Nishizawa et al. Progress in Earth and Planetary Science (2018) 5:2
DOI 10.1186/s40645-017-0159-0

Progress in Earth andPlanetary Science

RESEARCH ARTICLE

Open Access

Decomposition of the large-scaleatmospheric state driving downscaling: aperspective on dynamical downscaling forregional climate study
Seiya Nishizawa1* , Sachiho A. Adachi1 , Yoshiyuki Kajikawa1,2 , Tsuyoshi Yamaura1 , Kazuto Ando1 ,Ryuji Yoshida1,2 , Hisashi Yashiro1 and Hirofumi Tomita1

Abstract
In this study, we provide a perspective on dynamical downscaling that includes a comprehensive view of multiple
downscaling methods and a strategy for achieving better assessment of future regional climates. A regional climate
simulation is generally driven by a large-scale atmospheric state obtained by a global climate simulation. We
conceptualize the large-scale state based on reconstruction by combining decomposed components of the states,
such as climatology and perturbation, in different global simulations. The conceptualization provides a comprehensive
view of the downscaling methods of previous studies. We propose a strategy for downscaling regional climate studies
based on the concept of covering a wider range of possibilities of large-scale states to account for the uncertainty inglobal future predictions due to model errors. Furthermore, it also extracts the individual influences of thedecomposed components on regional climate change, resulting in better understanding of the cause of the change.
We demonstrate a downscaling experiment to highlight the importance of the simultaneous consideration of theindividual influences of climatology and perturbation.
Keywords: Dynamical downscaling, Regional climate, Uncertainty, Model errors

Introduction
Assessment of future regional climates is of growing
importance in the development of adaptation plans bypolicymakers. Numerical simulation is a necessary toolfor investigating the issue of climate change. However,global simulations are usually too coarse to represent
regional-scale atmospheric variability. In order to represent regional-scale variability, dynamical downscaling(DS) with a regional model driven by a large-scale state,i.e., initial and lateral boundary conditions generated fromglobal simulations or reanalyses, has been widely used
(e.g., Dickenson et al. 1989; Giorgi and Bates 1989; Mearns
et al. 1995; Rummukainen et al. 2015; Takayabu et al.
2016). DS has several advantages over coarser global*Correspondence: s-nishizawa@riken.jp
RIKEN Advanced Institute for Computational Science, 7-1-26
Minatojima-minami-machi, Chuo-ku, Kobe, Hyogo 650-0047, Japan
Full list of author information is available at the end of the article
1

simulations or reanalyses (e.g., Jones et al. 1995; Walshand McGregor 1995; Giorgi and Shields 1999), e.g., better
representation of surface conditions such as topography
and land use, and utilization of more sophisticated physical process models such as a cloud microphysics modelthat avoids the need for cumulus parameterization.
For DS, one of the most important issues is which largescale state is used to drive the DS because the statisticalcharacteristics of the downscaled state are significantly
affected by the large-scale state. There are several DS
methods in terms of derivation of the large-scale state.
One such method is direct DS (DDS), where the largescale state obtained by a general circulation model orglobal climate model (GCM) is directly used. It has been
pointed out that the climate bias in large-scale states has
a significant impact on the reproducibility of the downscaled state (e.g., Kato et al. 2001; Wang et al. 2004).

© The Author(s). 2018 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0
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Nishizawa et al. Progress in Earth and Planetary Science (2018) 5:2

Another DS method is unbiased downscaling (UnbiasedDS), where the large-scale state obtained from a GCM
experiment is used, as in DDS; however, the climate
bias in the state from the GCM is removed. The climate bias in a GCM is often estimated as the difference
between the climatology obtained by a GCM experiment
under the current climate conditions and that obtained
through reanalysis (e.g., Misra and Kanamitsu 2004;
Holland et al. 2010; Done et al. 2015). Here, the model bias
under future climate conditions is assumed to be identical to that under the present climate condition, although
the bias may change under different climates (Bellprat
et al. 2013). There is also an attempt to reduce the perturbation bias (e.g., Xu and Yang 2012; Jin et al. 2011).
Another DS method is pseudo climate change downscaling (Pseudo-Clim-DS), which is also used to reduce themodel climate bias, where the large-scale state is artificially constructed by adding a certain climate difference
to the reanalysis state. An ideally constructed climate difference was used in Schär et al. (1996). The difference
between the future projection and the present run in a
GCM is also used as the climate difference (e.g., Wu andLynch 2000; Kimura and Kitoh 2007; Sato et al. 2007;
Cook and Vizy 2008; Kawase et al. 2009; Patricola andCook 2010; Rasmussen et al. 2011), i.e., the climate bias in
the model is treated in the same way as in Unbiased-DS.
Wakazuki and Rasmussen (2015) constructed the climate
difference statistically using multiple GCM simulations.
Pseudo-Clim-DS attempts to reduce the perturbation bias
using the perturbation value from the reanalysis. The
validity of using the present perturbation in future DS projections was investigated by applying Pseudo-Clim-DS toa past climate in Kawase et al. (2008) and to an assumed
true climate (ATC), i.e., the so-called perfect model experiment, in Yoshikane et al. (2012). Another advantage of
the Pseudo-Clim-DS is that it allows us to investigate theinfluence of change in a target component on regional
climate (e.g., Rowell and Jones 2006; Adachi et al. 2012;
Kröner et al. 2016).
For future regional projections by DS, GCM results are
utilized to obtain the large-scale state driving the DS.
However, in GCMs, there are some inevitable limitations
caused by model errors in terms of the obtained largescale states for DS. These limitations result in errors or
uncertainties in the estimation of future regional change
by DS, as well as uncertainties in future external conditions, such as in a scenario of greenhouse gas emission.
A multi-model ensemble is a good strategy to evaluate
the uncertainty, and much valuable knowledge has beenobtained from ensemble experiments (e.g., van der Linden
and Mitchell 2009; Means et al. 2013; Evans et al. 2014).
However, uncertainties due to the limitations in individual models still have to be taken into account in orderto achieve more reliable evaluations. Therefore, it is very

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important to consider the large-scale state obtained by
GCM simulations in order to interpret the DS results. In
this study, we consider the limitation from a possible error
in the relationship between climatology and perturbationsin GCM simulations through a consideration of the phasespace of a large-scale state. On the basis of this consideration, we provide a comprehensive view of DS methods.
We also propose a strategy for regional climate simulations with the goal of achieving better estimations andunderstanding of future changes in regional climate.

Results
In this section, we first explain the basic idea in thisstudy, which is the decomposition of the large-scale state
and the phase space spanned by the decomposed components. Next, we consider the uncertainties due to GCM
errors and possible future states in the phase space. On
the basis of this consideration, we propose a strategy forregional climate DS simulations in which various largescale states reconstructed from the decomposed components are used. Then, we present its advantages: a wider
coverage of future possible states, better understandingof projected future change, and a comprehensive view ofprevious DS methods. Finally, we conduct a DS experiment to demonstrate how the strategy works to provide
a better understanding by consideration of the individual
influences of the decomposed components, which is oneof the advantages.
Decomposition of the large-scale state

The large-scale state can be divided into multiple components. As one of the simplest decompositions, we consider
climatology and the deviation from it (referred to as aperturbation) as two components.
Let the large-scale state be denoted as φ, and its components of climatology and perturbation as φ and φ  ,respectively. There are several definitions of climatology,
such as monthly long-term average. We discuss the definition in the “Discussion” section. Here, we consider states
under climatological equilibrium. Considering different
climates, the climatology is further decomposed into thereference climatology φ0  and climate difference {φ, φ0 }:φ = φ0  + {φ, φ0 } + φ  ,(1)where the climate difference is expressed as {φ, φ0 } =φ − φ0 . For example, for future climate projections, thefuture atmospheric state f can be decomposed into
 the
present climatology p, future climate difference
f,p ,


and future perturbation f  so that f = p + f , p + f  .
Let us assume an extended phase space (referred to as
just “phase space” in this paper) of a large-scale state. We
define the state as having a temporal dimension; the total
number of dimensions of the state vector in the phasespace is obtained by multiplying the number of variables

Nishizawa et al. Progress in Earth and Planetary Science (2018) 5:2

by the spatial degree of freedom and the temporal degreeof freedom. A schematic diagram of the phase space isshown in Fig. 1. Note that, although the phase space hasa large number of dimensions, the schematic diagram isdrawn as two-dimensional (climatology and perturbation)
by a dimensionality reduction, e.g., the principal component analysis, for ease of understanding. The horizontal
axis represents the subspace Vclim , where φ ∈ Vclim , andthe vertical axis represents the perpendicular complement⊥ , where φ  ∈ V ⊥ . In the phase space, a point
space Vclim
clim
corresponds to a state; state φ is located at point (φ, φ  ),e.g., the cross marks in Fig. 1.
Uncertainty due to GCM errors

The statistical characteristics of the climatology and perturbation are not independent of each other, since they are
determined through their interactions with one another.
Roughly speaking, they have a one-to-one correspondence, although there can be some ambiguities due to thepossible existence of multi-equilibrium states. Here, we
consider the statistical characteristics derived from theprobability distribution function of possible states under
the same climate condition, e.g., ensemble members in
a GCM experiment; the characteristics of possible perturbations under a climate do not depend on individual
realizations. The one-to-one correspondence means thatstates can exist only in a manifold in the entire phasespace because they are constrained by their relationship,as indicated by the yellow lines in Fig. 1.

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None of the numerical models are perfect, and the representation of interaction among components depends on
the GCMs. That is, their relationship in GCMs may be
distorted from that in nature. For example, an aqua-planet
intermodel comparison shows a variety of relationships:
there exist significant differences in precipitation systems
compared to the differences in mean flow (Blackburn
et al. 2013). The former is part of the perturbation, and thelatter is part of the climatology. Because of the distorted
relationship in a GCM, the states in a numerical simulation may exist in a different manifold from that of nature,
as shown in Fig. 2. One remarkable point here is that there
is a significant probability of a real atmospheric state existing outside the region covered by numerical simulationsin the phase space. DS driven only by the large-scale state
in a distorted manifold can lead to an incorrect estimationof a regional climate.
Therefore, there is a need to explore a wider region thanthat covered by GCM simulations for the large-scale statedriving the DS. The possible spuriousness in the relationship between the components in a GCM simulation is
one of the causes of uncertainty in the estimation of theinfluence of climate change. If the GCM was perfect andwe were confident about the perfection, the probability of
the future state would be restricted only on the GCM’s
manifold, which is identical to that in nature. This resultsin good projections with smaller uncertainties. However,
GCMs have errors; thus, the true state would be outside of
the GCM’s manifold because of the distorted constraint.

Fig. 1 Schematic diagram of the decomposition of the large-scale state in a climatology-perturbation phase space. Horizontal and vertical axes
represent climatology and perturbation, respectively. For simplicity, climatology and perturbation are represented as scalar values. Cross marks
show two states of a system. Stars represent the possible large-scale states driving the downscaling simulations. The yellow line shows the manifold
corresponding to the relationship between climatology and perturbation

Nishizawa et al. Progress in Earth and Planetary Science (2018) 5:2

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Fig. 2 Schematic diagram of the large-scale state driving the downscaling simulations. Cross marks show the states realized by reanalysis and GCM
simulations. Stars represent the possible large-scale states driving the downscaling simulations. The orange shaded area represents the range of
uncertainty in the estimation or existence probability distribution of the future state. The yellow line shows the manifold corresponding to therelationship between climatology and perturbation

That is, the possible GCM errors spread the probability distribution. The region covered by simulations with a
GCM in the phase space is limited to the spurious manifold. In fact, the trends in the CMIP5 historical runs
(Taylor et al. 2012) are overconfident, and the observed
trend is outside the range of the multi-model ensembles (van Oldenborgh et al. 2013). The bias-correcting
methods produce states away from the GCM manifold,but the methods only shift the region in the phase space
to another place and do not enlarge the region to be
explored.
Reconstruction of large-scale states

In order to obtain large-scale states that are outside of
the GCM’s manifold, we reconstruct the large-scale states.
The climatology and perturbation from different states are
not constrained in the distorted relationship of GCMs.
Therefore, reconstruction by combining them produces
large-scale states that are outside of the manifold. Let us
consider the case of present and future states. Two components, the climatology and perturbations of the twostates, are taken into account (Fig. 1). Considering theseas independent components, four large-scale states can beobtained through their combinations, as illustrated by thestars in the diagram. It can be seen that two of these states
are away from the spurious constraint. This independent
treatment of the components achieves evaluation of statesin a wider region of the phase space than the manifold ofa GCM. The technical procedure to reconstruct the largescale state is based on the Pseudo-Clim-DS in terms ofcombining components from different states. However, in
this conceptualization, the large-scale states are obtainedin multiple ways. The previous DS methods, such as DDS,
Unbiased-DS, and Pseudo-Clim-DS, are comprehensively
involved.
For practical purposes, we often have three large-scalestates: a reanalysis of the present climate state A, a GCM of
the present climate state Gp , and a GCM of the future climate state Gf (Fig. 2). Further, there are four climatologies:A, Gp , Gf , and UGf . The last one is the unbiased
future GCM climatology in which the climate bias of themodel estimated under the present climate is removed:




(2)
UGf  = Gf  − Gp , A = A + Gf , Gp .
For perturbations, there can be three states: A , Gp , and
Gf . Thus, in total, there exist 12 possible states for DS,
which are indicated by stars in the diagram. More possible states can be also obtained through combinations withother components, such as the ones obtained by ensemble
GCM simulations and/or artificially generated or modified states. These states are widely spread in the phasespace and are not limited by the GCM constraint. Here,
we should take into account the consistency between
the combined components in the combinations. Statistical checking of the consistency in spatial and temporal
aspects is an important issue. At least, we have to check
whether certain phenomena in the constructed state areconsistent with our knowledge. For instance, the locationof the mid-latitude westerly jet (i.e., a horizontal temperature gradient) and that of baroclinic eddies should

Nishizawa et al. Progress in Earth and Planetary Science (2018) 5:2

be consistent, and tropical cyclones (TCs) should not be
produced on the dry side of the Baiu front.
Our concept has another advantage in addition to wider
coverage of the large-scale state in the phase space. The
influence of changes in the individual components on thedownscaled regional states can be examined. As a typicalexample, let us assume the following case: each difference in the climatology and perturbation between the twostates in the spurious manifold has opposite influences on
the regional climate from each other, but not in nature’s
manifold. In this case, the DS would lead to an underestimation of the total influence. The above discussion
indicates the importance of evaluating individual influences in order to consider the total influence. Througha comparison of multiple DS simulations driven by thelarge-scale states that differ from one another by only one
component, the influence of the individual components
can be estimated. The regional state ψ obtained by DSdepends on the large-scale state φ: ψ = D φ  , φ , where
D is an operator representing the DS. The operator isinterpreted as




(3)
ψ = D φ  , φ = φ + P φ  ; φ + G [φ] ,where P is an operator representing modification of thelarge-scale perturbation φ  under climatology φ by DS
and G is one representing the variability generated or
excited spontaneously under the given large-scale environment in the DS simulation. G consists of sub-GCMgrid-scale variability, which does not get resolved in GCM
simulations, but gets resolved in DS simulations. The
differences in the downscaled
results
with the differ
ent states, D f  , f  − D p , p , can be divided into

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





D p , p + {f , p} − D p , p and D f  , p + {f , p} −D p , p + {f , p} . The first represents the difference dueto the change in climatology, and this is the quantity estimated with Pseudo-Clim-DS. This can be mainly interpreted as the difference in the intensification and/or
moving speed of a given perturbation under different climatologies in the DS simulations. The second represents
the difference due to the difference in a given perturbation under the same climatology, e.g., the influence ofthe number of cyclones passing through the calculation
domain.
The difference in the existing DS methods, clarified
through our concept of constructing the large-scale statefrom independent components as their decomposition,is summarized in Table 1. In addition, the location of
the states in the phase space is illustrated in Fig. 2. The
concept can be described as a generalization of existing
DS methods. Comparisons of the results obtained bydifferent existing DS methods can be used to estimate theindividual influence of the components. The influence ofthe difference in climatology can be estimated by comparing the results obtained by DDS driven by reanalysis
data and Pseudo-Clim-DS. A comparison can also bemade between DDS driven by present climate GCM data
and ATC-Pseudo-Clim-DS. The influence of perturbation
can be examined by performing a comparison between
the following DSs cases: (i) DDS with reanalysis data andpresent climate Unbiased-DS, (ii) future climate DDS and
ATC-Pseudo-Clim-DS, and (iii) future climate UnbiasedDS and Pseudo-Clim-DS. A comprehensive evaluation of
the results obtained by different DS methods in previous
studies helps us understand the contribution of various

Table 1 Possible large-scale states driving downscaling with reanalysis and GCM simulations in present and future climates
A

Gp

A

A

Gp − {Gp , A}(= A + {A, A})

A + {A, A} + AA + {A, A} + Gp

Present DDS (reanalysis)

Present Unbiased-DS

PerturbationGf

ClimatologyGp (= A + {Gp , A})

A + {A, A} + GfGp
A + {Gp , A} + AA + {Gp , A} + Gp

A + {Gp , A} + Gf

Present DDS (GCM)
UGf 

A + {Gf , Gp }(= A + {Gf , Gp })A + {Gf , Gp } + AGf − {Gp , A}
A + {Gf , Gp } + Gp

Pseudo-Clim-DSGf (= A + {Gf , A})

A + {Gf , A} + AA + {Gf , Gp } + Gf
Future Unbiased-DS

Gp + {Gf , Gp }Gf

A + {Gf , A} + Gp

A + {Gf , A} + Gf

ATC-Pseudo-Clim-DS

Future DDS

The top, middle, and bottom rows in each cell represent the original form, decomposition form, and corresponding downscaling method, respectively. The climatology andperturbation of a state are represented by   and prime, respectively, and the climate difference by { }Nishizawa et al. Progress in Earth and Planetary Science (2018) 5:2

components to the total regional climate change in the
future.
Demonstration of individual influences

In order to demonstrate an advantage of our concept,that is, the importance of estimating the individual influences of changes in climatology and perturbation in thelarge-scale state on regional precipitation, we conduct a
DS experiment based on the decomposition concept as an
example. We simultaneously consider the influences of thetwo components on regional precipitation through a comparison of three DS simulations. The experimental designis essentially the same as that of Yoshikane et al. (2012).
However, our interest here is to focus on the decomposition of the total influence into those of the climatology andperturbation, whereas the purpose of Yoshikane’s study
was to verify the validity of the Pseudo-Clim-DS method
for future DS projection.
The three DSs, i.e., the present climate DDS (PresentDDS) run, the future climate DDS (Future-DDS) run, and
the ATC-Pseudo-Clim-DS run, are performed. The largescale state driving the DS are denoted by Gp , Gf , andGp +{Gf , Gp } for the Present-DDS, Future-DDS, and ATCPseudo-Clim-DS runs, respectively, where the states forthe present and future climates in the GCM experimentare denoted by Gp and Gf , respectively. These can be
written as follows in the decomposed form:(4)
Gp = Gp  + Gp , Gp + Gp ,



(5)
Gf = Gp  + Gf , Gp + Gf ,
Gp + Gf , Gp = Gp  + Gf , Gp + Gp .
(6)
The influence of climatology is estimated from thedifference between the ATC-Pseudo-Clim-DS and
Present-DDS runs, D[ Gp , Gp  + {Gf , Gp }] −D[ Gp , Gp ],and that of the perturbation from the difference between
the Future-DDS and ATC-Pseudo-Clim-DS runs,
D[ Gf , Gp  + {Gf , Gp }] −D[ Gp , Gp  + {Gf , Gp }].
In this demonstration, experiments involving 25-yearlong time slices for the summer season (from Juneto September; referred to as JJAS) were performed
under the present (1979 to 2003) and future (2075 to2099) climate conditions in East Asia. Detailed descriptions of the experiment and the model are in the“Methods/Experimental” section. In the demonstration,
the daily mean is used as the climatology of the largescale state. We first obtained the monthly climatology by
25-year averaging. Next, we assumed that the monthly
mean is the value on the 15th of each month and constructed the daily climatology by linear interpolation of
the monthly climatology. Here, we assume that climatechange over 25 years is small enough to consider thatthe state is in climatological equilibrium. We ignore thebias in order to focus on demonstrating how individual

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influences can be considered with the concept, although aformal assessment of future regional climate will need toconsider the model climate bias. The analysis is conductedwith the simulation result in domain 2 described in the“Methods/Experimental” section, except for the lateralnudging region.
Figure 3 shows the summer climatology of the daily
precipitation in the Present-DDS, ATC-Pseudo-Clim-DS,
and Future-DDS runs. A large amount of precipitation
is found in the high mountain areas near the Pacific
Ocean. The precipitation in the Future-DDS is significantly weaker than that in the Present-DDS for the highprecipitation areas and the Pacific (Fig. 3f). The differencein precipitation resulting from climatology (Fig. 3d) ismuch smaller than the total difference. On the other hand,the difference resulting from perturbation is statisticallysignificant (Fig. 3e). In another analysis by month, we
confirmed significant differences due to perturbation in
all months from June to September. This shows that thedifferences due to perturbation result in significant differences in the DS simulations. Domain-averaged precipitation shows the same tendency (Fig. 4). The influences ofclimatology and perturbation have opposite signs. Since
the individual influences have uncertainties, the magnitude of each estimated change must be considered withsome range of the uncertainty. In our result, the positive change due to the climate difference is smaller than
the negative change due to the perturbation differencein terms of absolute magnitude. Because of the uncertainty, there is a possibility that the magnitude relationshipmay reverse; that is, the positive change due to the climate difference might be larger than the negative change
due to the perturbation difference. Therefore, although
the total difference in precipitation has a negative value
in this experiment, it is possible for the total difference
to be positive. This suggests that interpretations made byconsidering only the total change or the change in one
component face the risk of misunderstanding the future
regional climate. A simultaneous estimation considering
the total and individual components is thus necessary.
This result demonstrates the usefulness of the decomposition concept we propose in this study.
In order to show the usefulness of decomposition inunderstanding the future precipitation change, we conduct further decomposition of TC and non-TC precipitations. This can help readers in understanding theavailability of our proposed concept by showing theseries of our research process of the regional climatechange. Although this decomposition is not directly specified by the proposed concept of DS, it strengthens our
premise that decomposition is a useful way to understand future changes through understanding of individual influences of decomposed components on the futurechange. TCs have a large impact on precipitation inNishizawa et al. Progress in Earth and Planetary Science (2018) 5:2

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Fig. 3 Horizontal distribution of the 25-year JJAS mean daily precipitation in a the Present-DDS, b Pseudo-Clim-DS, and c Future-DDS runs, and thedifference due to d the climate difference (Pseudo-Clim-DS and Present-DDS), e perturbation difference (Future-DDS and Pseudo-Clim-DS), andf total difference (future and Present-DDS runs). The hatched regions in e and f represent the area in which the difference is statistically significant
with a 95% confidence level. The unit used is mm/day

this region. In the GCM future projection run used
to drive the DS, the number of TCs is smaller thanthat in the present run (Murakami et al. 2012). The
fewer TCs in future climate is also indicated by previous studies using other GCMs (e.g., Knutson et al.
2015; Roberts et al. 2015). The smaller number of TCs
in the future is consistent with the smaller amount ofprecipitation. We examine the precipitation associatedwith the TCs. Cyclone track detection is described in the“Methods/Experimental” section. We define TC precipitation as the precipitation within a distance of 1000 km
from the center of a TC. The contribution of the TC
precipitation to the total precipitation change is larger
than that of the non-TC precipitation, as shown in Fig. 4(top). The precipitation change associated with TCs is
primarily attributed to the perturbation difference. Thisis consistent with the fact that the number of TCs projected in the future perturbation is much smaller thanthat in the present. Increasing TC precipitation due to theclimate difference can be observed (Fig. 4, middle). Thisimplies that TCs are intensified in the future climatology
compared to the present. This result is consistent withprevious studies (e.g., Ying et al. 2012; Christensen et al.
2013). It is observed that the decreasing trend in the nonTC precipitation is mainly attributed to the perturbationdifference. The change is dominant in June, and it is not aslarge in other months. The smaller non-TC precipitationin June is consistent with the slower northward movementof the Baiu front in the GCM future projection than in thepresent (Kusunoki et al. 2011; Kanada et al. 2012). On theother hand, the influence of climatology on the non-TC
precipitation is quite small.

Discussion
Different areas, seasons, and quantities, i.e., different variables and statistics, can show the different contributionsof individual components to regional climate change. For
instance, the 2 m temperature in the experiment shows theNishizawa et al. Progress in Earth and Planetary Science (2018) 5:2

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Fig. 4 Contribution of each component to domain-averaged 25-year JJAS mean daily precipitation difference. The total difference, the difference
due to climate difference, and that due to perturbation are shown at the top, middle, and bottom, respectively, on the vertical axis. These
differences are further divided into ones associated with tropical cyclones and other factors. The error bars represent the 95% confidence interval of
Welch’s statistics. The percentages represent the ratios of the difference to the total precipitation in the Present-DDS run

dominant contribution of the climate difference relative tothe difference in the perturbation as shown in Fig. 5, andthe perturbation difference is dominant in the precipitation change. This suggests that applying this concept tovarious cases and fields is important in order to interpretthe regional future projections.
In the analysis discussed in the demonstration, nonlinear interaction between climatology and perturbationin the DS simulation, i.e., nonlinearity in operator D, is
not considered. Actually, operator D has some degree of
nonlinearity, and the estimation of individual influences
would be contaminatedbecause of thenonlinearity.
 The , p + f , p − D p , p andpDcomparison
between




 



D f  , p
D f  , p or D f  , p
− D p , p  + f , p −and D f , p + f , p − D p , p + f , p gives us a hintof the nonlinearity. The nonlinearity can also be investigated by comparing multiple DS simulations based on
the strategy. Adachi et al. (2017) proposed a procedure to
extract the interaction effect and showed that the interaction can have a greater influence on heavier precipitation,
whereas Kröner et al. (2016) showed that the nonlinearity could be negligible in their case. Careful considerations
for the nonlinearity are necessary in each case.
In the DS experiment in this study, climatology isdefined as the daily interpolated climatological monthly
mean. Interannual and inter-seasonal variability, such as
ENSO, is included in the perturbation. There are variations in the definition of climatology. For instance,
although seasonal and daily changes can be included inclimatology, they can also be treated as perturbations.

These components should be defined based on the
purpose of the study. In addition, the climatology–
perturbation decomposition is just one of several possible decompositions. In order to understand the influencesof other components, different decompositions would beappropriate. For instance, Adachi et al. (2012) investigated
the impact of urbanization on regional climate with a
Pseudo-Clim-DS experiment with the present and future
urbanization conditions. Kröner et al. (2016) decomposed
the future change into changes due to three effects (thelarge-scale thermodynamic effect, lapse-rate effect, andlarge-scale circulation) and other remaining effects. Comparisons between the individual impacts obtained throughsuch experiments would give us a better understanding of
future change. Here, it should be noted that dynamical orother balances should be considered in the independent
treatment of the decomposed components; otherwise, thevariability in DS simulations could be violated because of
non-physical factors. In addition, we consider that otherquantities (not just the mean) are important in climatechange, such as quantities related to extremes, although
we discuss only the mean as an example.
We focus on the GCM’s errors in this study. There also
exist model errors in regional climate models (RCMs),
which represent the operator D in Eq. 3, that can be acause of uncertainty as well (e.g., Déqué et al. 2012). The
RCM error can be interpreted as two errors. One error isthat in the operator P and is caused by the spurious modification of the large-scale perturbation. The other is thatin the operator G and is caused by the spurious excitation

Nishizawa et al. Progress in Earth and Planetary Science (2018) 5:2

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Fig. 5 Horizontal distribution of the 25-year JJAS mean 2-m temperature in a the Present-DDS, b Pseudo-Clim-DS, and c Future-DDS runs, and thedifference due to d the climate difference (Pseudo-Clim-DS and Present-DDS), e perturbation difference (Future-DDS and Pseudo-Clim-DS), andf total difference (future and Present-DDS runs). The hatched region in e and f represents the area in which the difference is statistically significant
with a 95% confidence levelof small-scale variability. In addition to considering theuncertainty due to the GCM’s errors by including a wider
coverage of possible large-scale states, it is important toconsider the uncertainty due to the RCM’s errors, which
can be evaluated by multi-RCM experiments.

Conclusions
We conceptualized dynamical downscaling and presented
a perspective on downscaling for regional climate studies. In this study, we provided a comprehensive view ofthe previous downscaling methods based on reconstruction of the large-scale state driving DS from independent decomposed components, such as climatology andperturbation.
The concept of the reconstruction of the decomposedcomponents provides not only a comprehensive viewof DS but also a strategy for coordinated experimental
design for future regional climate studies. We can obtainthe large-scale states from a wider region in the phasespace, whereas only the states in the spurious manifoldin the phase space distorted by interactions between thecomponents due to a GCM error are obtained by theprevious individual DS methods. Furthermore, we canestimate the individual influences of the change in thecomponents of the large-scale state on the downscaled
regional climate. The importance of the simultaneousconsideration of individual influences is demonstrated bya DS experiment. We estimated the influence of both theclimatology and perturbation change on the future precipitation simultaneously and found that the influence ofthe perturbation can be significant, as well as that of theclimatology.
Consideration of uncertainty due to the model error
and understanding of the influence of individual components are important for more reliable assessments offuture regional climates. The uncertainty of the projected
future regional climate is often estimated from an ensemble spread in ensemble experiments with various GCM

Nishizawa et al. Progress in Earth and Planetary Science (2018) 5:2

results. The region in the phase space covered by multimodel and/or multi-physics ensemble GCM simulations
is larger than that of a single-model and single-physics
case. However, the manifolds of the different GCMs canbe isolated from one another, and the covered region was
discretely distributed. In order to understand the characteristics of the output of a nonlinear operator, inputs thatare not only widely but also evenly distributed are generally preferable to those that are locally concentrated insome places because the operator has local linearity. In
this sense, in order to assess the uncertainty more reliably, DS simulations driven not only by the large-scalestates obtained by ensemble GCM simulations but also byreconstructed states from components of the ensembles
should be performed. In addition to the total uncertainty,
an estimation of the individual uncertainty associatedPage 10 of 13

with each component is as necessary as the absolutemagnitude of the influence due to individual components. The contribution of each component differs in its
uncertainty and absolute magnitude.

Methods/Experimental
Experimental settings

In the demonstration, the total 25-year summer time data
was obtained by performing five-day integrations overlapping a one-day spin-up term. Two nested domains areused for DS: domain 1, which is 2520 × 2520 km2 witha 7.5 km grid spacing, and domain 2 nested in domain
1, which is 1080 × 960 km2 with a 2.5 km grid spacing;both domains have the same domain center of 135.2 °E and34.7 °N (Fig. 6) The numbers of vertical layers are 36 and
60 for domains 1 and 2, respectively.

Fig. 6 Domain (top) 1 and (bottom) 2 for the numerical simulation in the demonstration. Contours represent surface elevation in the simulation andtheir interval is 500 m. The broken line shows the lateral nudging region (outmost 20 grids)

Nishizawa et al. Progress in Earth and Planetary Science (2018) 5:2

Regional model

The regional model used for the DS experiment is the
Scalable Computing for Advanced Library and Environment Regional model (SCALE-RM) (Nishizawa et al.
2015; Sato et al. 2015; available at http://scale.aics.riken.jp).
A six-category one-moment bulk scheme (Tomita 2008),
a k-distribution scheme (Sekiguchi and Nakajima 2008),
the MYNN level 2.5 scheme (Nakanishi and Niino 2009),
a similarity scheme (Beljaars and Holtslang 1991; Wilson
2001), a diffusion and bucket scheme, and a single-layerurban canopy model (Kusaka et al. 2001) are used to represent cloud microphysical processes, radiation transfer,planetary boundary layer turbulence, surface flux, land
processes, and urban processes, respectively.
Large-scale state

The large-scale state obtained by a 20-km resolution
Atmospheric Model Intercomparison Project (AMIP)type experiment with the Meteorological Research Institute atmospheric GCM (MRI-AGCM) (Mizuta et al. 2012)is used to drive the DS. In the AGCM experiment, thesea surface temperature (SST) of HadISST1 (Rayner et al.
2003) is prescribed in the present climate run (Mizuta
et al. 2012), and the multi-model ensemble averaged
SST of the CMIP5 (Taylor et al. 2012) coupled-GCM
runs with the Representative Concentration Pathways(RCP) 8.5 scenario is prescribed in the future climate run(Mizuta et al. 2014).
Cyclone track detection

The cyclone track is detected using the method proposedby Adachi and Kimura (2007), and a TC is defined asa cyclone that comes from south of 25 °N. The corresponding cyclones in the GCM simulation are used for
the TC determination, since the domain for the DS is
not wide enough for the determination. The numbersof TCs entering the domain of analysis are 150, 158,
and 90, in the Present-DDS, ATC-Pseudo-Clim-DS, andFuture-DDS runs, respectively. Here, the numbers aredifferent for the Present-DDS and ATC-Pseudo-Clim-DS
runs because of slight differences in TC tracks in the outerdomain.
Abbreviations
AGCM: Atmospheric general circulation model; AMIP: Atmospheric modelintercomparison project; ATC: Assumed true climate; DS: Downscaling; DDS:
Direct downscaling; GCM: General circulation model or Global climate model;
JJAS: June to September; MRI: Meteorological Research Institute;Pseudo-Clim-DS: Pseudo climate change downscaling; RCM: Regional climate
model; SST: Sea surface temperature; TC: Tropical cyclones
Acknowledgements
The MRI-AGCM3.2S data were provided by the Program for Risk Information
on Climate Change (SOUSEI) of the Ministry of Education, Culture, Sports,
Science, and Technology (MEXT) of Japan conducted by the MeteorologicalResearch Institute (MRI). This research used computational resources of the K
computer provided by the RIKEN Advanced Institute for Computational
Science through the HPCI System Research project (Project ID:hp160119). The

Page 11 of 13

analysis and visualization in this study was conducted using the products of
the GFD-Dennou Club (http://www.gfd-dennou.org/).
Funding
This work was supported by the FOCUS Establishing Supercomputing Centerof Excellence and JST CREST Grant Number JPMJCR1312, Japan.
Availability of data and materials
The regional model for the downscaling calculation in this study wasconstructed 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-AGCM3.2 data and the post analysis
code used in this study are also available from the corresponding author.
The downscaling data by SCALE-RM is deposited in local storage at RIKEN/AICS.
It is available from the corresponding author upon reasonable request. The
MRI-AGCM data was provided to the authors by MRI under a given condition
that the authors can use the MRI-AGCM data only for the 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 with the permissionof MRI. In this case, contact person is the corresponding author.
Authors’ contributions
SN, SAA, YK, and HT designed the research. SN, SAA, TY, and KA carried out thedownscaling simulation. SN, SAA, TY, KA, and RY analyzed the data. SN, SAA,
YK, and HT wrote the paper. YK, HY, and HT supervised the research. All
authors contributed to discussions of the results and read and approved themanuscript.
Ethics approval and consent to participate
Not applicable.
Consent for publication
Not applicable.
Competing interests
The authors declare that they have no competing interests.

Publisher’s NoteSpringer Nature remains neutral with regard to jurisdictional claims inpublished maps and institutional affiliations.
Author details
1 RIKEN Advanced Institute for Computational Science, 7-1-26
Minatojima-minami-machi, Chuo-ku, Kobe, Hyogo 650-0047, Japan. 2 ResearchCenter for Urban Safety and Security, Kobe University, 1-1 Rokkodai-cho,Nada-ku, Kobe, Hyogo 657-8501, Japan.
Received: 8 May 2017 Accepted: 13 December 2017

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