Estimation of the Future Distribution of Sea Surface
Temperature and Sea Ice Using the CMIP3
Multi-model Ensemble Mean

CMIP3 マルチモデルアンサンブル平均を利用した将来の海面水温・海氷分布の推定

Ryo Mizuta*1, Yukimasa Adachi*2, Seiji Yukimoto*2 andShoji Kusunoki*2

水田 亮*1・足立 恭将*2・行本 誠史*2・楠 昌司*2

*1

Advanced Earth Science Technology Organization

地球科学技術総合推進機構*2

Climate Research Department, Meteorological Research Institute

気象研究所 気候研究部

Preface
Future global climate change has been assessed in the Fourth Assessment Report of theIntergovernmental Panel on Climate Change (IPCC-AR4) with higher confidence than in previous
reports by using state-of-the-art atmosphere–ocean coupled general circulation models (AOGCM),
which have been developed at institutions worldwide and made available under Coupled Model
Intercomparison Project phase 3 (CMIP3) as an activity of the World Climate Research Programme(WCRP). The performance of AOGCMs in reproducing historical and present climate has been
improved, and the ensemble average of the multi-model results gives the best performance in many
aspects.
It has now been recognized that global warming is inevitable unless urgent countermeasures are
implemented, and the current emphasis is on the mitigation of the effects of global warming. For thispurpose, more precise and detailed information (both spatial and temporal) of future climate change isneeded. Such information can be obtained most effectively from atmospheric models with much higher
resolution than that of the AOGCMs used for long-term projection. Bottom boundary data (sea surface
temperature and sea ice distribution) for the present and future climate must be specified in such"time-slice" simulations. In time-slice simulations, it is essential for the bottom boundary data to beprecise and credible with regard to not only mean climate but also temporal variability.
The mean CMIP3 multi-model result is considered the best choice for the boundary data; however,the simple ensemble mean of multi-model data presents several problems. We developed a techniquethat incorporates the effects of future climate change along with realistic interannual variability, whichis smoothed out by the multi-model mean, while correcting for the climatic biases of each model. This
report documents this technique. Processed results from the CMIP3 multi-model data are alsopresented.
The technique was developed as part of the KAKUSHIN Program "Projection of the Change inFuture Weather Extremes Using Super-High-Resolution Atmospheric Models" of the Ministry of
Education, Culture, Sports, Science and Technology, Japan, with support from the research fund"Integrated Research on Climate Change Scenarios to Increase Public Awareness and Contribute to the
Policy Process, Global Environment Research Fund, Ministry of the Environment (Theme 2:
Evaluation of CMIP3 multi-model performances for various phenomena)". We hope that the techniquedescribed here will be utilized not only by the program for which it was developed but also in othertime-slice experiments to obtain precise and detailed information about future climate change invarious regions of the world, because its use will help reduce the uncertainty in the information thatstems from the use of inconsistent boundary data.
Akio Kitoh
November 2008

Director
Climate Research Department

序気候変動に関する政府間パネル第 4 次評価報告書（IPCC-AR4）
において、世界の研究機関で開発された最新の大気海洋結合モデル（AOGCM）
を用いて、これまでの報告書よりも高い信頼性をもって将来の世界的な気候変化が評価された。
それに用いられたモデルの結果は、
世界気候研
究計画
（WCRP）の活動の一つである結合モデル比較プロジェクト・フェーズ３（CMIP3）のもとで提供されている。
それら AOGCM による過去から現在に至る気候の再現性能は向上してきており、またそれら多くのモデルのアンサンブル平均は多くの観点からも最も良い性能を与えることが示されている。
今や、緊急の対策をしなければ地球温暖化は避けることができないことと認識されている。
また、
地球温暖化に対し、その影響の緩和策により重点が置かれるようになってきている。
このような目的のためには、将来の気候変化に関して（空間的にも時間的にも）より正確かつ詳細な情報が求められる。そのような情報は、長期の予測に用いられる AOGCM よりもむしろ、高解像度の大気モデルを用いる方がより効率的に得ることができる。
そのような、
いわゆる「タイムスライス」
シミュレーションのためには、下部境界条件（海面水温および海氷の分布）が必要とされる。
タイムスライス・シミュレーションにとって、
その下部境界データは、
平均的な気候値だけでなく時間的な変動性についても、
正確かつ信頼性の高いものであることが非常に重要な要素となる。
CMIP3 の多数のモデル（マルチモデル）の平均から得られる結果は、
その境界データとして最良の選択であると考えられる。
しかし、マルチモデルのデータを単純に平均するだけでは、いくつかの問題が生じてくる。
そこで我々は、それぞれのモデルのバイアスを補正し、マルチモデルを平均した場合に平滑化されて消えてしまう年々変動を現実的に表現しつつ将来の気候変化の効果を取り入れる手法を開発した。
この報告はその手法を記述するものである。
また、
CMIP3 のマルチモ
デル・データを用いた処理結果も示すことにする。
この技術開発は、
文部科学省２１世紀気候変動予測革新プログラム「超高解像度大気モデルによる将来の極端現象の変化予測に関する研究」の推進に資するために行ったものである。
また一部は、環境省地球環境研究総合推進費「地球温暖化に係る政策支援と普及啓発のための気候変動シナリオに関する総合的研究（テーマ2：マルチ気候モデルにおける諸現象の再現性比較とそ
我々は、それにとどまらず、
世界の各地域における将の将来変化に関する研究）」の支援も得た。
来の気候変化についての正確かつ詳細な情報を得るために、
これらのデータが多くのタイムスライ
ス実験に利用されることを願っている。
そのように利用されることにより、ばらばらな境界条件データを用いる場合に比べ、不確実性の低減に結びつくものと考える。
平成 20 年 11 月

気候研究部長鬼頭昭雄

Abstract
We estimated future distributions of sea surface temperature, sea ice concentration, and sea ice
thickness by using Coupled Model Intercomparison Project phase 3 (CMIP3) multi-model ensemble
data for the lower boundary conditions of atmospheric time-slice experiments. The estimation method
includes corrections for the present-day climate bias in the model relative to the observation data set
and future changes in the multi-model ensemble mean, while keeping the same interannual variability
as found in the observation data. These estimated sea surface temperature and sea ice data are usefulfor simulating, using high-resolution atmospheric models, the most likely effects of future climatechange on small-scale atmospheric phenomena, under the assumptions that oceanic variability is
unchanged in the mean future climate and that atmosphere–ocean interaction is negligible.

概要
結合モデル比較プロジェクト・フェーズ３(CMIP3)マルチモデルアンサンブル平均を利用して、
将
来の海面水温と海氷の分布を推定し、大気モデルによるタイムスライス実験で下部境界条件として用いる方法を考案した。
この方法は、観測された年々変動をそのまま用いながら、観測に対するモ
デルの現在気候のバイアスの補正と、マルチモデルアンサンブルで表現される将来変化の効果を含んだものとなっている。
この分布は、海洋の変動が将来気候においても変化せず大気海洋相互
作↪䈏ήⷞ䈪䈐䉎䈫䈇䈉઒ቯ䈱ਅ䈪㜞⸃௝ᐲ䈱ᄢ᳇䊝䊂䊦䈪૶↪䈜䉎䈖䈫䈮䉋䉍、もっとも起こりう
る将来の気候変化影響をシミュレートするのに有用である。

Contents
1. Introduction･････････････････････････････････････････････････････････････････

1

2. Methods･････････････････････････････････････････････････････････････････

2

2.1 Sea surface temperature････････････････････････････････････････････････････

2

2.2 Sea ice concentrations･････････････････････････････････････････････････････ 4

2.3 Sea ice thickness･････････････････････････････････････････････････････ 6

3. Verification of the estimated distributions･････････････････････････････････････････ 8

4. Discussion･････････････････････････････････････････････････････････････････ 10

Acknowledgements･････････････････････････････････････････････････････････････････ 11

References･････････････････････････････････････････････････････････････････ 11

Supplementary Information････････････････････････････････････････････････････ 13

Technical Reports of the MRI, No. 56

2008

1. Introduction
Climate experiments with atmospheric general circulation models (AGCM) using prescribed sea
surface boundary conditions are called "time-slice" experiments, and they require horizontal
distribution data for sea surface temperature (SST) and sea ice concentration and thickness. Although
we can use observation data sets for present-day climate experiments (AMIP-type experiments), datafrom atmosphere–ocean coupled general circulation models (CGCM) are often used for experiments
simulating the future climate, such as that during several decades after the present or during the last
decades of the 21st century. However, when we conduct a future-climate experiment by using an
AGCM to evaluate possible future changes, the direct use of a CGCM's output for future boundary
conditions gives rise to various problems as follows:
1. Because a CGCM's output for the present-day climate shows some bias when compared withobservation data, it is difficult to evaluate future changes simply by taking the difference between
AGCM results obtained by using the observed conditions and those obtained by using the output of a
CGCM for future conditions.
2. By using the present-day output of a CGCM for the AGCM present-day conditions as well as forexperiments on future conditions, we can evaluate future changes by taking the difference between thetwo results. However, it is difficult to obtain a good representation of the present-day climate with the
AGCM because of the bias in the CGCM.
3. The use of the multi-model ensemble mean (MMEM) of many CGCMs for the AGCM
present-day and the AGCM future conditions can cancel much of the bias of the individual models andcan reduce the uncertainty in the simulated future changes, but it also cancel the interannual variability
in the results of the individual models.
Therefore, it is appropriate to embed the changes from the present-day to the future in the CGCM
results in the observation data and then to use those data for the AGCM simulation of future conditions,
to compare with the AGCM results obtained using the observed conditions. However, the simple
superposition of the changes in the observation data is problematic because the trend and interannual
variability in the obtained data introduce inconsistency. This occurs especially near the ice edge, since
the location of the ice edge, where future changes of sea ice are largest, differs between in the CGCM
results and the observation data. As a result, the future retreat of the sea ice is not represented
appropriately as described later.
In this work, we present a method for estimating the future distributions of SST and sea ice thatavoids these problems by decomposing the observation data and the CGCM outputs into long-term
mean, linear trend, and interannual variability, and then combining some of these components.
Changes in the sea ice extent in each hemisphere are taken into account in the estimation of sea ice− -11−-

Technical Reports of the MRI, No. 56

2008

linear trend
in CGCMs
CGCMs
SRES A1B
experiments(2000-2100)

observed SST for
AMIP (1979-2003)
CGCMs C20C
experiments(-2000)
1979

2003

2075

present-day climate
linear trend in CGCMs(2075-2099)

future change
in CGCMs

ǍT

䋫

㰱T

2099

future climate
detrended observed
SST (1979-2003)

䋫䋽([2075-2099][1979-2003])

Fig. 1: The method used for estimating future SSTs.

concentrations. By using the estimated distributions of SST and sea ice for the lower boundary
conditions in the AGCM experiment on future conditions and using the observed conditions for the
AGCM present-day experiment, we can use the difference between the two results to represent theeffect of climate change caused by the lower boundary condition changes. By also including increases
in greenhouse gases and other effects in the experiments simulating future conditions, we can simulate
the changes that are most likely to happen in the future.

2. Methods
2.1 Sea surface temperature
After calculating the MMEMs of the CGCMs, the MMEM and observation SSTs are decomposed
into three terms as follows:
SSTobs ( y1 , m, x)

SSTobs_A ( m, x)  SSTobs_T ( y1 , m, x)  SSTobs_V ( y1 , m, x),

SSTmp ( y1 , m, x)

SSTmp_A ( m, x)  SSTmp_T ( y1 , m, x)  SSTmp_V ( y1 , m, x),

SSTmf ( y 2 , m, x)

SSTmf_A (m, x)  SSTmf_T ( y 2 , m, x)  SSTmf_V ( y 2 , m, x),− -22−-(1)

Technical Reports of the MRI, No. 56

observation

decrease in the CGCMs

2008

added change

(a)
+

=

+

=

(b)

Fig. 2: Inconsistencies that can arise in the sea ice distribution when the difference between thepresent-day and future conditions in the CGCM results (center) is simply added to the observation data(left), when the ice edge of the CGCM is located within the observational ice edge (a), or when the
MMEM ice edge is located outside the observational ice edge (b).

Fig. 3: Correlation coefficients between the sea ice extent in the Northern Hemisphere and the sea
ice concentration at each grid point.

− -33−-

Technical Reports of the MRI, No. 56

2008

where obs is the observation data; mp and mf are the MMEMs for the present-day and future climate,respectively; A indicates the long-term mean; T indicates the linear trend; and V refers to theinterannual variability, which is defined as the residual of A and T. Decomposition is performed atevery grid point x for every month m of every year, with y1 indicating present-day years and y2
indicating future years.
The values of future distributions, SSTfuture, are estimated as follows:
SSTfuture ( y 2 , m, x) { SSTobs_A (m, x)  SSTmf_A (m, x)  SSTmp_A (m, x)
 SSTmf_T ( y 2 , m, x)  SSTobs_V ( y1 , m, x).

(2)

The difference between the mean present-day and future values simulated in CGCMs is a crucialcomponent of climate change, so it is added to the observed mean to represent the estimated long-term
mean. The trend in the MMEM is used as the estimated future trend. For the interannual variability, theobserved variability is used as the estimated variability, under the assumption that the variability will
not change in the future, because SSTmp_V and SSTmf_V are both very small owing to the cancellation ofindividual model variabilities. For each y2, y1 is chosen so that y2 – y1 is a constant value, as describedin Section 3. A schematic diagram of this estimation method is presented in Figure 1.

2.2 Sea ice concentrations
If the future distribution of sea ice concentration, fice(y2, m, x), is estimated by the same method as
the SST, it is highly likely that some inconsistencies will occur near the ice edge, as shown in Figure 2.
This inconsistency occurs when the location of the ice edge, where the sea ice changes are largest,differs between the CGCM results and observation data. When the MMEM ice edge is located within
the observational ice edge, the largest ice change also occurs within the observational ice edge. Adding
the change to the observation data makes the distribution non-monotonic in the meridional direction(Fig. 2a). On the other hand, when the ice edge of the MMEM is outside the observational ice edge,
little or no ice change occurs within the observational ice edge. Therefore, when the change is added tothe observation data, no sea ice retreat as a result of climate change is represented (Fig. 2b).
Because the change that most affects the AGCM results is the change in the sea ice area extent, it isdesirable for the change of sea ice extent between the observation data and the estimated future to be
the same as the change from the CGCM present to the CGCM future. The correlations between the sea
ice extent in the Northern Hemisphere and the sea ice concentration at each grid point (Fig. 3) are high,except in the center of the ice cap, where variability is small. Therefore, the sea ice concentration
fice(y2, m, x) in the future can be estimated from the change in the sea ice extent in each hemisphere as
follows (Fig. 4):
1. In each hemisphere, the sea ice extent, Sice, is defined as a function of the sea ice concentration f,− -44−-

Technical Reports of the MRI, No. 56

2008㪽 㪪㫀㪺㪼㪶㫆㪹㫊 㪪㫀㪺㪼㪶㫄㫇 㪪㫀㪺㪼㪶㫄㪽 㪪㫀㪺㪼㪶㪽㫌㫋㫌㫉㪼㪲㪈㪇㪵㪍㩷㫂㫄㪉㪴㪑㪏㪇㩼 㪈㪊㪅㪈㪈㪈 㪈㪋㪅㪎㪌㪍 㪈㪉㪅㪌㪎㪎㪈㪇㪅㪋㪈㪈
㪑㪍㪇㩼 㪈㪋㪅㪊㪇㪏 㪈㪌㪅㪍㪈㪌 㪈㪊㪅㪋㪇㪏㪈㪈㪅㪌㪎㪋
㪑㪋㪇㩼 㪈㪌㪅㪇㪈㪌 㪈㪍㪅㪈㪏㪋 㪈㪊㪅㪐㪋㪊㪈㪉㪅㪈㪏㪉
㪑㪉㪇㩼 㪈㪌㪅㪍㪌㪌 㪈㪍㪅㪎㪉㪏 㪈㪋㪅㪋㪍㪐㪈㪉㪅㪎㪌㪇
㪑

observation

future estimation

80%
80%

Ciceobs(f ’)

60%

60%

40%

40%

20%

20%

Cicefuture(f)=Ciceobs(f ’)where f’ satisfies Siceobs(f ’)=Sicefuture(f)Fig. 4: Diagram of the method used for estimating future sea ice concentrations. Siceobs, Sicemp, andSicemf are functions of f. The example values in the table (top) are for y1 = 1994, y2 = 2090, and m = 3
in the Northern Hemisphere. (bottom) The correspondence between Ciceobs (y1, m, h, f), and Cicefuture(y2, m, h, f).

so that Sice(f) is the area in which the concentration is more than f. The extent in every month m ofevery year y is calculated separately for each hemisphere h.
2. The sea ice extent in the future is estimated in the same way as SST (Eq. 2) by using the monthly
sea ice extent, Sice:
Sicefuture ( y 2 , m, h, f ) { Siceobs_A (m, h, f )  Sicemf_A (m, h, f )  Sicemp_A (m, h, f ) Sicemf_T ( y 2 , m, h, f )  Siceobs_V ( y1 , m, h, f ).

(3)

3. For each month, ficefuture(y2, m, x) in the future is estimated by shrinking the observed extent,
ficeobs(y1, m, x), while keeping the shape of the ice cap, until Sicefuture(y2, m, h, f) is equal to Eq. (3). To
do so, we prepare the isopleth shapes Ciceobs(y1, m, h, f) as a function of f for the observed sea ice
distribution (Fig. 4, left), obtaining the correspondence between f, Siceobs (y1, m, h, f), and Ciceobs (y1, m,h, f). Next, we find f’ for each f that satisfies(4)

Siceobs ( y1 , m, h, f ' ) Sicefuture ( y2 , m, h, f ).

Then, the isopleth f in the future is estimated by
Cicefuture ( y 2 , m, h, f ) { Ciceobs ( y1 , m, h, f ' ).

(5)

− -55−-

Technical Reports of the MRI, No. 56

2008

By combining Cicefuture (y2, m, h, f) estimated for f from 0% to 100%, we can obtain the estimateddistribution of sea ice concentrations in the future.
2.3 Sea ice thickness
The sea ice thickness in the future is estimated so that the rate of change in the sea ice volume isequal to the rate of change in the MMEM results. For simplicity, the estimated thickness distribution
dicefuture(m, x) defined for each month is obtained by multiplying the observed thickness distribution by
a constant Į:
dicefuture (m, x) { D  diceobs (m, x).

(6)Here, since we have only the climatology of the thickness observations and do not have reliable
observed trends or interannual variability, we use a future thickness distribution that has only seasonalvariation and no interannual variability.
The constant Į is obtained as follows (Fig. 5). First, the sea ice volume, Vice, in each hemisphere forthe observation data and the MMEM is calculated:

observation

MMEM

present
1m
2m

㬍

80%
60%

3m

㹢

5m

Viceobs

Vicemp40%
20%

ficeobs

diceobs=㰿(ficeobs㬍diceobs)uuD

VicemfVicempfuture
0.8m
1.6m
80%

㬍

60%

2.4m
4m

Vfuture = Vobsu

㹢

40%

VicemfVicemp20%

ficefuture

dicefuture =㱍diceobs=㰿(ficefuture㬍dicefuture)=㱍㰿(ficefuture㬍diceobs)㺯 㱍=㰿(ficeobs㬍diceobs)
㰿(ficefuture㬍diceobs)uVicemfVicempFig. 5: Diagram of the method used for estimating future sea ice thickness.

− -66−-

VicemfTechnical Reports of the MRI, No. 56¦ ^ fice ( y , m, x) u dice (m, x)`,¦ ^fice ( y , m, x) u dice ( y , m, x)`,

Viceobs (m, h)

obs

1

obs

mp

1

mp

2008

x , y1

Vicemp (m, h)

1(7)

x , y1¦ ^ fice ( y , m, x) u dice ( y , m, x)`.

Vicemf (m, h)

mf

2

mf

2

x, y 2

Sea ice volume Vicefuture(m, h) in the future is estimated so that the rate of change from the observation
data is equal to the rate of change in the MMEM results:
Vicefuture (m, h) { Viceobs (m, h) u

Vicemf (m, h).
Vicemp (m, h)

(8)

Since
Vicefuture (m, h)¦ ^ fice( y 2 , m, x) u dicefuture (m, x)`¦ ^ fice( y 2 , m, x) u Ddiceobs (m, x)`

futurex, y 2

future(9)x, y 2D ¦ ^ ficefuture ( y 2 , m, x) u diceobs (m, x)`,x, y 2

Į can be calculated by¦ ^ fice ( y , m, x) u dice (m, x)` Vice (m, h)u.
¦ ^ fice ( y , m, x) u dice (m, x)` Vice (m, h)
obs

D

1

obs

x , y1

mf

future2obs

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Table 1: Data sets used for the CMIP3 models.
NameInstitutebccr_bcm2_0

Bjerknes Centre for Climate Research, Norway

cccma_cgcm3_1

Canadian Centre for Climate Modeling & Analysis, Canada

cccma_cgcm3_1_t63
cnrm_cm3

Météo-France/Centre National de Recherches Météorologiques, France

csiro_mk3_0

CSIRO Atmospheric Research, Australia

gfdl_cm2_0

U.S. Dept. of Commerce/NOAA/Geophysical Fluid Dynamics Laboratory,

gfdl_cm2_1

USA

giss_aomNASA/Goddard Institute for Space Studies, USA

inmcm3_0

Institute for Numerical Mathematics, Russia

ipsl_cm4

Institut Pierre Simon Laplace, France

miroc3_2_hires

Center for Climate System Research (University of Tokyo), Nationalmiroc3_2_medres

Institute for Environmental Studies, and Frontier Research Center for
Global Change (JAMSTEC), Japanmiub_echo_g

Meteorological Institute of the University of Bonn, MeteorologicalResearch Institute of KMA, and Model & Data Group, Germany/Korea

mpi_echam5

Max Planck Institute for Meteorology, Germany

mri_cgcm2_3_2a

Meteorological Research Institute, Japan

ncar_ccsm3_0

National Center for Atmospheric Research, USA

ukmo_hadcm3

Hadley Centre for Climate Prediction and Research/Met Office, UK

ukmo_hadgem1

3. Verification of the estimated distributions
We estimated the distributions for 2015–2039 and 2075–2099 by this method using the observation
data and the MMEM. Monthly mean data from the Hadley Center (Rayner et al., 2003) from 1979 to
2003 were used for the observed SST and sea ice concentration data, along with the monthly
climatology of sea ice thickness from Bourke and Garrett (1987). The results of the Climate of theTwentieth Century Project (C20C) experiments (until 2000) and the SRES A1B scenario experiments(after 2000) of 18 CMIP3 CGCMs (Meehl et al. 2007) were used for the MMEM. The CGCMs usedhere are listed in Table 1. We used only one experiment from models with multiple experiments.
Phases of the observed interannual variability SSTobs_V during y1 = 1979, … , 2003 were shifted 36 or
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Fig. 6: Sea surface temperatures averaged over 170°W–120°W and 5°S–5°N in January. Thin lines
are the CGCM results, and the thick black line is the ensemble mean of the CGCM results. The
thick red line is the observation data, and the thick blue lines denote SSTfuture, estimated by Eq. (2)for 2015–2039 and 2075–2099.

96 years to y2 = 2015, … , 2039 or y2 = 2075, … , 2099 for use in Eqs. (2) and (3). For example, y1 =1979 was used with y2 = 2015 or y2 = 2075, and y1 = 1980 was used with y2 = 2016 or y2 = 2076. Thissame correspondence between y1 and y2 was also used when shrinking the sea ice distribution (Eqs. (4)and (5)). In Eq. (5), we calculated Cicefuture (y2, m, h, f) for f with intervals of 0.1%.
Figure 6 shows SST averaged over the tropical Pacific region in the observation data, the CGCMs,
the MMEM, and the estimated future. The variability in this region is mainly due to ENSO. Althougheach CGCM (thin colored lines) shows more or less interannual variability, the MMEM (thick blackline) shows very small variability because of cancellation of variation phases. Since the observed SST(thick red line) is higher than the MMEM by about 0.7 K, the estimated SST (thick blue lines) obtainedby Eq. (2) is also higher than the MMEM.
Figure 7 shows Northern Hemisphere sea ice concentrations in March during three observation years(y1 = 1994, 1998, and 2002), and estimated concentrations in three future years (y2 = 2090, 2094, and2098). In the future estimations, sea ice decreases and retreats around Newfoundland and the Sea of

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Fig. 7: Horizontal distributions of sea ice concentrations in March in the observation data, ficeobs(y1, m,x) (top), and estimated ficefuture (y2, m, x) in the future (bottom).

Okhotsk. Some interannual variability in the observation data is apparent: in 1994, more sea ice wasobserved in the Western Hemisphere, and in 1998, more was observed in the Eastern Hemisphere. Thiskind of variability is kept in the estimated distribution: There is more sea ice in the Western
Hemisphere in 2090 and more in the Eastern Hemisphere in 2094, because in Eq. (5) the sea ice
distribution in y2 is calculated using the isopleths of the sea ice concentration in y1.
As supplemental information, monthly SST, sea ice concentration, and sea ice thickness and theirchanges averaged over the 25 years, along with monthly SSTmf_T and SSTobs_V, are shown in Figs.
S1–S16.

4. Discussion
There is large uncertainty with regard to the future changes in the amplitude and horizontal patternof interannual variability. A variety of changes in ENSO are found in CMIP3 CGCMs (IPCC 2007).
Whereas a linear trend induced by the greenhouse gas increase is dominant in the linear trend of the
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MMEM future experiments, that is not the case in the present-day climate (either in the observation
data or the MMEM present experiments). Decadal variability accounts for the calculated linear trend in
the present-day climate to a certain degree, mainly because of the short time period of the data. In thiswork, therefore, we used observation data alone for estimating future interannual variability, and
MMEM future results alone for estimating the future linear trend. Correction of the bias in the linear
trend between the MMEM present and the observation data might be desirable if the effect of decadal
variability could be removed from the calculated linear trend.
If we take the median sea ice concentration of the present-day CGCM experiments, a distribution
very similar to the observation data is obtained. Thus, it would be possible to estimate the long-termmean of the locations of future decreases by calculating ficemf – ficemp. However, interannual variability
in the location of the decrease is not represented in such a calculation because interannual variability in
MMEM is very small as a result of cancellations.
The estimated SST, sea ice concentration, and sea ice thickness have been used as boundary
conditions in simulations of an AGCM with a horizontal grid size of 20 km performed by the Earth
Simulator. Although the method described in this work would have difficulty estimating values for thevery near future, when the phases of the interannual variation would be continuous with thepresent-day observation data, it is nevertheless one of the most objective methods available by whichto estimate sea surface conditions 10 to 100 years from now by using the MMEM results.

Supplementary Information
Monthly SST, sea ice concentration, and sea ice thickness, their changes averaged over the 25 years,
and monthly SSTmf_T and SSTobs_V, are shown in Supplemental Figs. S1–S16.

Acknowledgements
This work was supported by the "Projection of Change in Future Weather Extremes Using
Super-High-Resolution Atmospheric Models" project as a part of the KAKUSHIN Program of the
Ministry of Education, Culture, Sports, Science and Technology of Japan, and by the Global
Environment Research Fund (S-5-2) of the Ministry of the Environment of Japan.

References
Bourke, R.H. and R.P. Garrett, 1987: Sea ice thickness distribution in the Arctic Ocean. Cold Regions
Sci. and Tech., 13, 259-280.
Intergovernmental Panel on Climate Change, 2007: Climate change 2007: The Physical Science
Basis—Contribution of the Working Group I to the Fourth Assessment Report of the
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Intergovernmental Panel on Climate Change, Cambridge Univ. Press, Cambridge, U. K., 996pp.
Meehl, G., C. Covey, T. Delworth, M. Latif, B. McAvaney, J. Mitchell, R. Stouffer, and K. Taylor,2007: The WCRP CMIP3 multimodel dataset: A new era in climate change research. Bull. Am.
Meteorol. Soc., 88, 1383–1394.
Rayner, N. A., D. E. Parker, E. B. Horton, C. K. Folland, L. V. Alexander, D. P. Rowell, E. C. Kent, and
A. Kaplan, 2003: Global analyses of sea surface temperature, sea ice, and night marine airtemperature since the late nineteenth century. J.
doi:10.1029/2002JD002670.

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Geophys.

Res.,

108(D14), 4407,

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Fig. S1: Observational distributions of annual mean SSTs and monthly SSTs averaged from 1979 to
2003.
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Fig. S2: Estimated near-future distributions of annual mean SSTs and monthly SSTs, averaged from2015 to 2039.
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Fig. S3: Differences in the annual mean SSTs and monthly SSTs between the observation data
(1979–2003) and the estimated near-future values (2015–2039).
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Fig. S4: Estimated future distributions of annual mean SSTs and monthly SSTs averaged from 2075 to
2099.
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Fig. S5: Differences in the annual mean SSTs and monthly SSTs between the observation data
(1979–2003) and the estimated future values (2075–2099).
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Fig. S6: Linear trends in the multi-model ensemble mean SSTs during 2015 to 2039. Units are
K/decade.
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Fig. S7: Linear trends in the multi-model ensemble mean SSTs during 2075 to 2099. Units are
K/decade.
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Fig. S8: Standard deviations of the interannual variations in the observed SSTs after removing thelinear trend during 1979–2003.
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Fig. S9: Observational distributions of monthly sea ice concentrations averaged from 1979 to 2003.
The values in the figure denote the sea ice extent for f = 95%, 55%, and 15%.
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Fig. S10: Estimated near-future distributions of monthly sea ice concentrations averaged from 2015 to2039. The values in the figure denote the sea ice extent for f = 95%, 55%, and 15%.
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Fig. S11: Differences in monthly sea ice concentrations between the observation data (1979–2003) andthe estimated near-future values (2015–2039).
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Fig. S12: Estimated future distributions of monthly sea ice concentrations averaged from 2075 to 2099.
The values in the figure denote the sea ice extent for f = 95%, 55%, and 15%.
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Fig. S13: Differences in monthly sea ice concentrations between the observation data (1979–2003) andthe estimated future values (2075–2099).
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Fig. S14: Observational distributions of monthly sea ice thickness.

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Fig. S15: Estimated near-future (2015–2039) distributions of monthly sea ice thickness. The values ofĮ calculated by Eq. (10) are shown.
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Fig. S16: Estimated future (2075–2099) distributions of monthly sea ice thickness. The values of Į
calculated by Eq. (10) are shown.
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