四次元変分法データ同化手法を用いた
全球海洋環境の再現
増田周平, 淡路敏之, 杉浦望実, 石川洋一,五十嵐弘道,
日吉善久, 佐々木祐二, 土居知将
JAMSTEC
Kyoto University
はじめに
海洋環境再現実験
近年、海洋・気候学の分野でデータ同化手法を用いた海洋観測データと数値モデル計算結果の
統合が活発に研究されるようになってきた。その背景には定常観測の難しい海洋亜表層の気候
変動現象に対する重要性の認識や計算機科学の発達などがある。（独）海洋研究開発機構では
京都大学と共同して四次元変分法アジョイント手法を応用した海洋データ同化システムを構築し
、過去50年間にわたる海洋環境の再現を試みた。
気候変動メカニズムの解明
得られた海洋環境統合データセットを用いて気候変動現象、とくに季節―経年スケールの現象
に着目し、力学解析を行うことでそのメカニズムの解明を目指す。
最適観測システム構築への応用
データ同化システムを用いた応用研究として海洋環境再現のためにどの海域を重点的に観測
すれば効率が良いかを示唆する観測システム研究を行った。主に赤道太平洋域に焦点を当て、
気候変動イベントに対する感度の高い海域を同定し、そこでの観測のインパクトを調べる。
Data Synthesis Efforts in Oceanography
Data Assimilaion
An optimal synthesis of observational data and model results.
Observations
Merit
Truth（real ocean）
Demerit Spatially and temporally sporadic
Numerical model
Equal quality in 4-d continuum
sometimes
Unrealistic; Model bias,
parameterization
Data assimilation can provide analysis fields in superb quality through
4-dimensional dynamical interpolation of in-situ observations.
World’s Ocean Data Synthesis efforts (CLIVAR/GSOP)
z-Level Model
No Model
NCEP
ERA40
OPA/NEMO
HOPE
Relax.
Relax.
EN3
.25ox.25o
Bias
corr.
E-P.
DePreSys
ECMWF
INGV
Mercator
MOM
POP
CORE
URDG
QSCAT
GPCP
SODA
Relax.
GFDL
Relax.
K-7
GECCO
4D-Var
3D-Var/OI
1ox1o
2ox2o
GODAS
MIT
DATA
4D-VAR approach
 A 4-dimensional variational (4D-VAR) adjoint data
assimilation system can provide a dynamically selfconsistent dataset.
 The obtained products are applicable to dynamical
analysis, adjoint sensitivity experiment, Observation
System Experiment, ecosystem modeling, forecast
study.
 High computational cost is required .
Adjoint sensitivity analysis by using a
4D-VAR ocean DA system
Heat flux
Wind stress
surface
ΔT＝Tmodel － Tobs
An adjoint sensitivity analysis moves the
ocean representation backward in time!
The adjoint sensitivity analysis gives the temporal rate of change of a
physical variable in a fixed time and space when model variables (e.g.,
water temperature, salinity, velocity, or surface air-sea fluxes) are
arbitrarily changed in the 4-dimensional continuum of one temporal
and three spatial coordinates. This is equivalent to specifying the
“sensitivity” of a variable to small perturbations in the parameters
governing the oceanic state.
Search of best time trajectory
 4D-VAR data assimilation approach seeks for optimized 4-dimensional
model states by minimizing a cost function (differences between observed
and model analysis fields).
 In that process, Forward & Backward model are executed iteratively within
assimilation window.
 Assimilation window should be well chosen taking the “memory” of
oceanic phenomena of interest into consideration.
In general, the longer the memory of the phenomenon is, the longer the
assimilation window must be.
forward
backward
Obs.
Obs.
First guess
field
Best time trajectory
Obs.
Assimilation
window
K7 Ocean Data Assimilation System
“Bottom-water warming”
Blue Earth (2004)
MIRAI RV participate in WOCE revisit
in the subarctic North Pacific in 1999
RecentThis
highbottom-water
quality observational
conducted
warmingsurveys
ranges in
oC in the
duringmagnitude
the WOCEfrom
and 0.003
the WOCE
revisit
have revealed
to 0.01
the sobering
thatover
the deepest
waters
of the major
Pacificfact
Ocean
the period
1985-1999.
oceans have warmed significantly during recent decades
Fukasawa et al. (2004), Kawano et al. （2006)
Such temporal changes are important to understand the variability of abyssal
circulation which have implications for large-scale thermohaline transport and
thus for the global 3-dimensional heat budget that is presently of vital concern.
System
OGCM：
GFDL MOM3, quasi-global 75oS-80oN
horizontal res：1ox1o, vertical res:45 levels
Spinup：
1. 3000-year with a climatological forcing (accelerated
method)
2. 120-year as climatological seasonal march.
3. 10-year with interannual forcings from NCEP/DOE.
Use of optimal parameters：
Green’s function method is applied to some physical
parameters (Toyoda et al.,20XX).
Data sysnthesis：
method： strong constrain 4D-VAR adjoint.
adjoint coding: by TAMC with some modifications.
assimilation window： 50 years (1957-2006)
control variables： initial conditions, 10-daily surface
fluxes
first guess：results from Spinup 3
assimilated elements：OISST,T,S （Ensembles ver.3 + Mirai
RV independent dataset ）,AVISO SSH anomaly.
Our efforts to reproduce
“bottom-water warming” in reanalysis dataset
(legacy of 4th研究開発促進アウォード)
Green’s function：
Optimization of physical parameters
Modeling:
1. Short-wave radiation scheme is modified
(collaboration with Ocean Circulation Team)
2. BBL scheme, GM scheme
3. Anomalous mending for polar region dynamics,
Bland-new QCed Data：
Download
EN3_v2a_NoCWT_WijffelsTable1XBTCorr
with independent RV MIRAI data
Deep ocean data synthesis：
State-of-the-art adjoint coding.
Low resolution compiling for deep ocean
obseravations.
Assimilation with long-term window
Control of model trend (collaboration with Univs.).
推定するパラメータ
 Tsujino and Suginohara (2000)は全球で水平一様な鉛直拡散係数の鉛直プロファイ
ルを経験的に推定した。
 Hasumi and Suginohara (1999)は地形性内部波による混合に注目し、海底地形の粗
度によるパラメタリゼーションを行った。
 Gargett (1986)は成層状態に依存したパラメタリゼーションを行い(κ~N-α)、OGCM
でも使用されている(Cummins et al., 1990)。
 3つの視点の異なる鉛直拡散パラメタリゼーションの線形結合を考え、観測デー
タをもとに客観的に結合係数を決定する。
 Gargett (1986)の拡散については、 KGGT=10-3N-1 (in cgs)とし、大西洋の恒久躍層に
対する議論(e.g., Marzeion et al., 2007)から2000m以深で有効とした。
 更に、鉛直拡散に寄与する二重拡散 (Schmitt, 1988; Marmorino and Caldwell,
1976)、等密度面・層厚拡散(Redi, 1982; Gent and McWilliams, 1990)のパラメタリ
ゼーション、海底境界層とモデル最深層との拡散係数も推定に加えた。
 これらチューニングパラメータ群の初期推定値は
η0=(fTJN,fGGT,fHSM,HHSM,fsf,fdc,Aisp,Athk,KBBL)
=(1/3,1/3,1/3, 700, 1, 1,103,103,2*10-4)
実験
 コントロールラン(CTL)として、静止状態から月平均気候値フォーシングを与えて、
加速法(Bryan, 1969)を用いて4000年積分後、加速しないで320年積分した。
（4000m以深平均の水温トレンドは最後の100年で0.0002℃。）
 320年の（加速なし）部分を9つのパラメータそれぞれについての擾乱実験を行い、
以下のグリーン関数法(Menemenlis et al., 2005)により、最適なパラメータ群ηを推
定した。
 線形を仮定（
）すると、
コスト関数：
を最小にするインクリメントは
である。
 ここで、xは状態ベクトル（最後の20年の年平均気候値）、yは観測値である。また、
R、Bはそれぞれ観測値、制御変数に対する誤差共分散行列（対角）で、R-1の成分
（観測の重み）は各モデルグリッドにおける、（グリッドの占める体積）/（観測
値の分散）から決定した。
 観測値は、既存の水温・塩分データ(EN3 by Met Office)に、海洋地球観測船みらい
によるCTD/XCTDデータを加えて作成した。このとき、南シナ海・スル海、日本海、
メキシコ湾はコストが集中するが、今回のパラメータ調整では修正しきれないモデ
ルバイアスがあるとして観測から除いた。
 得られた最適値は以下（コスト関数は約5%減）
η=(fTJN, fGGT, fHSM, HHSM, fsf, fdc, Aisp,
Athk,
KBBL)
TJN
GGT
HSM
TJN
GG
T
HS
M
AD
J
ADJ
CTL
Distributions of VDC at 2000m-depth
Mean profile of vertical diffusive
coefficient.
KADJ=0.43KTJN+0.08KGGT+0.72KHSM+…
Water temperature at 4000-5500m-depth
ADJ(Green’s functions)
WOA
（left）Tsujino
（mid）Gargett
（right）Hasumi
(Toyoda et al.
‘09JOS annual mtg.)
Observation
℃
Improved Ocean State Estimate
Cost function

J  x  x0  B x  x0   H x   y
T
1
1
 R H x   y 
* T
1
*
   x  x0  B21  x  x0 ,
T
*
here, y : observations (inc. model bias), x : controlvariable,
H : observation m atrix,
R : observation error (inc. representativenesserror).
Assimilated elements: Temperature, Salinity (ENSEBLES v.3+JAMSTEC observations),
SST (reconstructed Reynolds+OISST ver.2),
SSH anomaly data (AVISO).
First guess is generated from
momentum, net heat, shortwave, latent heat flux of NCEP/DOE .
Optimal Synthesis (dynamical interporation)
by 4D-VAR adjoint method
SST
Subsurface T (←Argo)
1991
SSHa
2006
Time change of the each component of the
cost function, i.e. the difference between
simulation and observation. Reduction by
iteration processes means progress in
synthesis.
Estimated net heat flux (a control variable)
NCEP2
Assim.
J-OFURO
NCEP atmospheric
reanalysis
Comparing

RE50
Reanarysis 50yr
with other products
Our results provides a consistent view
Estimated wind stress field (a control variable)
Stress
Jan
Curl
Jan
Stress
Jul
Curl
Jul
Our reanalysis data x ERA40
Climate indices during 1957-2006
Nino3 SST
DMI
ITF mass transport
(8-14Sv)
ACC mass transport
(130-140Sv)
*
*
* *
Atlantic MOC
(14-20Sv)
*Bryden et al. (2005)
Our result provides realistic time series of
important climate indices.
Temporal change of global heat content
• Comparison with observed heat
content trends.
Comparison of year to
year changes in heat
content from 1960
implies => Our trend
would be robust
Validation for un-easily-observable variables
Comparing with TOGA-TAO ADCP
Also, obtained 4-D velocity field is by and
large consistent with independent
observations by TAO array.
Atlantic 48N
Equatorial Pacific
CLIVAR/GSOP
Intercomparison:
Heat Transport Anomaly (PW)
Atlantic 25N
Indian Ocean 10S
Heat Transport Correlation (5 ys low pass)
Global
ECMWF GECCO INGV SODA GODAS K7
Advantage of our dataset
Number of obs. for subsurface salinity
Salinity variances
0-100m
100-400m
400-700m
700-2000m
2000m-
[ --] 1957-1966
[ ] 1967-1976
[ ] 1977-1986
[ ] 1987-1996
[ ] 1997-2006
The observation number of salinity had been
small before ARGO era (～‘00). As a result, the
interannual variance of an OI dataset is relatively
small for these periods. 4D-VAR dataset can
resolve this issue thanks to both numerical
model & adjoint method.
[blue] an OI dataset
[yellow] a model free run
[red] our 4D-VAR reanalysis
interannual variance (psu2)
Toyoda et al. (GSOP’08)
海洋環境再現データセット
作成した統合データのT,Sから見積もったsteric heightの経年変化。
Bottom water warming in our reanalysis field
Observed heat content
Estimation form 50yr DA exp.
 Bottom water warming is of particular interest as it can be closely related to
changes in the global thermohaline circulation and the warming trend of the
global ocean (e.g., Fukasawa et al., 2004).
 Water temperature difference between WOCE/WOCE-revisit periods at
4000-5500m-depth is O(0.001-0.003K).
 Bottom water warming seems to be successfully reproduced in our reanalysis
field.
Dynamical Analysis for Climate Change
Reanalysis data allow us to diagnose the real ocean
統合データセットを利用した海洋貯熱
量変動に関する研究（左）、水塊の経
年変動研究（下）。
NPZDモデル概念図
Kouketsu et al. (2010)
Toyoda et al. (2010)
Reanalysis data allow us to reveal the physical mechanism of
climate changes.
±8.6
±8.6
±14.8
(Masuda et al. 2008)
Adjoint Sensitivity Analysis
How about the Physical Mechanism?
?
The physical mechanisms governing
bottom-water warming are poorly
understood since in-situ observations
are spatially and temporally sporadic.
The changes in heat storage between
WOCE-WOCE revisit imply northward
running of the warming signal, but…
Difference of the heat storage between
WOCE-WOCE revisit observational periods.
Our aim is to identify the possible causal dynamics, timescales
and pathways involved in the observed bottom-water warming.
Adjoint sensitivity analysis by using a
4D-VAR ocean DA system
forcing
surface
ΔT(Bottom-water warming)
An adjoint sensitivity analysis moves the
ocean representation backward in time!
The adjoint sensitivity analysis gives the temporal rate of change of a
physical variable in a fixed time and space when model variables (e.g.,
water temperature, salinity, velocity, or surface air-sea fluxes) are
arbitrarily changed in the 4-dimensional continuum of one temporal
and three spatial coordinates. This is equivalent to specifying the
“sensitivity” of a variable to small perturbations in the parameters
governing the oceanic state.
感度解析
ある時刻t0・地点x0での熱量Qを変えるのに何が効いたのかという問題に対して、時刻
t(<t0)に固定して考えると、時刻tからt0までの海面フラックスFと時刻tでの場Xとが候補
になる。アジョイント方程式を解くことで各時間ステップｔにおけるこれらのアジョイント変
数(adF, adX=感度)を得る。それぞれの変化量に感度（＝アジョイント変数）をかけて足し
合わせたものが、熱量の変化量dQになる。
dQ = sum (dQ/dF_i) dF_i + sum (dQ/dX_i) dX_i = sum adF_i dF_i + sum adX_i dX_i
*単位の例
種: dQ [cal]
温度の場合、 adX_i [cal /K]=[cm3 s] , dX_i [K]
熱フラックスの場合、 adF_i [cal /(cal/cm2/s)], dF_i [cal/cm2/s]
感度計算によって、adX、adFが求められる。
時刻t場所xに温度1K（or フラックス1cal/cm2/s）与えたら、それが時刻t0におけるターゲッ
トのdQのうち何calになるかを定量的に評価できる。
Sugiura (2009)
Results of adjoint sensitivity analysis for a positive
temperature anomaly in the abyssal North Pacific
---A contour surface shows bottom-water warming rate
when a constant change in water temperature is given---
After 0-year
Results of adjoint sensitivity analysis for a positive
temperature anomaly in the abyssal North Pacific
---A contour surface shows bottom-water warming rate
when a constant change in water temperature is given---
After 5-year
Results of adjoint sensitivity analysis for a positive
temperature anomaly in the abyssal North Pacific
---A contour surface shows bottom-water warming rate
when a constant change in water temperature is given---
After 15-year
Results of adjoint sensitivity analysis for a positive
temperature anomaly in the abyssal North Pacific
---A contour surface shows bottom-water warming rate
when a constant change in water temperature is given---
After 25-year
Results of adjoint sensitivity analysis for a positive
temperature anomaly in the abyssal North Pacific
---A contour surface shows bottom-water warming rate
when a constant change in water temperature is given---
After 35-year
Results of adjoint sensitivity analysis for a positive
temperature anomaly in the abyssal North Pacific
---A contour surface shows bottom-water warming rate
when a constant change in water temperature is given---
After 45-year
Results of adjoint sensitivity analysis for a positive
temperature anomaly in the abyssal North Pacific
---Shade shows bottom-water warming rate when a
constant change in water temperature is given---
Tasman Sea
170oE cross-section
160oE cross-section
After 48-year
Results of adjoint sensitivity analysis for a positive
temperature anomaly in the abyssal North Pacific
---Contour shows bottom-water warming rate
when a constant change in surface heat flux is given---
Source region: Antarctic Sea off Adelie Coast
Time scale: 40 year
in contrast to the previous estimation of O(multi-centennium)!!
After 45-year
Possible mechanism for bottom water warming
Masuda et al. (2010)
WOCE
WOCE_rev
10
8.03
9.1
5
9.03
2.18
0.86
0.63
0.64
0.92
0
-5
底層水温上昇
-4.99
-4.28
-10 時間変化 水平移流 鉛直移流 水平拡散 鉛直拡散
（含む地熱効果）
Our scenario should be tested by direct observations…
Also, using 4D-VAR data synthesis, sustainable observations is
needed to better representation for a global ocean. Argo, revisit
cruise is really enhancing the quality of reanalysis products.
Atlantic Ocean
Africa
South America
Indian Ocean
Antarctica
Pacific Ocean
Australia
S04 line
P14S line
WOCE sections
Toward an Optimal Ocean Observing System
観測システム研究
アジョイント感度解析を用いたNINO3
亜表層水温の変動要因の分布（adT）。
0-month
-2-mont
0-month
四次元変分法データ同化システムを利
用しアジョイント感度解析を行うことで
ENSOに関する水温変動をひきおこす
水温変化の時間スケール、空間分布を
同定した。
-4-mont
３：観測システム研究
アジョイント感度解析から得られた結果を元に、
観測システムシミュレーション（同化）実験をお
こなった。
西部熱帯太平洋の観測網を変化させる(0100m0-200m）ことで、東部海域におけ
る水温構造の再現性に差が生じることを
確認した。
Adjoint source region
Summary
4D-VAR data assimilation method is applied to deep ocean
reanalysis experiment to obtain a dynamically-self consistent
ocean state estimation from surface to bottom (1967-2006).
The reanalysis dataset is capable of representation of the recent
climate change also in the abyssal ocean.
An adjoint sensitivity analysis implies that an increase in the
heat input into the Southern Ocean off the Adélie Coast of
Antarctica leads to bottom water warming in the North Pacific on
a relatively short time scale (within four decades).
An adjoint sensitivity analysis was applied to detect an optimal
ocean observation system in the equatorial Pacific. Tentative
results show further applications in line with this study are
promising.
Future Work
Down-scaling attempt with MOM4
 We are trying to implement a 1/16 x 1/16 x 45level regional
model with CDA products as boundary conditions (<=
Tropical Climate Variability Research Program).
 Polar region model is also starting; tri-porlar, ice model,…
(<= Northern Hemisphere Cryosphere Program)
 High-resolution data assimilation is now under
considerations.
Application to Ecosystem model
 NEMURO is incorporated in our system; collaboration
with Environmental Biogeochemical Cycle Research
Program
END