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Assimilation of Sea Surface Temperature
into a Northwest Pacific Ocean Model
using an Ensemble Kalman Filter
B.-J. Choi
Kunsan National University, Korea
Gwang-Ho Seo, Yang-Ki Cho, Chang-Sin Kim
Chonnam National University, Korea
Sangil Kim
Oregon State University, USA
Young-Ho Kim
KORDI, Korea
Assimilation of Sea Surface Temperature into a Northwest
Pacific Ocean Model using an Ensemble Kalman Filter
Contents
1. Northwest Pacific Ocean Model with ROMS
2. Ensemble Kalman Filter
3. Assimilation of Sea Surface Temperature
4. Assimilation of Temperature Profiles
Summary
Assimilation of Sea Surface Temperature into a Northwest
Pacific Ocean Model using an Ensemble Kalman Filter
Objectives of current research
(1) setup a Northwest Pacific Ocean Circulation Model
(2) develop an Ensemble Kalman Filter
(3) assimilate Sea Surface Temperature
(4) assimilate temperature profiles
(5) assimilate sea surface height data
(6) evaluate assimilative model output
Long Term Goal
• Developing a Regional Ocean Prediction System for the
Northwest Pacific Ocean and its marginal seas
• Providing initial condition and open boundary data for
high resolution (10km, 3km, 1km) coastal ocean models
Nesting of a coastal ocean modeling system
25 km
Nesting
10 km
3 km
1 km
Nesting of a coastal ocean modeling system
25 km
Assimilation of Sea Surface Temperature into a Northwest
Pacific Ocean Model using an Ensemble Kalman Filter
1. Northwest Pacific Ocean Model with ROMS
2. Ensemble Kalman Filter
3. Assimilation of Sea Surface Temperature
4. Assimilation of Temperature Profiles
Summary
Ocean Circulation Model for the
Northwest Pacific Ocean and its Marginal Seas
50˚ ROMS (Regional Ocean
Modeling System)
45˚ 1. Grid size:
CHINA - Horizontal: ¼ degree
40˚ - Vertical: 20 layers
KO
2. Topography - ETOPO5 data
RE
Hanghe
River JAPAN
A
35˚ 3. Initial - WOA2001
4. Surface forcing
Changjiang
30˚
River - ECMWF daily wind
- Heat flux : Bulk Flux
25˚ parameterization
AN
IW
Pacific Ocean 5. River: Changjiang, Hanghe
TA
20˚ Yellow rivers
6. Tidal forcing along the
15˚ boundary
115˚ 120˚ 125˚ 130˚ 135˚ 140˚ 145˚ 150˚ 155˚
7. open boundary data: ECCO
Ocean Circulation Model for the
Northwest Pacific Ocean and its Marginal Seas
Wind
Forcing
Ocean Circulation Model for the
Northwest Pacific Ocean and its Marginal Seas
FEB MAY
MODEL
SST
FEB MAY
SATELLITE
SST
AUG NOV
MODEL
SST
AUG NOV
SATELLITE
SST
Transport through Korea Strait
Transport through Korea Strait
5
Korea Strait
Obs. (Takikawa)
4 Obs. (Teague)
Transport (Sv)
3
2
1
0
97 98 99 00 01 02
Year
Northwest Pacific Ocean Model has problems to be
resolved:
1. Overshooting of western boundary currents
2. Temperature bias – model temperature is
warmer than observed temperature
Assimilation of Sea Surface Temperature into a Northwest
Pacific Ocean Model using an Ensemble Kalman Filter
1. Northwest Pacific Ocean Model with ROMS
2. Ensemble Kalman Filter
3. Assimilation of Sea Surface Temperature
4. Assimilation of Temperature Profiles
Summary
Data Assimilation in an Ocean
Modeling System
Ensemble Kalman Filter (EnKF)
The technical methods are based on the original
algorithm of Evensen (1994) and the modified algorithm
of Burgers et al. (1996).
It is relatively easy to implement the algorithm, the EnKF,
to a sophisticated nonlinear model (e.g. ROMS, POM,
ECOM, FVCOM, HYCOM) since the data assimilation
algorithm is independent of the forecast model.
Data Assimilation in an Ocean
Modeling System
Ensemble Kalman Filtering (a stochastic process)
Member1
Member2
Member16
Ensemble Kalman Filter (EnKF)
k
X new k
X old W k
( yo k
yf )
T
CH
k
X new k
X old ( yo y f )
k k
( HCH R)
T
X new X old CH T ( HCH T R) 1 ( yo y k )
k k k
f
X : state vector(T,S, U, V, zeta) W : weight
k
yo : observation vector H : measurent function
y f H X f : measurement vector
k k
Superscrip t k represents the kth ensemble member
Subscript f representsforward model
Identical Twin Experiment
Number of Ensemble: 16 member
Spin up time assimilation
True run
start 2003/01/01 Control run 2003/12/31
Ensemble run
Identical Twin Experiment
(30 SST observation points)
The 30 diamond
marks (♦) are
the locations for
measurement.
Identical Twin Experiment
Surface Surface Surface
Currents Currents Currents
Identical Twin Experiment
RMS error of SST
Assimilation of Sea Surface Temperature into a Northwest
Pacific Ocean Model using an Ensemble Kalman Filter
1. Northwest Pacific Ocean Model with ROMS
2. Ensemble Kalman Filter
3. Assimilation of Sea Surface Temperature
4. Assimilation of Temperature Profiles
Summary
Assimilation of Satellite-observed SST
Modeling Domain: Northwest Pacific Ocean
and its Marginal Seas
Duration: November 2003 to June 2004
SST data: NASA composite SST
(AVHRR, AMSR, buoy)
Assimilation method: Ensemble Kalman Filter
Assimilation interval: every 7 day
Ensemble number: 16
Number of observation points: 50
Assimilation of Satellite-observed SST
The 50 red
dots ( ) are the
locations for
SST
measurement
point.
Logitude
2 Mode 50˚
of 16 ensemble members using EOF analysis of
Initialization
19.6%
45˚ 400
model output p
40˚
200
E ( x) x a a
Latitude
35˚ ξ0a rm em
30˚
a 1-200
25˚
E (x) is ensemble initial, state vector on November 1, 2003,
-400
ξa is normal random number, r eigenvalues, e eigenvectors, and p mode number.
20˚ 0 300 600 900 1200
Time(day)
15˚
115˚ 120˚ 125˚ 130˚ 135˚ 140˚ 145˚ 150˚ 155˚ 160˚
Logitude
50˚
1 Mode
3 Mode
31.7%
50˚
6.4% 400
45˚
45˚
200
400
40˚
40˚
Latitude
0
Latitude
35˚ 200
35˚
30˚ -200 0
30˚
25˚ -200
-400
25˚
0 300 600 900 1200
20˚ -400
20˚ Time(day)
0 300 600 900 1200
15˚ 15˚ Time(day)
120˚ 125˚ 130˚ 135˚ 140˚ 145˚ 150˚ 155˚ 160˚
115˚ 115˚ 120˚ 125˚ 130˚ 135˚ 140˚ 145˚ 150˚ 155˚ 160˚
Logitude
Logitude
50˚
2 Mode (sea surface height)
-0.015
-0.011
-0.007
-0.003
0.001
0.005
0.009
0.013
0.017
0.021
0.025
19.6%
45˚ 400
Logitude
50˚
2 Mode
19.6%
45˚ 400
40˚
200
Latitude
35˚
0
30˚
-200
25˚
-400
20˚ 0 300 600 900 1200
Time(day)
15˚
115˚ 120˚ 125˚ 130˚ 135˚ 140˚ 145˚ 150˚ 155˚ 160˚
Logitude
50˚
3 Mode
6.4%
45˚
400
40˚
Latitude
200
35˚
0
30˚
-200
25˚
-400
20˚
0 300 600 900 1200
15˚ Time(day)
115˚ 120˚ 125˚ 130˚ 135˚ 140˚ 145˚ 150˚ 155˚ 160˚
Logitude
(sea surface height)
-0.015
-0.011
-0.007
-0.003
0.001
0.005
0.009
0.013
0.017
0.021
0.025
Assimilation of Satellite-observed SST
Ensemble Kalman Filtering (a stochastic process)
Member1
Member2
Member16
3.0
Control rmse
Assimilation rmse
Control rmse Avg.
Assimilation rmse Avg.
RMS ERROR
2.5
2.0
Sea Surface
Temperature
1.5
0 30 60 90 120 150 180 210 240
TIME (day)
0.24
RMS ERROR
0.20
0.16
Control rmse Sea Surface
Assimilation rmse
Control rmse Avg. Height
Assimilation rmse Avg.
0.12
0 30 60 90 120 150 180 210 240
TIME (day)
East Sea
(Japan Sea)
YS
ECS KE
RMSE in Sea Surface Temperature
Yellow Sea Area ( 122E~126E , 34N~38N ) East China Sea Area ( 122E~130E , 25N~32N )
5 5
Control rmse Control rmse
Assimilation rmse Assimilation rmse
4 4
RMS ERROR
RMS ERROR
3 3
2 2
1 1
0 30 60 90 120 150 180 210 240 0 30 60 90 120 150 180 210 240
TIME TIME
East Sea Area ( 129E~139E , 36N~42N ) Kuroshio extention Area ( 140E~155E , 30N~40N )
5 5
4 4
RMS ERROR
RMS ERROR
3 3
2 Control rmse 2
Control rmse
Assimilation rmse
Assimilation rmse
1 1
0 30 60 90 120 150 180 210 240 0 30 60 90 120 150 180 210 240
TIME TIME
RMSE in Sea Surface Height
Yellow Sea Area ( 122E~126E , 34N~38N ) East China Sea Area ( 122E~130E , 25N~32N )
Control rmse
0.4 Assimilation rmse 0.4
RMS ERROR
RMS ERROR
0.3 0.3
0.2 0.2
Control rmse
0.1 0.1 Assimilation rmse
0 30 60 90 120 150 180 210 240 0 30 60 90 120 150 180 210 240
TIME TIME
East Sea Area ( 129E~139E , 36N~42N ) Kuroshio extention Area ( 140E~155E , 30N~40N )
Control rmse
0.4 0.4
Assimilation rmse
RMS ERROR
RMS ERROR
0.3 0.3
0.2 0.2
Control rmse
0.1 0.1 Assimilation rmse
0 30 60 90 120 150 180 210 240 0 30 60 90 120 150 180 210 240
TIME TIME
RMSE of SST with respect to in-situ observation
February April June
Assi. Control Assi. Control Assi. Control
YELLOW SEA 1.393 1.507 1.412 1.547 2.289 2.423
EAST SEA 0.953 1.447 1.547 1.865 1.902 2.274
Comparison with observed Temperature (100 m)
Depth ( -40 -40 -40 Temperature (oc) Temperature (oc)
Temperature (oc)
0 5 10 15 20 25 0 5 10 15 20 25 0 5 10 15 20 25
-60
Feb.
-60 (a) 0
Apr. -60 (b) 0 June (c) 0
-80
YS -80 -20
YS -80 -20 YS -20
Depth (m)
0 5 10 15 20 25 0 5 10 15 20 25 0 5 10 15 20 25
of
Comparison (e) 0
(d) 0 (f) 0
-40 -40 -40
Temperature
-100 -100 -100
Depth (m)
-60 -60 -60
Profile
-200 -200 -200Feb. Apr. June
YS -80
YS -80
YS
-300 -300 -80
0 5 10 -300 20 25
15 0 5 10 15 20 25 0 5 10 15 20 25
Feb. (d) 0 (e) 0 June (f) 0
-400 -400 Apr. -400
-500
EJS -500
-100
-500
EJS -100 EJS -100
0 5 10 15 20 25 0 5 10 15 20 25 0 5 10 15 20 25
Depth (m)
(h) 0 -200 -200 -200
(g) 0 0 (i)
-200 -200 -300 -200 -300 -300
Depth (m)
-400 -400 -400 -400 Feb. -400 Apr. -400 June
-500
EJS -500
EJS -500
EJS
-600 -600 -600
0 5 10 15 20 25 0 5 10 15 20 25 0 5 10 15 20 25
-800 Feb. -800 (g) 0
Apr. -800 (h) 0 June (i) 0
KE -200 KE -200 KE -200
-1000 -1000 -1000
Depth (m)
ASSIM. -400 -400 -400
CON.
OBS. -600 -600 -600
-800 Feb. -800 Apr. -800 June
-1000
KE -1000
KE -1000
KE
ASSIM.
Assimilation of Sea Surface Temperature into a Northwest
Pacific Ocean Model using an Ensemble Kalman Filter
1. Northwest Pacific Ocean Model with ROMS
2. Ensemble Kalman Filter
3. Assimilation of SST
4. Assimilation of Temperature Profiles
Summary
Subsurface temperature data from CDT, XBT, and
ARGO floats.
we assimilated temperature data at 5, 10, 30, 50, 100, 200,
500 m depths every 7 day. The observation data within 7 days of
time window are sampled on the day of assimilation.
t = 7 day t = 14 day t = 21 day
t = 28 day t = 35 day t = 42 day
t = 49 day t = 56 day t = 63 day
RMSE of Sea Surface Height (m)
RMSE(meter) Control SST Assi. SST & Hydro Assi.
2004/5/27 0.222 0.187 0.181
Comparison of
Temperature
Profile
(May 2004)
Summary
• Setup a Northwest Pacific Ocean Circulation Model
• Developed an Ensemble Kalman Filter
• Performed an identical twin experiment to evaluate the
performance of Ensemble Kalman Filter
• Assimilation of SST
Work in Progress
• Assimilation of Subsurface Temperature Data from CDT,
XBT and ARGO Floats
Future Plan
• Setup a higher resolution model and assimilate Sea
Surface Height in order to resolve eddies and current
meandering
• Provide initial condition and open boundary data for
(3km and/or 1km resolution) coastal ocean models
Assimilation of Sea Surface Temperature into a Northwest
Pacific Ocean Model using an Ensemble Kalman Filter
Thank you !
