Hasegawa et al. Progress in Earth and Planetary Science
https://doi.org/10.1186/s40645-020-00390-8(2020) 7:78

RESEARCH ARTICLE

Progress in Earth andPlanetary Science

Open Access

Impact of air–sea coupling on theprobability of occurrence of heat waves inJapan
Akira Hasegawa1* , Yukiko Imada2, Hideo Shiogama1,3, Masato Mori4, Hiroaki Tatebe5 and Masahiro Watanabe1

Abstract
In extreme event attribution, which aims to answer whether and to what extent a particular extreme weather event
can be attributed to global warming, the probability of an event is generally estimated through large ensemble
simulations, using an atmospheric general circulation model (AGCM). In islands, such as Japan, it has been consideredthat surface air temperature (SAT) can be significantly affected by the surrounding sea surface temperature (SST), whichmostly is affected by atmospheric circulation at mid- and high-latitudes. Therefore, the absence of SST responses toatmospheric variability in AGCMs impacts the estimation of the occurrence of extreme events, such as heat waves inJapan. In this study, we examined the impact of air–sea coupling on the probability of occurrence of severe heat waves
that occurred in Japan in the summer of 2010 by analyzing the probability differences obtained from AGCM and coupledgeneral circulation model (CGCM) large-ensemble experiments. The observed ocean temperature, salinity, and sea ice
were assimilated in the 100-member CGCM experiments, as they were assigned as boundary conditions in the 100member AGCM experiments. The SAT around Japan in the northern summer is largely related to the Bonin high, whose
interannual variability is largely affected by the Silk Road and Pacific-Japan (PJ) pattern teleconnections in the real world.
The SAT anomaly over Japan was related to the pressure variability due to the Silk Road and PJ patterns in the CGCM
experiment. By contrast, the SAT over Japan simulated by AGCM was less sensitive to such pressure variability, and theSAT ensemble spread became narrower in AGCM. The results suggest that the probability of occurrence of the 2010 heatwave in Japan would tend to be underestimated by the AGCM ensemble compared to the CGCM ensemble, provided
that the ensemble averages of the SAT anomalies were equal between CGCM and AGCM experiments. This study raised
the issue of the absence of SST response to atmospheric variability in AGCMs, which can critically impact the estimationof extreme event probability, particularly in mid-latitude islands, such as Japan.
Keywords: Atmosphere-ocean coupling, Heat waves, Probability density function, Atmospheric internal variability, Silk
Road wave train, Pacific-Japan pattern, Event attribution

1 Introduction
Extreme event attribution (EA) has been developed overthe past decade to address questions regarding the impact of global warming on specific extreme weather
events. Various types of approaches have been used to
conduct EA, including observational analyses, model* Correspondence: hakira@aori.u-tokyo.ac.jp
1
Atmosphere and Ocean Research Institute, The University of Tokyo, 5-1-5
Kashiwanoha, Kashiwa, Chiba 277-8564, Japan
Full list of author information is available at the end of the article

analyses, and multi-method studies (Stott et al. 2016;
Easterling et al. 2016; Otto 2017). Shepherd (2016)highlighted two aspects of attribution questions: how anthropogenic climate change has altered the probabilityof occurrence of individual extreme events (risk-based
approach), and how the severity (magnitude or intensity)of a particular event has changed due to climate change(storyline approach). Generally, the risk-based approachis based on two model experiments—for current conditions and a counterfactual world without anthropogenic© The Author(s). 2020 Open Access This article is licensed under a Creative Commons Attribution 4.0 International License,
which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give
appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate ifchanges were made. The images or other third party material in this article are included in the article's Creative Commonslicence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commonslicence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain
permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

Hasegawa et al. Progress in Earth and Planetary Science(2020) 7:78

emissions (with pre-industrial concentrations of CO2
and other greenhouse gases, including aerosols)—as
described by Allen (2003). By preparing large ensembles
to simulate the current climate and a counterfactual
climate without anthropogenic climate change, the presumption of the shape of the extremal distribution is not
required to compare the probability.
The selection of a numerical model depends on themost relevant type of natural variability for the case analyzed. In many cases, an atmospheric general circulation
model (AGCM) has been used for EA studies because
the timescale of the most concerning extreme weather
events is usually within 1 month. Compared to thistimescale, dominant intrinsic oceanic or sea ice variability has a considerably longer timescale, represented byinterannual, decadal, and multi-decadal variability. Thus,
the state of the ocean or sea ice during an extreme event
can be considered the boundary condition for AGCM asa background climate condition of the extreme event infocus. However, in mid- and high-latitude oceans, atmospheric circulation is rather a driver of ocean circulation and considerably affects surface heat fluxes at
shorter time scales. The atmospheric model led to unrealistic heat flux at the air–sea interface (Yu andMechoso 1999) and the absence of important feedback
processes (Kitoh and Arakawa 1999). These issues raise
the question whether air–sea interaction critically affects
the estimation of event probability in the EA approach,particularly for islands surrounded by ocean, such as
Japan. Fischer et al. (2018) showed that sea surface
temperature (SST)-forced models underestimate thetemperature variability, whereas Uhe et al. (2016) indicatedthat the effect of air–sea interaction on extreme events is
considerably smaller. Therefore, whether air–sea coupling
critically affects an EA framework remains unclear. It also
appears to depend on the location of the focus.
In this study, we propose a new framework to estimate
the probability of extreme events, based on a conceptually more realistic approach, which considers both thelonger time-scale background situation and the shorter
air–sea coupling processes around mid-latitude small
islands. It should be noted that a true probabilistic distribution of an observed event remains unknown because
the observation is only a single realization among infinite
possibilities. Thus, a numerical simulation is needed todeduce the distribution. Figure 1 shows a conceptual illustration explaining the composing elements of thevariance of a probability density function (PDF) for acertain extreme index. When we use long-term coupledmodel intercomparison project (CMIP) type historicalsimulations (see Section 2) during some decades to draw
a PDF (Fig. 1a, assuming single model), its variance iscomposed of an intrinsic natural variability of the ocean
and atmosphere and the climatological tendency inPage 2 of 12

response to external forcings, such as greenhouse gases
and aerosols. When a large ensemble of CMIP-type historical simulations is available, we can draw a PDF using
only the data of a certain period (e.g., a certain month ofa certain year) when an extreme event occurred (Fig.
1b). In this case, the external forcings are fixed to a specific level, and the variance of the PDF is composed of
atmospheric and oceanic (sea ice) natural variabilities.
By contrast, when we use AGCM simulations with
fixed boundary conditions for the observed ocean andsea ice focusing on the period of a certain extreme event(Fig. 1d), the variance of its PDF is composed only of atmospheric intrinsic natural variability, which has been
the most used in many EA studies. In shorter timescales, which can be perceived by humans, probabilistic
behaviors that can trigger extreme weather are induced
by atmospheric intrinsic variability, whereas the effect ofoceanic fast responses to the atmospheric stochastic
variability should also be considered as a component of
the probabilistic behaviors in the mid-latitude coastal regions. Given the fixed SST, the coastal air temperaturemight have a narrower variance. Thus, the conventional
approach using AGCM might be inadequate to consider
those probabilistic behaviors of the ocean.
In this study, we tested the estimation of extreme
event probabilities using large-ensemble simulations ofocean data assimilation with a coupled general circulation model (CGCM) that can consider both short-term
oceanic responses to atmospheric variability and prescribed long-term oceanic intrinsic variability (Fig. 1c).
By comparing event probability between large ensemblesof AGCM and the assimilated CGCM runs, we evaluatedthe impact of air–sea coupling on the shape of a PDF,
particularly on its tail. The difference would be criticalto the estimation of a risk ratio in EA studies. In thispaper, we will not discuss the impact of air–sea coupling
on a risk ratio but focus on the shape of PDFs, thus only
using factual simulations.
As an example, we compared the probability of extreme events between large ensemble simulations of
AGCM and CGCM, focusing on the extreme warm
event that occurred in 2010 in Japanese islands, which
are surrounded by the ocean. The surface airtemperature (SAT) around Japan in the northern summer is largely related to the Bonin high. Two types ofteleconnection patterns—the Pacific-Japan pattern (Nitta
1987; Kosaka and Nakamura 2010) and the Silk Road
pattern (Enomoto et al. 2003; Enomoto, 2004)—largely
affect the interannual variability of the Bonin high (e.g.,
Wakabayashi and Kawamura 2004; Yasunaka and
Hanawa 2006). Thus, we focused on the representationof the causal relationship between SAT variability
around Japan and the Silk Road and PJ teleconnections
in AGCM and CGCM simulations.

Hasegawa et al. Progress in Earth and Planetary Science(2020) 7:78

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Fig. 1 Schematic illustration of the probability density functions for SAT and SST, compared between a CGCM historical experiment during somedecades, b CGCM historical experiment, c CGCM assimilation, and d AMIP-type experiments for a certain year

The data, methods, and experimental design are described in the following section. The impact of air–sea
coupling on the probability of the Japanese heat wave
event in 2010 is described in Section 3. The different contributions of the PJ and Silk Road teleconnections between
AGCM and CGCM simulations are discussed in Section
4, and the conclusion is presented in Section 5.

2 Methods and experimental design
We used the sixth version of the Model for Interdisciplinary Research on Climate (MIROC6), described by
Tatebe et al. (2019) in more details. MIROC6 is composed of T85L81 atmosphere and 1L62 ocean. It is oneof the CMIP phase 6 (CMIP6; Eyring et al. 2016)
models.
To estimate the probabilities of extreme events, weprepared two types of large ensemble simulations withthe atmospheric component of MIROC6 (MIROC6AGCM) and the coupled version of MIROC6 (MIROC6CGCM). Using MIROC6-AGCM, a 20-member ensemble of the Atmospheric Model Intercomparison Project(AMIP)-type experiment was conducted from 1979 to2014, which was driven by the observed SST, sea ice
concentration (COBE-SST2; Hirahara et al. 2014), andhistorical anthropogenic and natural external forcing
agents. The probability of the Japanese heat wave wassubsequently evaluated by increasing the ensemble size
to 100 only for 2010, which corresponds to a factual
simulation of a traditional EA framework.
To reproduce seasonal and interannual variabilities in
the CGCM framework, we adopted 10-member full-field
assimilation experiments, in which observed ocean
temperature, salinity, and sea ice were assimilated for
1951–2014, which were conducted as an initialization
process for the CMIP6 Decadal Climate Prediction Project(DCPP, Kataoka et al., 2020. under review). To increase thenumber of ensemble members from 10 to 100, we reran
the full-field assimilation runs from February to December
2010 with 100 different combinations of atmosphere andocean restart files. This full-field assimilation experiment istermed as CAssm.
For reference, CGCM runs without any data assimilation were also analyzed. A 50-member ensemble of theCMIP6 historical experiment (hereafter denoted as

Hasegawa et al. Progress in Earth and Planetary Science(2020) 7:78

CHist) was available from 1851 to 2014 as a noassimilation CGCM case.
The anthropogenic and natural external forcing agentsare common among AMIP, CHist, and CAssm experiments. SST and sea ice concentrations assimilated in
CAssm are the same as the boundary conditions in
AMIP runs.
For verification, we used COBE-SST2 (Hirahara et al.
2014), Global Precipitation Climatology (GPCP; Adler
et al. 2003), and a 55 year Japanese reanalysis dataset(JRA-55; Kobayashi et al. 2015).
We defined SST around Japan (SSTJP) as the area
average of SST in the longitude-latitude box (125–150°
E, 25–50° N). The SAT averaged over Japanese islands isdenoted as SATJP.
The Silk Road pattern index is defined as the second
mode of empirical orthogonal function (EOF) analysis ofdetrended 200 hPa geopotential height in the box (30–50° N, 30–130° E) for each 30 year ensemble simulation

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and JRA-55. The first mode of EOF corresponded to the
Arctic Oscillation-like mode (not shown). The PacificJapan pattern index is defined as the second mode of
EOF analysis of 850 hPa relative vorticity in the box (0–60° N, 100–160° E). We assumed the multiple linear regression of SATJP anomaly (y) as the response variable
for each teleconnection pattern, as follows:y ¼ β0 þ βPJ ∙xPJ þ βSR ∙xSR þ εwhere xPJ and xSR are the PJ and Silk Road pattern indices defined above, βPJ and βSR are multiple regression
coefficients for the PJ and Silk Road patterns, and β0 andε are the intercept and error terms, respectively.

3 Results
3.1 Thirty-year simulations

Figure 2a–c shows the time-series of SSTJP anomalies inAugust from 1981 to 2010 for AMIP, CAssm, and CHist

Fig. 2 Time series of SST anomalies around the Japanese islands (SSTJP, left) and SAT anomalies over land of the Japanese islands (SATJP, right) for
August 1981 to 2010, obtained from a, d AMIP, b, e CAssm, and c, f CHist experiments. Black lines of SSTJP and SATJP anomalies mean those in
COBE-SST2 and JRA-55, respectively. Colored thin and thick lines show the anomalies of each ensemble member and the ensemble
average, respectively

Hasegawa et al. Progress in Earth and Planetary Science(2020) 7:78

experiments, respectively. The black line in each panel
indicates the SSTJP anomaly in COBE-SST2 dataset,
whereas the colored thick lines represent ensemble averages, and the colored thin lines represent the 20-, 10-,and 50-member ensembles for AMIP, CAssm, and CHist
experiments, respectively. With regards to the ensemble
mean response, as shown in Table 1, CAssm shows arelatively high reproductivity of the observed interannual
SSTJP variability (R ~ 0.74) due to the ocean temperatureassimilation, compared to CHist (R ~ 0.30) without assimilation. Table 1 shows that the averages and standard
deviations of SSTJP in both CAssm and CHist are relatively lower than those in COBE-SST2, used as a boundary condition for JRA-55 and the AMIP experiment.
Figure 2d–f shows the time-series of SATJP anomalies
in August from 1981 to 2010 for AMIP, CAssm, andCHist experiments, respectively. The black lines indicate
the SATJP anomaly in the JRA-55 reanalysis dataset(Kobayashi et al. 2015). The number of ensemble members in AMIP (20) was twice that of CAssm (10). Nevertheless, SATJP in the AMIP ensemble shows a relatively
smaller variance compared to that in the CAssm ensemble, indicating a relatively small noise in AMIP ensemble.
The ensemble mean response of SATJP in AMIP
showed similar interannual variability as that found in
the JRA-55 dataset, as shown in Fig. 2d, whereas CAssm
showed a relatively weak coherency with JRA-55, asshown in Fig. 2e. Table 2 shows that the correlation coefficients of SATJP with JRA-55 are approximately 0.65
and 0.27 for AMIP and CAssm, respectively. Based on
the comparison of the correlation coefficients, AMIP
seems to be more reproducible. However, to deduce the
PDF of extreme events, it can be said that AMIP overestimates a signal-to-noise ratio (underestimates the noise)because of the absence of the intraseasonal responses ofthe ocean to the atmospheric internal variability, which
can affect the probability of SATJP extremes. Because of
the absence of the oceanic intraseasonal responses to theatmosphere, SATJP in AMIP appeared to be strongly restricted around the observed SST field. Hence, we deduced the range of noise created by the intraseasonal
internal variabilities of both atmosphere and ocean to estimate the probability of extreme events from largeensemble simulations. It is considered that the absenceof noises induced by the ocean could lead to overestimation of a signal-to-noise ratio, resulting in a larger

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correlation in AMIP. Thus, we assume that CAssm withrelatively larger noise and smaller correlation would capture a more realistic probabilistic distribution. By contrast, the interannual variability simulated by CHist issignificantly different from that in JRA-55 (R ~ 0.10) because of the model-own internal variability, which is freefrom the long-term observed variation in the ocean andsea ice.
Figure 3a–i shows the SAT, sea level pressure (slp),
and 200 hPa geopotential height (z200) anomalies forAugust 2010 (reference period of climatology: 1981–2010) in JRA-55, AMIP, and CAssm, respectively. Bothobserved and simulated SAT showed a positive anomaly
around Japan in August 2010. On this date, the Japaneseislands were covered by positive pressure anomalies atlower (slp) and upper (z200) levels (Fig. 3d–i). In the ensemble mean field (Fig. 3e, f, h, i), the simulated slp
anomalies near Japan are off to the south and the wave
trains along the subtropical jet are unclear. This is because noise components are compensated, whereas theobserved field includes atmospheric noises. When we
focus on the one specific member whose PJ and Silk
Road indices are similar to those of the observation, thecirculation patterns are comparable with JRA-55 (notshown).
Figure 3j shows that GPCP had a relatively low precipitation anomaly around Japan in August 2010. In Fig. 3k
and l, low precipitation anomalies over the Japaneseislands are also shown in AMIP and CAssm, respectively,
but they are unclear. Both AMIP and CAssm represent
the dry region on the east side of the Philippines, associated with the cold SST region (not shown) in Fig. 3k andl. The contrast between dry and wet regions of the maritime continent is more enhanced in AMIP than in CAssm
and JRA-55. The correlation coefficient between SST and
precipitation in August 1981–2010 is mostly positive over
the western North Pacific in AMIP, and negative inCAssm and observation (not shown), as indicated by
Wang et al. (2005). These differences between AMIP and
CAssm indicate that CAssm could reproduce the waterand energy cycles more reasonably than AMIP in the
Asian-Pacific summer monsoon region.
The climatological error of the simulated SATJP in
August 1981–2010 against the SATJP in JRA-55 was +0.13 K for AMIP and CAssm, and − 0.28 K for CHist, asshown in Table 2. The standard deviation of SATJP for

Table 1 Averages and standard deviations of SSTJP for August 1981 to 2010 and correlation coefficients of SSTJP with COBE-SST2 forAugust over the 30 years. Numbers in parentheses represent the number of samples for the 30 years
COBE-SST2 (30)

CAssm (300)

CHist (1500)

Average [K]298.46298.14297.47

Standard deviation [K]

0.452

0.420

0.400

Correlation coefficient with COBE-SST2

1.000

0.741

0.299

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Table 2 Averages and standard deviations of SATJP for August 1981–2010 and correlation coefficients of SATJP with JRA-55 forAugust over the 30 years. Numbers in parentheses represent the number of samples for the 30 years
JRA-55 (30)

AMIP (600)CAssm (300)

CHist (1500)

Average [K]297.29297.42297.42297.01

Standard deviation [K]

0.919

0.635

0.633

0.639

Correlation coefficient with JRA-55

1.000

0.649

0.271

0.105

August 1981–2010 was approximately 0.92 K in JRA-55
and 0.63 K in AMIP, CAssm, and CHist. Therefore,
MIROC6 tended to underestimate the temperature variability than the reanalysis around Japan in August, regardless of the atmosphere–ocean coupling. When
comparing the simulation results with the observation orreanalysis, the anomaly from the climatological average

was used to avoid climatological errors in this study.
The bias of the interannual variance was not corrected.
Next, we investigated the relationship of the interannual variability of SATJP in August with the Silk Road
and PJ patterns in the AGCM and CGCM simulations.
Regression patterns for August 200 hPa geopotential
height onto August SATJP, obtained from the 350 year

Fig 3 Anomaly maps of the a–c SAT, d–f sea level pressure, g–i 200-hPa geopotential height, and j–l precipitation for August 2010 obtained
from JRA-55 and GPCP (left column), MIROC6 AMIP (center column), and CAssm (right column) experiments, respectively

Hasegawa et al. Progress in Earth and Planetary Science(2020) 7:78

samples (10-member ensemble for 35 years for 1980–2014), showed wave trains over Eurasia forming a positive anomaly over Japan, with a 98% significance levelfor both AMIP and CAssm, as shown in Fig. 4a and b. It
is known that the Tibetan high extends eastward andbrings heat waves over Japan, associated with the Silk
Road teleconnection (Imada et al. 2019). The difference
between Fig. 4a and b shows that the Silk Road patternis emphasized in CAssm compared to AMIP (Fig. 4c).
By contrast, regression patterns for August 850 hPa
relative vorticity (vor850) onto August SATJP obtained
from the 350 year samples showed a negative (anticyclonic) anomaly over Japan and positive (cyclonic) anomalies to the north and south of Japan with a 98%
significance level for both AMIP and CAssm, as shown in
Fig. 4d and e. This is consistent with the PJ pattern, which
is often observed during Japanese high-temperature events(Imada et al. 2019).
Figure 5 shows the multiple linear regression of thedetrended SATJP (SAT*JP) anomaly in August for the
350 year ensemble simulations of AMIP and CAssm.
The horizontal and vertical axes indicate the PJ and Silk
Road indices, respectively. The positive (negative) valuesof horizontal and vertical axes of Fig. 5 mean that the
anticyclonic (cyclonic) anomalies cover the Japaneseislands, associated with the PJ and Silk Road patterns,
respectively. The PJ and Silk Road pattern indices in Fig.
5 are normalized by each standard deviation. The 350

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scattered circles show the SAT*JP anomaly colored witha temperature level for each experiment. The background tiles show the average of SAT*JP anomalies
within them. Figure 5a shows that SAT*JP is less correlated to the PJ and Silk Road pattern teleconnections in
the 350 year ensemble simulations of AMIP. By contrast,
hot (cold) SAT*JP cases are located at the upper-right(lower-left) side of the diagram in CAssm (Fig. 5b).
Thus, the anticyclonic (cyclonic) anomaly over the Japanese islands, associated with the positive (negative)
values of the PJ and Silk Road pattern indices, makes thedetrended SATJP hotter (colder) in August for 1980 to2014 in CAssm, as we expect in the real world. The
multiple regression coefficients βPJ and βSR are listed inFig. 5 with the 95% confidence intervals as the numbers
within parentheses. Although βPJ is not significant in
AMIP, it is significantly positive in CAssm for August
1980–2014. The detrended SAT over the Japaneseislands is more sensitive to the PJ pattern in CAssm thanin AMIP. Nonetheless, βSR is significant but small (~0.09) in AMIP and CAssm. The contribution of the Silk
Road pattern to SAT*JP is similar regardless of the air–sea coupling.
We also calculated the multiple linear regression ofSAT*JP anomaly against both the teleconnection indicesin August 1980–2014 using JRA-55. The multiple regression coefficients βPJ and βSR are not significant in
JRA-55 dataset. As the number of samples is quite

Fig. 4 Regression maps of 200 hPa geopotential height (z200; upper panels) and 850 hPa relative vorticity (vor850; lower panels) onto SATJP
obtained from the 350 year (10 members from 1980 to 2014) ensemble simulations using a, d AMIP and b, e CAssm experiments. Differences
between CAssm and AMIP experiments are shown for the regressions of c z200 and f vor850, respectively. The red boxes show the target areasof EOF analysis for a Silk Road and d PJ pattern indices, respectively

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Fig. 5 Multiple linear regression of the detrended SATJP anomalies against PJ and Silk Road pattern indices obtained from 350 year (10 members
for 1980 to 2014) ensemble simulations using a AMIP and b CAssm experiments. Each circle shows the detrended SATJP anomaly for each year,
and the background tiles show the average of the detrended SATJP anomalies within them. The gray tiles mean there are no circles within them.
βPJ and βSR are the regression coefficients of PJ and Silk Road pattern indices with 95% confidence intervals as the numbers withinparentheses, respectively

smaller in the reanalysis than in large ensemble simulations, the relationship between SAT*JP and the PJ and
Silk Road teleconnection patterns is not clear in JRA-55(figures not shown). The PJ and Silk Road pattern indices are approximately − 0.59 and 1.07 in August 2010 in
JRA-55, respectively. Thus, the positive contribution of
the Silk Road teleconnection to SATJP is partly canceledby the negative effect of the PJ pattern in August 2010
in the reanalysis dataset.
3.2 Large ensemble simulations for August 2010

Figure 6a and b shows the PDFs of SATJP and SSTJP
anomalies in August 2010 for each experiment, respectively, estimated by the kernel method (Silverman 1986;
Kimoto and Ghil 1993).
Table 3 shows the comparison of SSTJP for August2010 between COBE-SST2 and the 100-member CAssm
experiments. The 100-member ensemble average of
SSTJP in CAssm was approximately 0.76 K smaller thanthe SSTJP in COBE-SST2 for August 2010. In CAssm,
we can estimate the possible SST variance induced by
the atmospheric intrinsic variability using the 100member ensemble, whereas it is not possible with a single realization of the observation. The standard deviationof SSTJP in August 2010 is approximately 0.22 in
CAssm. Figure 6b shows the PDFs of SSTJP in August2010 for COBE-SST2, AMIP, and CAssm. The blackand blue dashed lines are fixed at approximately 0.86 K
because COBE-SST2 is used as a fixed boundary

condition for 100-member AMIP simulations. The exceedance probability of SSTJP in August 2010 was approximately 9.1% in CAssm.
Table 4 shows that the 100-member ensemble averages of SATJP in AMIP and CAssm were approximately
0.79 and 1.26 K smaller than those in JRA-55 for August
2010, respectively. One reason for this is the systematic
biases of SATJP in MIROC6, as shown in Table 2. The
other reason is the difference between the observation(including the stochastic noise) and ensemble meanvalues (without the stochastic noise). The ensemble
average of SATJP in AMIP is higher than that in CAssm
in August 2010 because the AMIP simulations arestrongly constrained by the observed SST. Table 4 also
shows that the standard deviation of SATJP among the
100-member ensemble was larger in CAssm (approximately 0.49 K) than in AMIP (approximately 0.37 K).
Figure 6a shows the PDFs of SATJP anomalies inAugust 2010 for JRA-55, AMIP, and CAssm. The blackline at 1.94 K indicates the SATJP anomaly in JRA-55.
The exceedance probabilities over the threshold of 1.94
K were estimated for each experiment (Fig. 6a and Table4). The exceedance probability was approximately 1.1%
and 0.18% in AMIP and CAssm, respectively. The difference in the shape of the PDFs between AMIP (narrow
and tall) and CAssm (wide and short) was similar to that
expected from Fig. 1. Figure 6a also shows a large difference in the PDF peaks between AMIP and CAssm.
These differences imply that the AGCM framework used(2020) 7:78

Hasegawa et al. Progress in Earth and Planetary Science

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Fig. 6 Probability density functions of a SATJP and b SSTJP anomalies for August 2010 obtained from CAssm (red), AAssm (green), and AMIP
(blue) experiments, estimated by the kernel method (Silverman 1986; Kimoto and Ghil 1993). Vertical lines at approximately a 1.94 K and b 0.86 Kshow the SATJP and SSTJP anomalies obtained from JRA-55 and COBE-SST2, respectively

in the conventional EA approach might underestimate
the variance of PDF and be strongly constrained by theobserved value, resulting in overestimation of the probability of occurrence of an extreme event compared to
the CAssm framework, because of the absence of the internal variability associated with the air–sea coupling.

4 Discussion
We could not detect a pure effect of atmosphere–
ocean interaction by comparing AMIP and CAssm
because the SST boundary condition of AMIP is a
Table 3 Averages and standard deviations of SSTJP for August
2010, and exceedance probabilities over ΔSSTJP in COBE-SST2
for August 2010 in CAssm. Numbers in parentheses represent
the number of samples for August 2010
COBE-SST2 (1)CAssm (100)Average [K]299.32298.56

Standard deviation [K]

–

0.223

Exceedance probability [%]

–

9.06

single realization among the possible perturbed SST
patterns used in CAssm. The differences in the PDFs
between AMIP and CAssm could be strongly affectedby different SST patterns (one-way direct impact from
SST). To examine the effect of pure air–sea coupling(two-way interaction), we conducted additional 100member ensemble experiments using AGCM, obtaining the daily boundary conditions of SST and sea ice
concentration from the 100-member outputs ofCAssm. The additional 100-member experiment is denoted as AAssm in this study.
We compared the PDFs of SATJP between CAssm andAAssm in Fig. 6. The anomalies in AAssm were definedby the deviation from their climatological averages inCAssm. In Fig. 6a, the shape of the SATJP PDF curve for
CAssm is wider and shorter than that of AAssm. Figure
6a and Table 4 show that the exceedance probability wasslightly smaller in AAssm as a result of smaller variancedue to the absence of air–sea interaction. Furthermore,
the PDF of CAssm showed negative skewness comparedto that of AAssm.

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Table 4 Averages and standard deviations of SATJP for August 2010, and exceedance probabilities over ΔSATJP in JRA-55 for August2010 in AMIP, AAssm, and CAssm experiments. Numbers in parentheses represent the number of samples for August 2010JRA-55 (1)AMIP (100)AAssm (100)CAssm (100)Average [K]299.23298.45298.06297.97

Standard deviation [K]

–

0.369

0.390

0.488

Exceedance probability [%]

–

1.09

0.147

0.183

This can be understood from the relation with the PJ
and Silk Road pattern indices. Figure 7 shows the multiple
linear regression of the SATJP anomalies from the 100member ensemble averages (δSATJP) against the PJ and
Silk Road pattern indices for August 2010 of AMIP,
AAssm, and CAssm, as shown in Fig. 5. The PJ and Silk
Road pattern indices for both AAssm and CAssm in Fig. 7
are commonly normalized by the standard deviation forthe 350 year ensemble simulations of CAssm, while those
for AMIP in Fig. 7a is normalized by the standard deviation for the 350 year ensemble simulations of AMIP.
Figure 7a and b shows that the SATJP anomaly fluctuates in AMIP and AAssm regardless of the pressure variability over Japan due to PJ and Silk Road patternvariabilities in August 2010, which are consistent with
Fig. 5a. Both regression coefficients βPJ and βSR are notsignificant to the 100-member AAssm experiment inAugust 2010, as shown in Fig. 7b. By contrast, Fig. 7cshows that SATJP becomes higher (lower) under the
anticyclonic (cyclonic) anomaly over the Japanese islands
associated with the positive (negative) teleconnection indices in August 2010, which is consistent with Fig. 5b.
Both regression coefficients βPJ and βSR are positive with
95% significance level in August 2010 in CAssm, as
shown in Fig. 7c. SATJP variability associated with the PJ
and Silk Road teleconnection patterns is reasonably
reproduced in CGCM simulations.

The SATJP variance among the 100-member ensemble
was larger in CAssm than in AAssm for August 2010.
The standard deviations are approximately 0.39 and 0.49
for AAssm and CAssm, respectively, as shown in Table
4. Figure 6a shows that the enhanced variance of SATJP
in CAssm is mainly due to the lower SATJP cases, which
are located at the lower-left side in Fig. 7c. Therefore,
the SAT variance over Japan could be increased in association with the increase of negative skewness induced
by atmospheric teleconnection patterns and atmosphere–ocean coupling. Because anticyclonic anomalieschange the surface temperature through the adiabatic
heating and less cloudiness, the nonlinear variation ofcloud covers is one of the reasons of the negativeskewness.

5 Conclusions
This study investigated the impact of air–sea interaction
on the probability of occurrence of extreme events in
mid-latitude small islands surrounded by the ocean. We
compared the event probability, estimated by AGCM
and CGCM large-ensemble experiments, of the heatwaves that occurred in Japan in August 2010. The observed ocean temperature, salinity, and sea ice were assimilated into 100-member CGCM experiments. We
compared the CGCM assimilation ensemble (CAssm)for August 2010 with two types of 100-member AGCM

Fig. 7 Multiple linear regression of SATJP anomalies against PJ and Silk Road pattern indices for August 2010 from a AMIP, b AAssm, and c CAssm
experiments. βPJ and βSR are the regression coefficients of PJ and Silk Road pattern indices with 95% confidence intervals as the numbers withinparentheses, respectively

Hasegawa et al. Progress in Earth and Planetary Science(2020) 7:78

experiments: the AGCM ensemble with the boundary
conditions from the CGCM assimilation experiment(AAssm), and the AMIP-type ensemble with the single
boundary condition from the observation (AMIP). The
AMIP-type ensemble has generally been used in the
study of event attribution.
We can interpret the difference of SAT anomaly
around Japan between AMIP and CAssm experiments,
illustrated in Fig. 1c and d, by decomposing the difference into two parts: one between AMIP and AAssm,and the other between AAssm and CAssm experiments.
One difference between AMIP and AAssm is the ensemble average shift of the SAT anomalies due to the
SST distribution difference between the observation andassimilated fields. The ensemble-averaged intensity of
the Japanese heat wave in 2010 in AAssm becomes
smaller than that in AMIP, as shown in Fig. 6a. The
other difference between AMIP and AAssm is the ensemble variance of the SAT due to the different varianceof the SST field. The SAT ensemble spread under the
100-kind boundary conditions in AAssm becomes larger
than that under the single boundary condition in AMIP.
These are the main sources of the difference in the SAT
PDFs between the two types of AGCM experiments in
Fig. 6, and both differences depend on the assimilation
intensity in the CGCM.
The difference between AAssm and CAssm is inducedby the pure effect of the air–sea coupling. The assimilated CGCM experiment can reproduce the SAT variability due to the pressure variability related with the
Silk Road and PJ pattern teleconnections, as expected in
the real world. Such a mechanism could expand the ensemble spread of the SAT over Japan under the air–sea
coupled condition. However, the absence of air–sea
coupling in AAssm could distort the response mechanism of the SAT over Japan to such atmospheric internalvariability. Even if the SST fields are common between
AGCM and CGCM ensembles, the ensemble spread of
the SAT over Japan in August 2010 is reduced in the
AGCM experiment. Note that we did not investigate
whether the air–sea coupling modified the PJ and Silk
Road pattern teleconnections themselves in this study.
The results showed that the ensemble spread of the
SAT over Japan in the CGCM experiment was larger
than those in the two types of AGCM experiments forAugust 2010. If the ensemble average of the SAT anomaly is equal in CGCM and AGCM ensembles, the probability of occurrence of the heat wave over Japan inAugust 2010 could be estimated to be smaller by
AMIP ensemble, compared to CAssm. However, as
the ensemble average of the SAT anomaly was large
in AMIP, the probability of occurrence of the heatwave was estimated to be smaller in CAssm ensemble, compared to AMIP.

Page 11 of 12

Further analysis suggested that the SAT anomaly overJapan was well related to the pressure variability due tothe Silk Road and PJ pattern indices in the CGCM assimilation experiment, as reported for the real world. By
contrast, the simulated SAT over Japan by AGCM wasless sensitive to these atmospheric internal variabilities,
and the ensemble spread became narrower in the
AGCM experiment.
In many extreme EA studies, the probability of anevent has been estimated using large ensemble simulations performed by AGCMs. This study raised the issueof the absence of SST response to atmospheric variability in AGCMs, which can critically impact the estimationof extreme event probability, particularly in mid-latitudeislands, such as Japan. The new framework using the
CGCM assimilation system proposed in this study conceptually provides a more realistic probability distribution. Our next step is to produce a counterfactual
ensemble without anthropogenic climate change by applying the CGCM assimilation system and verify the impact of air–sea coupling on the estimated probability
ratio from the two ensembles.
Abbreviations
AGCM: Atmospheric general circulation model; AMIP: Atmospheric modelintercomparison project; CGCM: Coupled general circulation model;
CMIP: Coupled model intercomparison project; EA: Event attribution;
PDF: Probability density function; SAT: Surface air temperature; SST: Sea
surface temperature
Acknowledgements
We thank the support from the TOUGOU program funded by MEXT, Japan.
GPCP precipitation data was procured from NOAA/OAR/ESRL PSD, Boulder,
Colorado, USA, from their website at https://www.esrl.noaa.gov/psd/. The
authors are also grateful to Japan Meteorological Agency for providing JRA55 and COBE-SST2 datasets.
Authors’ contributions
AH performed the experimental study and analyzed the data. YI proposedand designed the study and analyzed the data. HS proposed and designed
the study. MM prepared the MIROC6 AGCM system and related datasets. HT
created the full-field assimilation system of MIROC6 and the long-term assimilation simulation. MW assisted in its interpretation. All authors have readand approved the final manuscript.
Authors’ information
MW serves as the area representative of Area Theme A “Prediction and
Projection of Large-Scale Climate Changes Based on Advanced Model
Development” under TOUGOU program (Integrated Research Program for
Advancing Climate Models). HT serves as the representative of subject(i)-a “Near-future climate change predictions and promotion of CMIP6
experiments” in Area Theme A of TOUGOU program. MW also serves as
the representative of subject (ii)-b “Analysis of factors in past climatechanges and unusual weather and future projections” in Area Theme A.
YI, HS, MM, and AH have been studying event attribution under the subject (ii)-b of Area Theme A of TOUGOU program.
Funding
This study was supported by Integrated Research Program for Advancing
Climate Models (TOUGOU program) Grant Number JPMXD0717935457, of
the Ministry of Education, Culture, Sports, Science and Technology (MEXT),
Japan.

Hasegawa et al. Progress in Earth and Planetary Science(2020) 7:78

Availability of data and materials
A part of ensemble members of CHist are available as the historicalexperiment in CMIP6. The other data supporting the conclusions of thisarticle are available upon request.
Competing interests
The authors declare that they have no competing interests.
Author details
1
Atmosphere and Ocean Research Institute, The University of Tokyo, 5-1-5
Kashiwanoha, Kashiwa, Chiba 277-8564, Japan. 2Meteorological ResearchInstitute, Japan Meteorological Agency, Tsukuba, Ibaraki, Japan. 3Center for
Global Environmental Research, National Institute for Environmental Studies,
Tsukuba, Ibaraki, Japan. 4Research Institute for Applied Mechanics, Kyushu
University, Fukuoka, Japan. 5Research Center for Environmental Modeling andApplication, Japan Agency for Marine-Earth Science and Technology,
Yokohama, Kanagawa, Japan.
Received: 27 March 2020 Accepted: 6 November 2020

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