Ocean Dynamics (2012) 62:645–659
DOI 10.1007/s10236-011-0516-2

Open and coastal seas interactions south of Japan
represented by an ensemble Kalman filter
Yasumasa Miyazawa & Toru Miyama &Sergey M. Varlamov & Xinyu Guo & Takuji Waseda

Received: 4 August 2011 / Accepted: 21 December 2011 / Published online: 2 February 2012
# Springer-Verlag 2012

Abstract We investigated the feasibility of the ensemble
Kalman filter (EnKF) to reproduce oceanic conditions southof Japan. We have adopted the local ensemble transformation Kalman filter algorithm based on 20 members’ ensemble simulations of the parallelized Princeton Ocean Model(the Stony Brook Parallel Ocean Model) with horizontal
resolution of 1/36°. By assimilating satellite sea surface
height anomaly, satellite sea surface temperature, and in situ
temperature and salinity profiles, we reproduced the Kuroshio variation south of Japan for the period from 8 to 28
February 2010. EnKF successfully reproduced the Kuroshio
path positions and the water mass property of the Kuroshio
waters as observed. It also detected the variation of the steep
thermohaline front in the Kii Channel due to the intrusion of
the Kuroshio water based on the observation, suggesting
efficiency of EnKF for detection of open and coastal
seas interactions with highly complicated spatiotemporalvariability.
Responsible Editor: Leo Oey
This article is part of the Topical Collection on the 3rd International
Workshop on Modelling the Ocean 2011
Y. Miyazawa (*) : T. Miyama : S. M. Varlamov : X. Guo :T. Waseda
Research Institute for Global Change, Japan Agency for MarineEarth Science and Technology, Yokohama,
3173-25 Showamachi, Kanazawa-ku,
Yokohama, Kanagawa 236-0001, Japane-mail: miyazawa@jamstec.go.jp
X. GuoCenter for Marine Environmental Studies, Ehime University,
Matsuyama, Ehime 790-8577, JapanT. Waseda
Graduate School of Frontier Science, The University of Tokyo,
Kashiwa, Chiba 277-8563, Japan

Keywords Ensemble Kalman filter . Kuroshio . Kii channel
front . OGCM

1 Introduction
Variability of geophysical systems is highly chaotic (Lorenz
1963). An ultimate goal of geophysical predictability studies
is to exactly evaluate probability distributions associatedwith target phenomena. The ensemble Kalman filter (EnKF;
Evensen 1994) is based on the Monte Carlo method using
ensemble model simulations. It allows dynamical update of
two important moments of the probability distribution:mean and error covariance. Applications of EnKF havecovered a wide range of research fields because of its simple
implementation and effectiveness (Evensen 2003).
So far, there have been no studies on EnKF for the
analysis of the Kuroshio variations south of Japan. Other
types of data assimilation methods frequently used for operational applications to the Kuroshio variations: optimum
interpolation (Miyazawa et al. 2005; 2008) and threedimensional variational method (Miyazawa et al. 2009)
assumed temporally constant and spatially isotropic error
covariance. Main target phenomena of the previous studies
were the typical mesoscale phenomena such as the Kuroshio
path variation and mesoscale eddies with O (10 days) and O(100 km) scales. Recent development of downscaled models
allows simulating smaller scales phenomena associated with
the Kuroshio and coastal topography interactions (Miyama
and Miyazawa 2010). The open and coastal seas interactions
involve significant variations of temporal and spatial scalesof the relevant phenomena (e.g., Isobe et al. 2010), and theassociated error covariance is also highly variable. Dynamic
representation of error covariance by EnKF is hence required to effectively reproduce the open and coastal seas

646interactions. This study aimed to elucidate the feasibility of
EnKF for the analysis of the Kuroshio variations south ofJapan, especially focusing on roles of error covariance information in representation of the Kuroshio and coastal sea
interactions.
The temporal and spatial sampling intervals of the remotesensing observations are approximately regular, and theirsampling coverage is mainly limited in open oceans. Thisis one of main reasons that the operational ocean forecastingfor open oceans has been established over the past decade(Miyazawa et al. 2009). Full utilization of the in situ temperature and salinity data locally and irregularly samplednear the coast is crucial for establishing the ocean forecast of
the open and coastal seas interactions. Our research interests
include roles of the dynamic representation of the forecast
error covariance in assimilating the localized in situ observation data.
The Kii Channel between the Shikoku Island and Kii
Peninsula (Fig. 1) has approximately 50 m bottom depth.
In winter, very steep oceanic front, ‘Kii Channel Front’, isformed due to convergence of warm-salty water from open
ocean and cold-fresh water from coastal regions (Yosioka1983). The S-shape front is frequently generated due to the
Coriolis effect (Harashima and Oonishi 1981). The existence of these fronts is recognized in many areas of thewestern North Pacific including Tokyo Bay (Yanagi andSanuki 1991), Ise Bay (Yanagi et al. 1997), and the South
China Sea coasts (Wang et al. 2001). In the Kii Channel, theKuroshio water intrusions frequently affect the front

Fig. 1 Topography of the model domain. Thick (thin) contours denote
shorelines (iso-depth lines: 10, 20, 30, 40, 50, 100, 200, 500, 1,000,
2,000, 3,000, 4,000, and 5,000 m). The abbreviations represents locations (S Shikoku Island, K Kii Peninsula, and IOR Izu-Ogasawara
Ridge). The Kii Channel is between the Shikoku Island and Kii
Peninsula

Ocean Dynamics (2012) 62:645–659

variations and sometimes disturb the stable condition of
the S-shape front (Toda 1992). This study examined the
reproducibility by EnKF of the Kuroshio and its related
Kii Channel Front variations in February 2010.
This paper is organized as follows. Section 2 provides
brief descriptions of an ocean model and an implementationof EnKF in the present study. Section 3 discusses the reproducibility of the Kuroshio south of Japan and Kii Channel
Front in February 2010. Impact of localized in situ data
assimilation and predictability of the front variations are
discussed in Sections 4 and 5 in terms of time-dependent
anisotropic error covariance represented by EnKF. Section 6
is devoted to summary and discussion.

2 Ensemble Kalman filter system
We have developed an ocean model for south of Japan basedon a parallelized version of the Princeton Ocean Model(Stony Brook Parallel Ocean Model, sbPOM; available fromhttp://www.imedea.uib-csic.es/users/toni/sbpom/). The
model covers a square region of 31°–35° N and 133°–140° E (Fig. 1) with a horizontal resolution of 1/36° and31 sigma levels in vertical. The bottom topography of themodel was created from the 1/120° grid data provided by
Japan Hydrographic Association, ‘JTOPO30’. The model
was driven by wind and heat fluxes calculated using thebulk formulae (Kagimoto et al. 2008) with 6-houly atmospheric variables provided from the National Centers forEnvironmental Prediction Global Forecast System (NCEP
GFS). The surface salt flux was relaxed to surface salinity ofthe monthly mean climatology, World Ocean Atlas 2001
(Conkright et al. 2002) with a restoring rate of 10 m/30 days.
The lateral boundary condition was specified from the JAMSTEC operational ocean model product with the same horizontal resolution of 1/36°(Miyama and Miyazawa 2010),
which assimilated satellite sea surface height anomaly datausing a three-dimensional variational method (Miyazawa et
al. 2009). Tide forcing was not included in the model. Notethat not only the data assimilation module but also theforcings and/or numerical schemes are effective to improve
the representation skill for the open and coastal seas interactions. But our focus in the present study is to investigate
the roles of the data assimilation in the skill improvements.
The model was spun up for the period from November 2008
to March 2010 starting from temperature and salinity data of
the JAMSTEC operational model on 1 November 2008 withno motion.
We have implemented the Local Ensemble Transformation Kalman Filter (LETKF; Hunt et al. 2007; Miyoshi et al.
2010) algorithm on the JAMSTEC scalar parallel processors
system on the basis of SGI Altix 4700. Twenty numbersof ensemble runs were produced using different initialOcean Dynamics (2012) 62:645–659

647

conditions sampled from the background simulation datawith time interval of 3 days during the simulation period
from 13 January to 11 March 2010.
Here we briefly describe the formulation of LETKF(Hunt et al. 2007). The ensemble mean of the analyses isobtained by the following equation,xa ¼ x f þ X f wa ;where x ¼

ð1Þ

K
P
xi
i¼1

f a
K , size of the ensemble is K, x (x ) is am-dimensional vector representing each member of ensemble forecasts (analyses), X f is a m×K matrix that is composed of K-number columns of deviations of the forecasts
from the ensemble mean of the forecasts, and wa is a Kdimensional vector calculated from the observation data andensemble forecasts. Update of each analysis member isrepresented as follows,xaðiÞ ¼ xa þ X f W aðiÞ ;ð2Þ

where W a(i) is a K-dimensional vector corresponding to ith
column of a K×K matrix W a, calculated from the ensemble
forecasts. Not only the ensemble mean but also the ensemble spread,vﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
u K
uX ð x i  x Þ 2;
Sprd ¼ t
K
i¼1

ð3Þ

provides the useful information for the predictability
analysis.
Localized use of observation data is one of key methodologies of LETKF (Hunt et al. 2007). We defined two
localization scales (Miyoshi et al. 2010):
distzero ¼ σobs pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
10=3  2;

distzerov ¼ σobsv pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
10=3  2 ;same days after were used for one time filter analysis (seventh and eighth rows of Table 1). Figure 2 plots the observation data points used in the LETKF analyses on 14(Fig. 2a), 20 (Fig. 2b), and 26 (Fig. 2c) February 2010. Data
points of the remote sensing observations (sea surface heightanomaly and sea surface temperature) were regularly distributed in open ocean. Numbers of in situ observation data
were generally few but sometimes the data points werelocally and densely distributed around the Kii Channel(see Fig. 8). Mean sea surface height for evaluation of model
sea surface height anomaly, which is an important parameterof the satellite altimetry data assimilation (Miyazawa et al2009), was calculated from the hindcast data of the JAMSTEC operational model for the period from 1 August 2009
to 1 August 2010.
Parameters of LETKF (Miyoshi et al. 2010) were determined (Table 1) based on examination of their sensitivity
using ‘identical twin experiments’, in which pseudoobservation data were sampled from the background simulation data, and quantitative skill evaluation for eachparameter using known ‘true’ state was feasible. The observation errors shown in Table 1 are not simple measurement errors but include the representativeness errors
associated with unresolved smaller scales variability andmodel discretization (Cohn 1997). Since the LETKF analysis was conducted every 2 days, which was not so long atime to induce the typical bimodality of the Kuroshio pathvariations (Miyazawa et al. 2005), it was not necessary toconsider the possibility of non-Gaussian type probability
distributions that were not simply described by mean anderror covariance mainly targeted by the Kalman filter
analysis.
To examine the data assimilation effects of EnKF and its
implications on representation of open and coastal seasinteractions, we have conducted following experiments:(1) the basic case, ‘ENKF’, (2) the free running forecasts

ð4Þ
where σobs (grid number) and σobv (m) are horizontal
and vertical localization scales, respectively. Observation
data far from the target grid with horizontal distance(dist) larger than distobs or vertical distance (distv) larger
than distobsv were not used for the EnKF analysis there.
In addition, observation errors of the data far from thetarget grid were enhanced by multiplying a factor, expð0:5 ððdist=distobs Þ2 þ ðdistv=distobsv Þ2 ÞÞ.
LETKF assimilated satellite sea surface height anomaly(Jasons-1 and Jasons-2), satellite sea surface temperature(NOAA MCSST and AMSR-E), and in situ temperatureand salinity profiles (GTSPP) every 2 days during the target
period from 8 to 28 February 2010. All sea surface heightanomaly (temperature and salinity) data obtained during theperiod from 4 days (1 day) before the analysis time to theTable 1 LETKF parameters
Horizontal localization scale (σobs; number of grids)

12 (1/3 degree)

Vertical localization scale (σobv; m)
Covariance inflation parameter (%)
Observation error of sea surface height anomaly (m)Observation error of temperature (°C)
Observation error of salinity (psu)Time window of sea surface height anomaly (day)Time window of temperature and salinity (day)Time interval of LETKF (day)

2,000
21
0.2
1.0
0.1
±4
±1
2

Positive covariance inflation parameter means that the forecast ensemble spread is inflated by a factor slightly greater than unity (Miyoshi etal. 2010). Miyazawa et al.: Open and coastal seas interactions represented by EnKF

648

Ocean Dynamics (2012) 62:645–659

a

b

c

Fig. 2 Positions of the observation data assimilated on a 14 February
2010, b 20 February 2010, and c 26 February 2010. Closed circles
satellite sea surface height anomaly. Crosses satellite sea surface temperature. Closed triangles in situ temperature. Closed squares in situ
salinity. Thick contours in background denote iso-depth lines of 200,
500, 1,000, 2,000, 3,000, 4,000, 5,000, and 6,000 m

produced by running the ensemble runs without any data
assimilation, ‘FRF’, and (3) EnKF without in situ data
assimilation ‘NO IN SITU’.

3 Reproduced oceanic condition south of Japanin February 2010
In this section, we discuss the general skill of EnKF bycomparing the Kuroshio path variations and water mass
variability with their observations. Synthetic sea surface
temperature maps provided by Japanese local fishery agencies around the Kuroshio region (Xie et al. 2006) indicatethat the small Kuroshio meander around 33° N and 138° E
observed on 14 February 2010 (Fig. 3a) moved eastward toaround 140° E on 26 February (Fig. 3c). The Kii Channel
Front was formed between the colder and warmer waters innorthern and southern sides, respectively (Figs. 3a–c). The
warmer water in the southern side of the front intruded
northward into the channel on 14 and 26 February(Fig. 3a, c), but on 20 February, the warmer waters moved
southward out of the channel.
The ENKF analysis mean (see Eq. 1) reasonably reproduced these features as shown in Fig. 4. The small meanderof the Kuroshio moved eastward during the period, and thevariation of the Kii Channel Front was generally reproduced. ENKF basically represented the typical S-shape front
characterized by the colder (warmer) temperature in western(eastern) side of the channel throughout the target period.
However, the observation maps indicate that the opposite
shape of the front with the colder (warmer) temperature ineastern (western) side of the channel occurred for the periods from 8 to 10 (not shown) and from 20 to 23 February(e.g., see Fig. 3b). We note that the synthetic observation
maps (Fig. 3) were not completely independent from ENKF,
because they included the remote sensing sea surface temperature data as same as those used for the EnKF analysis.
But production of them involved many other data including
in situ observations and manual modifications based on
empirical knowledge about oceanic conditions south ofJapan (Xie et al. 2006).
We compared the reproduced Kuroshio path potions of
ENKF with the positions evaluated by the Japan Coast
Guard (JCG Kuroshio axis positions) defined as the strongest flow positions in the Kuroshio flow band. The modeled
path positions denoted by the thick lines shown in Fig. 5
were defined as the grid positions of strongest kinetic energy
at 50 m depth. Root mean square deviation (RMSD) between ENKF and JCG Kuroshio axis positions was 0.27° forthe target period. The JCG Kuroshio path positions also
show the propagation of the small meander depicted in boththe ENKF analyses and synthetic maps (Fig. 3). ENKF
reproduced the smaller amplitude of the meander as compared to that indicated by the JCG Kuroshio path positions.
To confirm fitting to the in situ data of the assimilation
products, we plotted in upper (lower) panels of Fig. 6 the insitu observation points with colors indicating RMSD between the reproduced and observed vertical temperatureOcean Dynamics (2012) 62:645–659

a

b

649

a

b

c
c

Fig. 4 Ensemble mean sea surface temperature (shade and contours)
and flows (vectors) of the ENKF analyses on a 14 February 2010, b 20
February 2010, and c 26 February 2010
Fig. 3 Synthetic maps of sea surface temperature observations (Xie et al.
2006) on a 14 February 2010, b 20 February 2010, and c 26 February 2010,provided by local fishery research agencies around the mapping area. Thickdashed lines denote northern and southern edges of the Kuroshio(salinity) profiles. ENKF (Fig. 6a) well reproduced theobserved water mass in open ocean with RMSD smaller
than 1°C and 0.1 psu, which are the prescribed observation

650

Ocean Dynamics (2012) 62:645–659

a

b

c

error values (Table 1). Comparatively large RMSD values
indicated by red color contours are shown near the coast,
especially inside of the Kii Channel. Ensemble spread (3) ofmaximum temperature in the vertical column plotted in background of upper panels of Fig. 6a exhibits that large magnitude of the spread is distributed along the Kuroshio path andcoastal seas including the Kii Channel. Large values of salinity spread (lower panels of Fig. 6a) are shown in the coastal
seas. Comparatively large values of RMSD and bias are foundaround the Kii Channel, and the magnitude of the spread there
is also large. This kind of errors is possible because the real
horizontal gradient of the Kii Channel Front is very steep,
usually exceeding 5°C/km (Yosioka 1983), and it is difficult toexactly represent it by hydrostatic dynamics of the present
model framework with the horizontal resolution of 1/36°,
approximately 3 km (Akitomo et al. 1990).
Comparison between the skills of ENKF (Fig. 6a) andFRF (Fig. 6b) indicates that the data assimilation effectively
reduced RMSD and the magnitude of ensemble spreads,suggesting some relations between skills and ensemble
spreads. In particular, the data assimilation corrected warm
bias near the coast (Fig. 7) by suppressing the tendency of
the Kuroshio water intrusion toward the coast represented in
FRF. Note that RMSD between the Kuroshio path positionsof the ensemble mean of FRF and JCG was 0.39°, larger
than RMSD (0.27°) between EnKF and JCG. The mean
Kuroshio path of FRF during the target period showed
unrealistic troughs and ridges south of Japan (Fig. 7).
The case without in situ data assimilation (NO IN SITU;
Fig. 6c) exhibits improvements of water mass property andreduction of the ensemble spread as compared to FRF(Fig. 6b). Figure 6c demonstrates the skill improvement bycomparing the results with the ‘independent’ data because
the in situ data was not assimilated into the NO IN SITU
case. Inside of the Kii Channel, the water mass property was
not improved and magnitude of the spread was unchanged
due to low density of the remote sensing data there (Fig. 2).
RMSD between the Kuroshio path positions of the ensemble
mean of NO IN SITU and JCG was 0.28°, slightly larger
than that of ENKF (0.27°).

4 Assimilation of the in situ observation data by EnKF

Fig. 5 Same as Fig. 4 except for temperature at 50 m depth. Thick
contours denote the Kuroshio path positions evaluated from the ensemble mean flows at 50 m depth by tracking grids with the strongest
kinetic energy at each longitude. Open circles represent the weekly
mean observed path positions provided from the Japan Coast Guard.
The duration of the weekly mean period was daily updated and then all
position data including the target day in their weekly mean periods
were plottedTemporal frequency and spatial density of the in situ temperature and salinity observation were irregular as comparedto those of the remote sensing data (e.g., Fig. 2). Sometimes inFig. 6 Maximum analysis ensemble spread from surface to bottom b
averaged for the period from 8 to 28 February 2010. Left temperature,right salinity. Closed circles denote all positions of the in situ observations whose numbers were larger than 4 and their colors indicate root
mean square deviation between the reproduced and observed in situ
profiles. a ENKF, b NO IN SITU, c FRF

Ocean Dynamics (2012) 62:645–659

a

RMSD

EnKF

S

T

b

RMSD

651

FRF

T

S

c
RMSD

T

No

in-situS

652

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situ data were distributed locally and densely. Figure 8 showsthat the in situ temperature and salinity were observed densely
inside of the Kii Channel around 18 February 2010. In particular, since the altimetry data were basically unavailable in the
coastal regions due to their low quality (Vignudelli et al.
8
>
<x x
w
w=o
IS 
>
0
not
:

2000), the in situ data around the coastal regions were quite
important for the reproduction of the oceanic condition there.
Using information of the ensemble means, we can evaluate
impacts of the in situ data assimilation. Impact signal (IS) of
the assimilation is defined as qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃðSpreadw 2 þ Spreadw=o 2 Þ=ðK  1Þ > t95%
if xw  xw=owhere xw  xw=o is difference of ensemble mean variables
between with (w) and without (w/o) the assimilation of someobservation data, K is ensemble size (020), and t95% is a
T -BIAS

FRF;

critical t-distribution value of 95% significance with K−1
degree of freedom (Moteki et al. 2011). IS of sea surface
temperature and salinity between with (ENKF) and without(NO IN SITU) the assimilation of the in situ temperatureand salinity profiles on 18 February were plotted in
Figs. 9a and b, respectively. ISs of temperature and salinity were almost similar to each other. Positive (negative)
anomaly is found along the west coast of the Kii Peninsula (inside of the Kii Channel), indicating that the in situ
data assimilation enhanced the intensity of the Kii Channel Front. In particular, positive anomaly along the west
coast of the Kii Peninsula contributed to reproduce theanti-clockwise circulation of the Kuroshio water intrusion(Figs. 9c and d). Warm water patches corresponding to thewarm water intrusion was also identified in the synthetic
observation maps provided by Japanese local fisheryagencies for the period from 18 to 19 February 2010
(not shown). Positive IS of temperature and salinity
around 33.3° N, 135.4° E at the main axis of the Kuroshio
came from the upstream in situ observation of temperature
at 33° N, 135° E shown in Fig. 8. The temperatureobservation affected IS of salinity around there througha multivariate assimilation effect of EnKF, which allowed
evaluating a variable by the observations of different
kinds of variables.

EnKF

Fig. 7 Temperature at 50 m depth averaged for the period from 8 to 28
February 2011. Closed circles denote all positions of the in situ
observations whose numbers were larger than 4 and their colors indicate mean error (bias) between the reproduced and observed in situ
profiles. Upper FRF, lower ENKF

ð5ÞFig. 8 Same as Fig. 2 except for 18 February 2010

Ocean Dynamics (2012) 62:645–659

653

a

b

c

d

Fig. 9 a Impact signal (5) of ensemble mean of sea surface temperature analyses on 18 February 2010 with (ENKF) and without (NO IN
SITU) in situ temperature and salinity profiles. b Same as Fig. 9a

except for salinity. c Ensemble mean of sea surface temperature analyses in ENKF on 18 February 2010. d Same as Fig. 9c except forsalinity

To examine possible relations between the horizontal
distribution of IS and the forecast error covariance represented by EnKF, we plotted some components of forecast
error covariance in Fig. 10,that upper (lower) panel of Fig. 10 visualizes covariance
between an observation of surface temperature (salinity) at apoint (33.705° N, 135.162° E) indicated by a closed circle
and surface temperature (salinity) at grids that surround theobservation point. The horizontal covariance distributions oftemperature and salinity were almost similar to each other as
the comparison of IS (c.f. Figs. 9a, b). A positive region
shown in the warmer (offshore) side of the Kii Channel
Front was associated with the Kuroshio water intrusion
along the west coast of the Kii Peninsula (Figs. 9c, d).

P f ðV1 ðx0 Þ; V2 ðxÞÞ  ðK  1Þ1KX

ðV1 ðx0 ÞðiÞ  V1 ðx0 ÞÞðV2 ðxÞðiÞ  V2 ðxÞÞ;

i¼1

ð6Þ
where V1(x0) (V2(x)) is a value of variable V1(V2) at a gridx0 (x), and overbar denotes ensemble mean. We can consider

654

Ocean Dynamics (2012) 62:645–659

tt

spatial localization scales (4). The distribution of the covariance between temperature (salinity) at the target point andsalinity (temperature) at the surrounding grids (not shown)was similar to that of the salinity (temperature) covarianceshown in upper (lower) panel, suggesting the effectiveness ofthe multivariate assimilation effect of EnKF.
Figure 10 indicates that the horizontal distributions of thecovariance were strongly related to the basic structures ofthe oceanic conditions (Figs. 9c, d). In particular, the positive region around the target point was associated with the
Kuroshio water intrusion along the west coast of the Kii
Peninsula. The positive region almost disappeared on theother analysis days after and before 18 February since theKuroshio water intrusion did not occur at those times (notshown).
To examine comprehensive impacts of the in situ data
assimilation during the whole period, we evaluated reduction rate of the analysis ensemble spread (Moteki et al.
2011) defined as

ss

100 

Sprdw=o 2  Sprdw 2
Sprdw=o

2



Ns
N

½% ;

ð7Þ

where Sprdw(w/o) denotes the analysis ensemble spread with
(without) the in situ data assimilation. N is number of all grids,
and Ns is number of grids where the reduction of spread isdiagnosed to be significant at 95% level of confidence by F
test. The reduction of ensemble spread could be a qualitative
indication of actual error reduction. The reduction rates oftemperature averaged for the target period shown in Fig. 11
indicate the reduction of the spread over the whole model
region. The reduction was clearly found inside of the Kii
Channel. Patterns of the reduction of temperature (Fig. 11)
and salinity (not shown) spreads were almost similar to eachother but the magnitude of salinity spread reduction was
generally larger than that of temperature.
Fig. 10 Upper the forecast error covariance of ENKF between sea
surface temperature at a target point (33.705° N, 135.162° E) and sea
surface temperature at surrounding grids on 18 February 2010. Lower
same as upper left panel except for sea surface salinity. Values on thegrids with distance from the target point larger than distzero (4) are not
shown

Positive covariance region appeared in only the warmer sideof the front, suggesting that the observation at the point
hardly affected the oceanic state in the colder side of thefront. The salinity covariance showed a slightly different
feature around 33.3° N, 134.8° E (lower panel of Fig. 10) as
compared to the temperature covariance (upper panel ofFig. 10), which was related with a small scale front variationof salinity around there. Negative covariance around 33.2° N,
134.5° E did not affect IS there, suggesting that the impacts
from the in situ observations at the other places and/or the

5 Ensemble forecasts of the Kii channel front variation
We further investigated impacts of the in situ observation on
detecting the Kii Channel Front variation by analyzing theensemble forecasts around the Kii Chanel front region.
Figure 12 compares snapshots on 20 February 2010 of acomposite map of satellite sea surface temperature provided
by the fishery research institute of Tokushima Prefecture(Fig. 12a), an ensemble mean of sea surface temperatureand flows of forecasts after 2 days starting from the ENKF
analyses at 0:00, 18 February 2010 (Fig. 12b), and that of
FRF (Fig. 12c). The ensemble mean forecast of ENKF
(Fig. 12b) reproduced the anti-cyclonic circulation due tothe Kuroshio water intrusion along the west and east coastsof the Kii Peninsula and Shikoku Island, respectively, asOcean Dynamics (2012) 62:645–659

655

a

b

Fig. 11 Reduction rate (7) of the analysis ensemble spread for sea
surface temperature averaged for the period from 8 to 28 February 2010

shown in the observation (Fig. 12a). Comparison between
the ENKF (Fig. 12b) and FRF (Fig. 12c) forecasts indicatesthat EnKF modified the Kuroshio path and removed warm
bias inside of the Kii Channel. The assimilation of theobservation data around the Kii Channel Front (Fig. 8)
effectively reproduced the steep front structure. However,
ENKF (Fig. 12b) seemed to fail the temperature gradientalong the west coast of the Kii Peninsula and have cold bias
along the east cost of the Shikoku Island as compared to thecomposite observation (Fig. 12a).
We calculated the ensemble heat budgets at points aroundthe Kii Channel (see points in plotted in Fig. 12b) of theforecasts starting from the ENKF analyses on 0.00, 18
February 2010 (Fig. 13). Around of the Kuroshio northernedge (Fig. 13a), the ensemble mean forecast temperatures
were around 18°C and their tendencies were basically determined by the advection (left panel of Fig. 13a). The
ensemble mean advection terms show positive (negative)
east–west (vertical) heat advection terms (right panel ofFig. 13a), confirming that the Kuroshio frontal variations
dominantly governed the heat budget there. At a point along
the west coast of the Kii Peninsula (Fig. 13b), negative
vertical diffusion terms including the surface heat flux wereslightly dominant over the advection terms and temperature
values gradually decreased (left panel of Fig. 13b). The
Fig. 12 a A composite map of satellite sea surface temperature on 20 b
February 2010 provided by the fishery research institute of Tokushima
Prefecture. b Ensemble mean sea surface temperature (contours) andflows (vectors) of the ensemble forecasts on 20 February 2010 startingfrom the EnKF analyses on 18 February 2010. c Same as Fig. 12 b
except for FRF

c

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Ocean Dynamics (2012) 62:645–659

a33.4N 135.5E

33.4N 135.5E

0.0001

0.002
0.0015

16
14

0

12
-5e-05-0.000118

19(deg.C/sec)

18

5e-05

(deg.C)(deg.C/sec)

20

0.001
0.00050-0.000510-0.0018-0.0015

6-0.002

20

18

(Day)
adv

b

vdif

tend

temp

wadv

33.6N 135.3E

20

yadv

xadv

33.6N 135.3E

0.00010.002
200.0015

16
14

0

12
-5e-05-0.000118

19(deg.C/sec)

18

5e-05

(deg.C)(deg.C/sec)

19

(Day)

0.001
0.00050-0.000510-0.0018-0.0015

6-0.002

20

18

(Day)
adv

vdif

19

20

(Day)
tend

temp

wadv

yadv

xadv

c
33.8N 135.1E

33.8N 135.1E

0.0001

0.002
0.0015

5e-05

16
14

0

12
-5e-05-0.000118

19(deg.C/sec)18(deg.C)(deg.C/sec)

20

0.001
0.00050-0.000510-0.0018-0.0015

6-0.002

20

18

(Day)
adv

vdif

19

20

(Day)
tend

temp

wadv

yadv

xadv

Fig. 13 Left time sequences of 4-hourly ensemble mean sea surface
temperature (thick lines), advection terms of temperature transport
equation (dotted lines), vertical diffusion terms including surface heat
flux effect (dashed lines), tendency terms (double-dotted lines) fromthe ensemble forecasts initialized by the ENKF analyses on 0:00, 18
February 2010 at a 33.4° N, 135.5° E, b 33.6° N, 135.3° E, c 33.8° N,

135.1° E, d 34.0° N, 134.9° E, e 33.8° N 134.8° E, and f 33.6° N
134.4° E. Horizontal diffusion terms were not plotted here because
their magnitudes ware small. Error bars denote the ensemble spread of
the variables. Right as in left panels except for vertical advection terms(short dashed lines), north–south advection terms (long dashed lines),and east–west advection terms (double-dotted lines)

advection terms (right panel of Fig. 13b) indicates positive(negative) north–south (east–west) advection terms thatwere consistent with the Kuroshio water intrusion along
the west coast of the Kii Peninsula. A point inside of theOcean Dynamics (2012) 62:645–659

d657

34.0N 134.9E

34.0N 134.9E

0.0001

0.002
0.0015

16
14

0

12
-5e-05-0.000118

19(deg.C/sec)

18

5e-05

(deg.C)(deg.C/sec)

20

0.001
0.00050-0.000510-0.0018-0.0015

6-0.002

20

18

(Day)
adv

e

vdif

tend

temp

wadv

33.8N 134.8E

20

yadv

xadv

33.8N 134.8E

0.00010.002
200.0015

16
14

0

12
-5e-05-0.000118

19(deg.C/sec)

18

5e-05

(deg.C)(deg.C/sec)

19

(Day)

0.001
0.00050-0.000510-0.0018-0.0015

6-0.002

20

18

(Day)
adv

vdif

19

20

(Day)
tend

temp

wadv

yadv

xadv

f
33.6N 134.4E

33.6N 134.4E

0.0001

0.002
0.0015

16
14

0

12
-5e-05-0.000118

19(deg.C/sec)

18

5e-05

(deg.C)(deg.C/sec)

20

0.001
0.00050-0.000510-0.0018-0.0015

6-0.002

20

18

(Day)
adv

vdif

19

20

(Day)
tend

temp

wadv

yadv

xadv

Fig. 13 (continued)

channel (Fig. 13c) shows the similar features but the weakeradvection compared to the southern point (Fig. 13b). At apoint around the front (Fig. 13d), the tendency was basicallydetermined by the vertical diffusion including the surface
heat flux effect (left panel of Fig. 13d) and positive(negative) vertical (east–west) advection terms balanced toeach other (right panel of Fig. 13d). Around the steep front(Fig. 13e), large amplitude of the spread indicates that theforecast values were significantly scattered and temporally
variable due to the advection (left panel of Fig. 13e).

658

Positive (negative) horizontal (vertical) advection terms(right panel of Fig. 13e) suggest the warm water tended into
the colder side of the front. At a point along the east coast of
the Shikoku Island (Fig. 13f), positive vertical diffusion
including the surface heat flux effect tended to increase
temperature values (left panel of Fig. 13f) and negative(positive) north–south (east–west) advection terms almost
balanced to each other (right panel of Fig. 13f), suggestingthat the cold (warm) water was transported from the northern (eastern) region by the current.
In summary, ENKF reproduced the two types of front
variations: the Kuroshio northern edge (Fig. 13a) and the Kii
Channel Front (Figs. 13d, e), the Kuroshio water intrusion
along the west coast of the Kii Peninsula (Figs. 13b, c), andits relevant circulation along the east coast of the Shikoku
Island (Fig. 13f). The ensemble heat budget of FRF indicates that it failed to reproduce the anti-clockwise circulation due the Kuroshio intrusion and steep front variations(not shown). Slight difference between the composite observation (Fig. 12a) and ENKF ensemble mean forecast(Fig. 12b) near the coasts of the Kii Peninsula and Shikoku
Island suggests more requirements of the observation dataaround there (see Fig. 8). The less predictability around thesteep front was clearly indicated by the larger amplitude of
the spread (Fig. 13e).

6 Summary and discussion
This study demonstrates the feasibility of the ensemble Kalman filter to the investigation of the real Kuroshio variations
south of Japan in February 2010. We assimilated satellite
sea surface height anomaly, satellite sea surface temperature,and in situ temperature and salinity profiles into an ocean
general circulation model with horizontal resolution of
1/36° using EnKF. Twenty ensemble members of 2-day lead
forecasts were updated by EnKF for the period from 8 to
28 February 2010. EnKF well reproduced the Kuroshio
path positions. Also, EnKF well reproduced the observed
water mass property in the Kuroshio region with RMSD
of temperature and salinity smaller than 1°C and 0.1 psu,
respectively.
The impacts of the assimilation of localized in situ
observation data spread over the whole model region.
The data impacts dynamically propagated from their
origins to far owing to the effects of the temporally
and spatially variable forecast error covariance represented by EnKF. In particular, EnKF effectively assimilated the in situ temperature and salinity data to represent
the sharp structure of the Kii Channel Front and its
variation affected by the warm water intrusion from theKuroshio region. The ensemble heat budget analysis forthe period from 18 to 20 February 2010 demonstrates

Ocean Dynamics (2012) 62:645–659

that EnKF generally reproduced the warm water intrusion into the channel in this period as observed. EnKF
suggested that the variation around the steep front wascomparatively unpredictable; more observations and inclusion of non-hydrostatic dynamics with higher horizontal resolution (Akitomo et al. 1990) were required formore exact representation of the variation of the steep
front.
So far, the data assimilation methods used in operational
ocean forecasting models for south of Japan have basicallyassumed time-constant and isotropic error covariance basedon empirical knowledge of the oceanic conditions there(e.g., Miyazawa et al. 2008; 2009). This assumption is
acceptable for typical mesoscale variations such as the Kuroshio path variations and mesoscale eddies with temporaland spatial scales of O (10 days) and O (100 km), respectively (Kuragano and Kamachi 2000). However, recent
efforts of downscale modeling have allowed us to simulate
the open and coastal seas interactions with highly variable
temporal and anisotropic spatial scales due to coexistence ofmulti-scales phenomena (Isobe et al 2010). In particular, theinteractions between the currents and coastal topography(Miyama and Miyazawa 2010) enhance the anisotropic features of horizontal scales of the phenomena. In such cases,
the assumption is not valid. Our study demonstrates that
EnKF is quite effective for detection of the open and coastal
seas interactions because of its ‘seamless’ representation of
the forecast error covariance from meso- to sub-mesoscales.
Some diagnostic methods for the evaluation of the error
covariance based on the model dynamics have been alreadydiscussed in the literature (e.g., Jameson et al. 2002). Skill
comparison of EnKF with combinations of the operational
data assimilation and the diagnostic methods will be usefulfor improvements of the existing operational ocean forecast
systems in terms of representation of the open and coastal
seas interactions.
Localization scales of the observation data are importantparameters of LEKF (Miyoshi et al. 2010). For example, weused horizontal radius of 1/3° (Table 1) as the horizontal
localization scale. This value was determined based on
the results of the sensitivity experiments with pseudoobservation data sampled from the simulation (‘identicaltwin experiments’). Figure 10 depicts that the large valuesof covariance were found far away from the target pointwith more than 1/3° distance. But the representation of theerror covariance was highly temporally and spatially variable. The corresponding error covariance distribution on 20
February 2010 showed quite smaller values around thetarget point (not shown), suggesting weak correlations
between the target and surrounding points at this time. The
present parameter of 1/3° is considered as a representative
one averaged over the whole simulation period, whole model
region, and all variables.

Ocean Dynamics (2012) 62:645–659
Acknowledgments This work is part of the Japan Coastal Ocean
Predictability Experiment (JCOPE) promoted by the Japan Agency for
Marine-Earth Science and Technology (JAMSTEC). The code of thelocal ensemble transformation Kalman filter (LETKF) was obtained fromhttp://code.google.com/p/miyoshi/, which is maintained by Dr. Takamasa
Miyoshi. Sea surface height anomaly data of Jasons-1 and Jasons-2 andsea surface temperature of NOAA MCSST were downloaded from the
US-GODAE website: http://www.usgodae.org/. AMSR-E data were produced by remote sensing systems and sponsored by the NASA Earth
Science MEaSUREs DISCOVER Project and the AMSR-E ScienceTeam. Data are available at http://www.remss.com/. In situ temperatureand salinity profiles were obtained from the Global Temperature-Salinity
Profile Program (GTSPP) website: http://www.nodc.noaa.gov/GTSPP/.
Comments from two anonymous reviewers were useful for improvements of the earlier version of the manuscript.

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