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DOI: 10.1038/s41467-017-02360-z

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Contributions of changes in climatology andperturbation and the resulting nonlinearity toregional climate change

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Sachiho A. Adachi 1, Seiya Nishizawa 1, Ryuji Yoshida 1,2, Tsuyoshi Yamaura1, Kazuto Ando
Hisashi Yashiro 1, Yoshiyuki Kajikawa1,2 & Hirofumi Tomita1

1,

Future changes in large-scale climatology and perturbation may have different impacts onregional climate change. It is important to understand the impacts of climatology and perturbation in terms of both thermodynamic and dynamic changes. Although many studies
have investigated the inﬂuence of climatology changes on regional climate, the signiﬁcance of
perturbation changes is still debated. The nonlinear effect of these two changes is also
unknown. We propose a systematic procedure that extracts the inﬂuences of three factors:
changes in climatology, changes in perturbation and the resulting nonlinear effect. We thendemonstrate the usefulness of the procedure, applying it to future changes in precipitation.
All three factors have the same degree of inﬂuence, especially for extreme rainfall events.
Thus, regional climate assessments should consider not only the climatology change but also
the perturbation change and their nonlinearity. This procedure can advance interpretations of
future regional climates.

1 RIKEN Advanced Institute for Computational Science, 7-1-26 Minatojima-minami-machi, Chuo-ku, Kobe 650–0047, Japan. 2 Research Center for Urban
Safety and Security, Kobe University, 1-1 Rokkodai, Nada-ku, Kobe 657–8501, Japan. Correspondence and requests for materials should be addressed to
S.A.A. (email: sachiho.adachi@riken.jp)

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Recently, studies analysing in situ observational data havereported an increase in heavy rainfall events1,2. Further
increases due to global warming are a concern3,4. Heavy
rainfall events often lead to serious human losses and social
damage by causing landslides and ﬂooded rivers. To minimise
such risks and develop adaptation strategies, there is an increasing need for future regional climate projections.
Changes in the amount, frequency and intensity of regional
precipitation are affected by thermodynamic and dynamicchanges in the large-scale atmospheric conditions. Increasing
greenhouse gases are known to raise the air temperature bymodifying the atmospheric radiative balance5. The temperature
warming enriches the moisture content in the atmosphere, whichleads to an increase in precipitation6. This type of changes in theatmosphere is deﬁned as thermodynamic changes. At the sametime, the shift of the energy balance induces modiﬁcations in theatmospheric circulation patterns and the frequency, intensity andtrack of synoptic disturbances7,8. Such changes are deﬁned as
dynamic changes.
To understand the causes of regional precipitation change, theinﬂuences of large-scale thermodynamic and dynamic changes
need to be understood. Emori and Brown9 attempted to evaluate
the inﬂuences of thermodynamic and dynamic changes in theatmosphere on global precipitation by using results from multiple
general circulation models (GCMs). They reported that thermodynamic change, rather than dynamic change, plays a dominantrole for both the mean and extreme precipitation in most areas,
especially in the mid latitudes and high latitudes.
Some studies have addressed these inﬂuences from anotherperspective using a regional climate model (RCM)10–13. In thesestudies, a large-scale atmospheric state is decomposed into meanstates and ﬂuctuations from it, and the inﬂuences of thedecomposed components on the regional climate were subsequently evaluated by constraining a boundary condition of theRCM. In this paper, the mean and ﬂuctuation components of thelarge-scale atmosphere are called climatology and perturbation,
respectively.
The evaluation separating the inﬂuences of the climatology andperturbation changes can be interpreted from the viewpoint of
the thermodynamic and dynamic changes in the large-scale state
as follows. Here, we assume that one component is changed,
while the other remains unchanged. The changes in climatology

between two climates include both the thermodynamic anddynamic changes. The thermodynamic change due to the climatology change corresponds to the increase in the atmosphericmoisture content associated with temperature warming, while thedynamic change corresponds to changes in the large-scale ﬂow
pattern caused by global circulation such as Hadley circulationand the position and strength of the westerly jets. The perturbation change also includes both the thermodynamic anddynamic changes. The dynamic change due to the perturbation
change refers to changes in the frequency, intensity and track of
disturbances such as tropical and extratropical cyclones, while thethermodynamic change refers to the changes in the temperatureand humidity of the disturbances, accompanied by their changes
in track.
The pseudo-warming method is one approach for evaluating
the inﬂuence of changes in climatology using an RCM10,11,14.
This method uses a boundary condition that modiﬁes only theclimatology. Although the changes in both the precipitation
amount and intensity have been explained mainly by the changes
in climatology thus far, there is a possibility that changes in theperturbation also signiﬁcantly inﬂuence the precipitation, especially its intensity, in a limited region. This is because the changes
in the track and frequency of cyclones directly affect the region
through which they pass. Because the changes in perturbation are
not considered in the pseudo-warming method, the degree ofinﬂuence of the perturbation change on the regional climate
projection has become a concern when using this method15.
A few studies have evaluated the contribution of future changes
in perturbation to the regional climate change12,13. However, thesigniﬁcance of the perturbation changes is still debated. One
reason for the contradictory results is a lack of a standard evaluation method; therefore, a sophisticated procedure is needed formore precisely evaluating the individual contributions of changes
in climatology and perturbation.
We propose a new procedure for evaluating these contributions
to regional climate change. The proposed procedure requires anexperimental set consisting of four experiments: two direct
dynamical downscaling (DDS) experiments for the present andfuture climates and two experiments with boundary conditions
exchanging either climatology or perturbation components
between the two climates. The DDS experiments are conventional
downscaling simulations, for which boundary conditions are

Detection of contributions from <A> and A’
Differenceof precipitation

Perturbation: A’

Future-DDS
[F’ ;‹F›]
Δcp

Pseudo-Perturb-DS
[F’ ;‹P›]F’

ΔP0 + ΔC0

Δ

ΔP1

ΔC1

ΔP0

Expected
future climate
ΔC0
P’
‹P›

Present-DDS
[P’ ;‹P›]‹F›: Input (GCM output)

Pseudo-Clim-DS
[P’ ;‹F›]: RCM output

Climatology: <A>

F : Future

P : Present

Fig. 1 Diagram of impact assessment due to changes in climatology and perturbation. The triangles and circles indicate the boundary conditions andcorresponding RCM outputs for each experiment, respectively. Δ is the future precipitation change estimated using the direct dynamical downscaling(DDS) method. ΔP and ΔC represent the contributions of changes in the perturbation and climatology, respectively. The expected climate change isdeﬁned by the sum of ΔP0 and ΔC0. Δcp is the difference between the actual and expected future climates
2

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NATURE COMMUNICATIONS | DOI: 10.1038/s41467-017-02360-z

Table 1 Experimental design for estimating the contributions of climatology and perturbation changes and their nonlinear effectto regional climate change
Run name
Present-DDS
Pseudo-Clim-DS
Pseudo-Perturb-DS
Future-DDS

Description of experiment
Present climate experiment by DDS method
Pseudo-climatology-change downscaling experiment
Pseudo-perturbation-change downscaling experiment
Future climate experiment by DDS method

Boundary dataP′ þ hPi
P′ þ hFi
F′ þ hPi
F′ þ hFi〈 〉 and ′ indicate the climatology and perturbation, respectively, of the large-scale boundary condition. P and F indicate the present and future climate data, respectively, provided by MRI-AGCM3.2S
DDS direct dynamical downscaling

given directly from GCM outputs. An analysis with four experiments allows not only for the inﬂuence of each component to be
estimated but also for the inﬂuence due to the nonlinear effectbetween the two components to be extracted. Thus, by using thisprocedure, we can divide the causes of regional climate change
into three factors: climatology change, perturbation change andthe nonlinear effect between them. The demonstration of thisprocedure shows the importance of the symmetric treatment of
the changes in climatology and perturbation to precisely understand the regional climate change. At the same time, the nonlinear effect also shows some signiﬁcant inﬂuence, especially for
extreme rainfall events.
Results
Principal concept and procedure. Before presenting the procedure, we explain the principle, which was inspired by the theoretical basis provided in Nishizawa et al.13. Consider thedecomposition of a large-scale atmospheric state A into the climatology and perturbation, A ¼ hAi þ A′, where 〈 〉 and ′ denotethe temporal average and ﬂuctuation, respectively. Figure 1 showsa schematic diagram of the principal concept. The two horizontal
axes represent the climatology and perturbation used as boundary
conditions for an RCM. The vertical axis expresses the variable
estimated by downscaling simulations, namely, the precipitation.
The boundary condition and corresponding RCM output for eachexperiment are expressed by a triangle and circle, respectively.
Here, we aim at understanding the regional climate change
between the present and future large-scale atmospheric states, P
and F, obtained by a GCM. The RCM outputs using P and F as
boundary conditions are denoted as functions φ of each largescale state: φ½P′; hPi and φ½F′; hFi. These DDS simulations are
named Present-DDS and Future-DDS for the present and futureclimate experiments, respectively, in this study.
As shown in Fig. 1, the total change in the regional climate
between the present and future can be estimated as the difference
between Present-DDS and Future-DDS:
Δ ¼ φ½F′; hFi  φ½P′; hPi:ð1Þ

We deﬁne the total change Δ as the “actual climate change”.
The total change includes the regional climate responses to largescale atmospheric changes in both the climatology and perturbation and their nonlinear effect. Therefore, it is difﬁcult to extract
only the contribution of a change in a particular large-scaleatmospheric component from the results of the two DDS
experiments. To estimate the contribution of each component,
two other boundary conditions need to be constructed: replacing
only the climatology from P to F, i.e., hFi þ P′, and replacing only
the perturbation, i.e., hPi þ F′. The RCM outputs constrained bythese artiﬁcial boundary conditions can be expressed as φ½P′; hFiand φ½F′; hPi. The experiment using the boundary condition ofhFi þ P′ is designated the pseudo-climatology-change downscaling (Pseudo-Clim-DS) experiment, whereas that using hPi þ
F′ is designated the pseudo-perturbation-change downscaling
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(Pseudo-Perturb-DS) experiment. Table 1 summarises the above
four simulations.
By comparing the four downscaling experiments, we canextract the individual contributions of the changes in climatology
and perturbation from the regional climate responses. Based on
the reference state P, the regional climate changes due to thelarge-scale climatology and perturbation changes are, respectively,
described by
ΔC0 ¼ φ½P′; hFi  φ½P′; hPi;ð2Þ

ΔP0 ¼ φ½F′; hPi  φ½P′; hPi:ð3Þ

Here, we deﬁne a regional climate change expressed only by alinear summation of ΔC0 and ΔP0 as the “expected climatechange”, corresponding to the cross in Fig. 1. The nonlinear effectbetween the climatology and perturbation changes is notconsidered in the expected climate change. If the difference
between the actual climate change and expected climate change isdenoted as Δcp, Eq. (1) can be expressed as follows:
Δ ¼ ΔC0 þ ΔP0 þ Δcp:ð4Þ

Δcp in Eq. (4) has an important implication for the physicalmeaning. Regarding the two large triangles parallel to theclimatology axis in Fig. 1, the height of the front triangle, ΔC0,
is the regional climate response derived from Eq. (2). If thepresent perturbation is replaced by the future one under the same
climatology changes, we can expect a different response, indicatedas the height of the back triangle, ΔC1. The difference between thetwo estimations equals the nonlinear effect: Δcp = ΔC1 − ΔC0.
The same is true with regard to the perturbation change; ΔP0 and
ΔP1, respectively, are the differences by changing the perturbation under the present and future climatology and Δcp = ΔP1 −ΔP0. Previous studies12,13 have attempted to compare thecontributions of the climatology and perturbation changes byusing ΔC0 and ΔP1. However, the nonlinear effect was notconsidered in these evaluations. Our procedure starts fromnullifying the hypotheses of ΔC1 = ΔC0 and ΔP1 = ΔP0. The
procedure considers the response to changes in perturbation as
well as that to changes in climatology equivalently. Thissymmetric treatment of these two components reveals thenonlinear effect.
Next, we consider the implications of the three factors ΔC0,
ΔP0 and Δcp relative to the total change Δ with a focus on theirsigns. When ΔC0 ⋅ ΔP0 > 0, these two contributions affect theregional climate in the same direction. When ΔC0 ⋅ ΔP0 < 0, thesign of the expected climate change is determined by that of theregional climate change due to the component having a larger
inﬂuence. The relationship between the signs of the nonlinear
effect Δcp and the expected climate change is important;compared to the expected climate change, the actual climatechange is enhanced by Δcp when Δcp ⋅ (ΔC0 + ΔP0) > 0, whereas
it is suppressed by Δcp when Δcp ⋅ (ΔC0 + ΔP0) < 0.

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Table 2 The precipitation indices evaluated in this study
Notation
RAVE
R1D
CDD

Deﬁnition of Index
25-year mean of the daily precipitation
25-year mean of the maximum 1-day precipitation
25-year mean of the maximum number of consecutive dry
days(Note that a dry day is deﬁned as one with a precipitation of<1 mm day−1.)

In short, the combination of the four downscaling experiments
and the relationship described above allows the procedure to
extract the contributions of the changes in the climatology andperturbation as well as the nonlinear effect to the regional climatechange at a time.
Demonstration of the proposed procedure. To demonstrate theprocedure, we applied it to future precipitation changes in western Japan. The Paciﬁc side of western Japan has high rainfall inthe summer season, which is characterised by typhoons, extratropical cyclones, seasonal stationary fronts and local rainfall due
to convective instability. SCALE-RM16–18, which is an RCM, wasused for the downscaling simulations. The boundary conditionsfor SCALE-RM were constructed from the results of MRIAGCM3.2S19, which is an atmospheric general circulation model.
See the Methods section for more details on the experimental
setup. Three indices, indicated in Table 2, were used for theevaluation.
To simplify the subsequent discussion, we consider that the
major factors affecting the precipitation change due to climatology and perturbation changes are roughly understood to be thethermodynamic and dynamic changes, respectively. This would
be reasonable in at least the mid latitudes and high latitudes; forthe climatology change, a previous study9 already showed that theinﬂuence of thermodynamic change is larger than that ofdynamic change, while for the perturbation change, the indirect
thermodynamic inﬂuence due to slight changes in the disturbancetrack may be relatively low compared with the direct dynamic
inﬂuence due to changes in the frequency, intensity and track of
the disturbance in a limited area.
RAVE in the Present-DDS, Future-DDS and their difference
are shown in Fig. 2a–c, respectively. RAVE in the futureclimate decreases from that in the present climate formost areas. Figure 2d, e show the changes in RAVE due to thechanges in the climatology and perturbation, respectively.
Changing the climatology slightly increases RAVE, especiallyfor the northern area, while changing the perturbation accounts
for a large part of the total decrease in RAVE. The areal mean of
the RAVE change is summarised in Fig. 3a. The rate of increase inmean precipitation due to the changes in climatology isapproximately 3% under the 3.6 °C warming of the surface
temperature from the present climate; this value is consistent withthose in previous studies20,21. On the other hand, the rate ofdecrease due to the changes in perturbation is ~14%; the reason
for the large decrease is explained later. The change in RAVE forthe expected climate change (Fig. 2f) has a similar distribution tothat of the total mean precipitation change (Fig. 2c) in most areas.
This means that the mean precipitation change can largely be
explained by summing the inﬂuences of the climatology
and perturbation changes. Figure 2g shows the nonlinear effectΔcp between the changes in the two components. Although
the magnitude of the nonlinear effect is small over most areas,
it is comparable to the inﬂuence of the changes in the
climatology. The relationship between the expected climate
4change and Δcp varies with the location. In terms of the areal
mean, the nonlinear effect tends to enhance the expected climatechange for RAVE because (ΔC0 + ΔP0) ⋅ Δcp > 0, as shown in
Fig. 3a.
To investigate whether the results of the mean precipitation
would hold true for extreme precipitation, other precipitation
indices, R1D and CDD, were also evaluated. Although R1D shows
little change between the present and future climates (Fig. 3b),this result does not mean that the changes in each large-scaleatmospheric component have no effect. The decrease in R1D due
to the perturbation change is comparable to the increase due tothe climatology change; the small change in R1D between thepresent and future climates is simply a consequence of cancellingthe contributions from the two component changes. The
nonlinear effect suppresses the expected climate change for
R1D, because the expected climate change slightly increases and(ΔC0 + ΔP0) ⋅ Δcp < 0. The total change in CDD increases as aresult of the changes in both components (Fig. 3c). Because (ΔC0
+ ΔP0) ⋅ Δcp > 0, the nonlinear effect enhances the expectedclimate change in CDD. Thus, the magnitude and direction of thecontributions of the climatology and perturbation depend on thetarget index. The role of the nonlinear effect also depends on theindex. Its magnitude is relatively small but not negligible for the
total change.
The changes in climatology increased both the mean andextreme precipitations. The increasing rate of the extreme
precipitation (R1D) was larger than that of the mean precipitation (RAVE); this result is consistent with those of previous
studies9,21. Regardless of the mean and extreme precipitation,
increases due to the climatology change can be explained by thethermodynamic changes in the large-scale atmosphere, i.e. theprecipitation increases due to the enriched water vapour in thewarm atmosphere related to the Clausius–Clapeyron relationship.
On the other hand, the mean and extreme precipitations weredecreased by the changes in perturbation. This decrease exceededor was comparable to the increase due to the changes inclimatology, as shown in Fig. 3a, b. The perturbation change isparticularly characterised by the changes in the frequency andintensity of the disturbances causing precipitation. According to a
cyclone analysis based on the detection method of Adachi andKimura22, the decrease in precipitation associated with typhoons
and extratropical cyclones accounted for more than 95% of the
precipitation decrease due to the perturbation change between
Present-DDS and Pseudo-Perturb-DS, whereas changes in the
precipitation due to weather events other than cyclones werequite small. Further analysis showed that the numbers of
typhoons and extratropical cyclones affecting the studied region
were projected to decrease by 40 and 15%, respectively, whereas
the precipitation brought on by a single event, i.e. one typhoon or
one extratropical cyclone, to the region remained almost
unchanged between the two experiments. Thus, the precipitation
decrease due to perturbation changes can be explained by thedecreases in the numbers of typhoon and extratropical cyclone
events in this case.
When an adaptation strategy is considered, evaluating not only
the changes in the cumulative precipitation amount but also thosein the frequency and intensity of precipitation is important. The
former information would be useful for securing water resources,
while the latter information can help reduce the risk of disaster.
From the viewpoint of reducing disaster risk, Fig. 4a shows therelationship between the precipitation intensity and changes inwet days. The total change in wet days between the present andfuture climates is small across all categories. However, the small
total change is a result of the counteracting contributions of thethree studied factors. The changes in the perturbation decrease
the wet days for all categories, while the changes in the

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a
38N

b

Present–DDS

Future–DDS

c

Δ

f

ΔC0 + ΔP0

g

Δcp

37N
36N
35N
34N
33N
32N
31N
2

d

4

6

8

12

14

e

ΔC0

38N

10

16

(mm/day)

ΔP0

37N
36N
35N
34N
33N
32N
31N
–3

–2

–1

–0.5

0.5

1

2

3 (mm/day)

38N
37N
36N
35N
34N
33N
32N

31N
130E 132E 134E 136E 138E 140E

Fig. 2 Spatial distribution of precipitation changes. Twenty-ﬁve-year averages of the daily precipitation in a Present-DDS, b Future-DDS and c the difference
between Present-DDS and Future-DDS. The contributions of the climatology, perturbation and nonlinear effect are shown in d,e, g, respectively. The daily
precipitation change estimated by the expected climate change is shown in f. The hatched regions in c–e represent the area in which the difference fromPresent-DDS is statistically signiﬁcant with a 95% conﬁdence levelclimatology drastically increase the wet days in heavier precipitation. On the other hand, the nonlinear effect drastically decreases
the wet days for extreme precipitation of more than 300 mm
per day. That is, the nonlinear effect suppresses the precipitation
increase due to the climatology change, especially for extreme
precipitation. The increase in the frequency of extreme
precipitation results from an increase due to the changes in the
climatology outweighing the sum of the decrease due to theperturbation changes and counteraction from the nonlinear
effect.
From the viewpoint of securing water resources, Fig. 4b shows
the amount of cumulative precipitation against the precipitation
intensity. Most of the precipitation amount results from weak
precipitation of less than 100 mm per day. The cumulative
precipitations in Future-DDS and Pseudo-Perturb-DS are only
~90% of that in Present-DDS because the frequency of weak
precipitation of less than 100 mm per day decreases in FutureDDS and Pseudo-Perturb-DS compared to in Present-DDS, as
shown in Fig. 4a. This means that the changes in the perturbation
affect the frequency of weak precipitation, which changes theamount of precipitation.
We had presumed that the precipitation amount would be
affected by climatology changes, whereas the intensity might
rather be inﬂuenced by perturbation changes. However, thedemonstrated results were different from our expectation. The
cumulative precipitation was largely inﬂuenced by the changes in
the perturbation, whereas the precipitation intensity was mainly
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affected by the changes in the climatology, at least in thedemonstrated case.
Discussion
Most of changes in the precipitation due to climatology changes
can be explained by the thermodynamic change in the large-scaleatmosphere associated with the Clausius–Clapeyron effect. On
the other hand, the changes in climatology also include changes
in the dynamic structure of the atmosphere, such as the atmospheric stability, as described above. Because the temperature
increase due to global warming is greater in the upper troposphere, the vertical stability increases23. The climatology projected in MRI-AGCM3.2S also indicates such stabilisation, andthe downscaled results in Pseudo-Clim-DS and Future-DDS
reﬂect this tendency. Regarding the inﬂuence of changes in climatology on the precipitation intensity, the results from PseudoClim-DS indicate that heavy precipitation was enhanced andweak precipitation was slightly suppressed (Fig. 4). The reductionof weak precipitation seems to be attributable to the stabilisationof the atmosphere in the future climate. To more quantitatively
evaluate these two effects, further experiments using appropriate
boundary conditions are required. As an example, Kröner et al.24
proposed a downscaling approach to evaluate the separate contributions of vertically homogeneous warming and a verticalstructure change in the temperature associated with changes inclimatology to the regional climate change.

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NATURE COMMUNICATIONS | DOI: 10.1038/s41467-017-02360-z(mm/day)
1.5 a(mm/day)
20

1.0
0.5

10

0.0

0

−0.5
−1.0
−1.5

RAVE

(Days)
4 c

b

Δ
ΔP0

3

ΔC0

2

−10

1

−20

0
R1D

Δcp

CDD

Fig. 3 Changes in the precipitation indices for evaluation. Differences from the present climate in domain-averaged 25-year means of the a daily mean
precipitation (RAVE), b maximum one-day precipitation (R1D) and c maximum number of consecutive dry days (CDD), respectively. Δ is the total change
estimated by the DDSs (Future-DDS − Present-DDS). ΔP0 and ΔC0 indicate the contributions of the perturbation and climatology, respectively. Δcp is thecontribution of the nonlinear effectIf the changes in perturbation are considered along with thosein climatology, the regional precipitation change can be determined by the balance of the thermodynamic effect in the meanstate, the changes in the mean atmospheric structure, and changes
in perturbation. Among these, the inﬂuence of the perturbation
changes is strongly dependent on the location and size of anevaluated area; the smaller the size of the evaluated area is, thelarger the inﬂuence due to the perturbation change becomes. Thechanges in perturbation are potentially crucial for the future
regional climate.
The demonstrated results show a view regarding a debatable
point whether the use of the pseudo-warming method is valid
for projecting the future regional climate. The pseudo-warming
method has the advantage of reducing the model bias in a
GCM projection by using the reanalysis data for the present
climate. However, the future downscaling projection is
performed using the present perturbation14,25,26. There have been
concerns that the pseudo-warming method may underestimate
or overestimate extremes for the projected climate, because
the activities of atmospheric disturbances, such as tropicaland extratropical cyclones, are projected to change due toglobal warming in some models27,28. In our demonstration of the
proposed procedure, perturbation changes have a large impact
on the precipitation change. This means that the effect of thechanges in perturbation cannot be negligible for the projectionin areas where the frequency and intensity of large-scaledisturbances are projected to change in the future climate.
The demonstration further indicates that the nonlinear effectinhibits the intensiﬁcation of precipitation due to climatology
changes. This result implies the possibility that the pseudowarming method overestimates the extreme precipitation
events, at least in the area and season evaluated. Further
evaluation of the physical meaning of the nonlinear effect isnecessary for a greater understanding of the essence of thepseudo-warming method.
Although many studies have concentrated on projecting
the future climate and evaluating the effect of climatology
changes so far, the results of our procedure emphasise theimportance of the symmetric treatment of changes in climatology
and perturbation along with the nonlinear effect to precisely
understand the regional climate projection. By considering theinﬂuence of each change and their nonlinear effects, the procedure could provide clues to the mechanisms that cause future
regional climate change. To understand the mechanisms in moredetail, it would be helpful to separate the factors affecting theregional climate and evaluate their contributions quantitatively;
for example, thermodynamic and dynamic changes in climatology, those in perturbation and ground surface conditions such as
land use.
6

In this study, only a pair of present and future climates estimated by a single GCM was used. However, there is uncertainty
in future climate projections with GCMs because of imperfections
regarding the emission scenario and model, amongst others. The
uncertainties would be involved in both the climatology andperturbation of the future projections. By applying our procedure
to multi-regional climate projections using multi-GCM projections, the procedure may also provide information on the characteristics of uncertainty in regional climate projections, such as
which atmospheric component causes a spread in regional climate projections.
Methods
Regional climate model used in this study. The regional model used for thedownscale experiments is based on Scalable Computing for Advanced Library andEnvironment-Regional Model (SCALE-RM)16–18 version 4.2.5. The calculation
domains cover an area of 2520 × 2520 km2 with a grid spacing of 7.5 km for theouter domain and an area of 1080 × 960 km2 with a grid spacing of 2.5 km for the
inner domain. In the vertical direction, the outer and inner domains have 36 and60 layers, respectively. The calculation period for the downscaling experiments wasfrom 31 May to 30 September during 1979–2003 for the present climate experiment and during 2075–2099 for the future climate experiment. This 4-monthcalculation in each year was divided into 31 runs, and each run was conducted
every four days. The integration period of one run was ﬁve days, which consisted of
one day for model spin-up and four days for analysis. The outputs from the last
4 days were connected sequentially and used for the analysis. Thus, the period from
1 June to 30 September of each year was analysed.
The large-scale climate data used for the initial and boundary conditions of the
RCM were provided from 6-hourly data in the present and future climatesestimated by MRI-AGCM3.2S19, as explained in the next subsection. The following
variables are used for the initial and boundary conditions: atmospherictemperature, geopotential height, pressure, speciﬁc humidity, zonal and meridional
winds, surface pressure, skin temperature, sea surface temperature (SST), soil
temperature and soil moisture. Note that the SST was given as a temporally
averaged value in each integration period and then kept constant throughout a ﬁveday simulation. The initial and boundary conditions for the Present-DDS and
Future-DDS experiments are directly given from GCM outputs, whereas these
conditions for the other two experiments are prepared according to the following
procedure using GCM outputs. First, the climatology and perturbation were
calculated for the present and future climate. The climatology of the large-scaleatmospheric state was determined via two steps: (1) monthly means averaged over
25 years were prepared from May to October; (2) regarding these as the 15th day ofeach month, the climatology on each day was determined by their linear
interpolation. Thus, the climatology varied from day to day. The perturbation was
calculated by subtracting the obtained daily climatology from the 6-hourly data.
Then, the initial and boundary conditions of the RCM were prepared by combining
these climatology and perturbation according to the experimental design listed inTable 1, except for the speciﬁc humidity. The speciﬁc humidity is calculated fromthe temperature constructed by the procedure described above and the relative
humidity. The relative humidity used for Pseudo-Clim-DS and Pseudo-Perturb-DS
is assumed to depend on the climate of perturbation, namely, the relative humidity
for these experiments were obtained from the present and future GCM simulations,
respectively. The assumption that the relative humidity remains unchanged
between present and future climates is common in the pseudo-warming
method24,25. This assumption is based on reports that the change in relative
humidity is projected to be quite small in future warmer climates6,29. The

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NATURE COMMUNICATIONS | DOI: 10.1038/s41467-017-02360-zab (mm)
Δ

1.0

ΔP0

0.5

ΔC0

0.0

Δcp

−0.5
−1.0
−1.5

Accumulated precipitation

1000

1.5

1.0
800
0.8
600

0.6

Present−DDS
400

Pseudo−Perturb−DS

200

Pseudo−Clim−DS

0.4
0.2

Future−DDS0.0

00.5≤ 10≤ 100≤ 200≤ 300≤ 400≤
pi
pi
pi
pi
pi
pi
<10 <100 <200 <300 <400
Precipitation intensity (mm/day)

Relative to present-DDS

Changes in wet days
relative to present climate

2.0

0

100

200

300

400

Precipitation intensity (mm/day)Fig. 4 Changes in precipitation characteristics for different precipitation intensities. a Difference in the number of wet days from the present climate foreach category of precipitation intensity and b the cumulative precipitation amount. The value in a is normalised by the number of wet days in Present-DDS
for every intensity category. Δ is the total change estimated by the DDSs (Future-DDS − Present-DDS). ΔP0 and ΔC0 indicate the contributions of theperturbation and climatology, respectively. Δcp is the contribution of the nonlinear effect. The right scale in b indicates the ratio to the accumulated
precipitation of the present climate (Present-DDS)
advantage of using this assumption is to be able to avoid super-saturated andsuper-dried conditions.
The cloud microphysics and turbulence processes were calculated according to
the six-class single-moment bulk scheme30 and Mellor–Yamada Nakanishi–Niino
level 2.5 TKE scheme31, respectively. The radiation process was calculated with the
MSTRN-X radiative scheme32. The concentrations of CO2 and other greenhousegases in the atmosphere used in the radiative scheme are taken from those for the
scenario of representative concentration pathway (RCP) 8.5, except for PresentDDS. The land variables were solved with the ﬁve-layer heat diffusion and bucket
model using surface ﬂux parameterisation33. The ﬂuxes from urban areas were
calculated with the single-layer urban canopy model34. No nudging techniques
were used in this simulation, because the integration period for each run was only
5 days.
Present and future climate data with MRI-AGCM3.2S. The climate data for theboundary conditions of SCALE-RM were calculated by MRI-AGCM3.2S19. MRIAGCM3.2S is a high-resolution hydrostatic atmospheric GCM developed at theMeteorological Research Institute (MRI) for climate simulations. The SST forcing
data for MRI-AGCM3.2S were taken from the Hadley Centre Sea Ice and SST data
set version 1 (HadISST1)35 for the present climate. The future climate was projected using the multi-model mean of 28 SST data projected by the Coupled Model
Intercomparison Project Phase 5 (CMIP5) atmosphere-ocean coupled GCMs
(CGCMs) under the RCP8.5 scenario36.
Code availability. The regional model for the downscaling calculation in this study
was constructed by using SCALE, which is freely available at https://scale.aics.riken.
jp/download/index.html under the 2-Clause BSD license. The model code used isbased on SCALE-RM version 4.2.5 including some improvements such as theusability of the microphysics scheme. The model code and the set of conﬁguration
parameters are available from the corresponding author upon reasonable request.
The pre-process code that generates the boundary conditions for SCALE-RM from
the MRI-AGCM3.2S data and the post analysis code used in this study are alsoavailable from the corresponding author.
Data availability. The downscaling data by SCALE-RM are deposited in local
storage at RIKEN/AICS. It is available from the corresponding author upon reasonable request. The MRI-AGCM3.2S data were provided to the authors by MRI
under a given condition that the authors can use the MRI-AGCM3.2S data only forthe current and related studies. The data is not publicly available. However, upon
reasonable request with regards to this study, the data are provided from MRI withthe permission of MRI. In this case, contact person is the corresponding author.

Received: 18 May 2017 Accepted: 21 November 2017

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8

Acknowledgements
This study was supported by the Foundation for Computational Science (FOCUS)
establishing the Supercomputing Center of Excellence and JST CREST (Grant Number
JPMJCR1312), Japan. The results of this study were obtained using the computational
resources of the K computer at RIKEN/AICS. We thank Drs I. Takayabu, R. Mizuta andO. Arakawa for providing the MRI-AGCM3.2S data. The climate simulations with MRIAGCM3.2S were carried out by the MRI under the Program for Risk Information on
Climate Change (SOUSEI) of the Ministry of Education, Culture, Sports, Science andTechnology (MEXT) of Japan. We thank the two anonymous reviewers for their fruitful
discussions on improving this paper.

Author contributions
S.A.A., S.N., Y.K. and H.T. designed the research; S.A.A., S.N., T.Y., K.A. and H.Y.
prepared the boundary data and performed the simulations; S.A.A., S.N., R.Y. and T.Y.
analysed the data; and mainly S.A.A. and H.T. wrote the paper.

Additional information
Supplementary Information accompanies this paper at https://doi.org/10.1038/s41467017-02360-z.
Competing interests: The authors declare no competing ﬁnancial interests.
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