; Marsh, R.; McCarthy, G.D.; Sinha, B.;
Berry, D.I.; Hirschi, J.J.-M. Drivers of exceptionally cold North Atlantic Ocean temperatures and their link to
the 2015 European heat wave. Environ. Res. Lett. 2016,11, 074004. [CrossRef]
36.
Frajka-Williams, E.; Beaulieu, C.; Duchex, A. Emerging negative Atlantic Multidecadal Oscillation index in
spite of warm subtropics. Sci. Rep. 2017,7, 11224. [CrossRef] [PubMed]
©
2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access
article distributed under the terms and conditions of the Creative Commons Attribution
(CC BY) license (http://creativecommons.org/licenses/by/4.0/).