Development of an incremental 4D-VAR
system for ocean model downscaling
Yoichi Ishikawa1, Toshiyuki Awaji1,2, Teiji In3,
Satoshi Nakada2, Tsuyoshi Wakamatsu1,
Yoshimasa Hiyoshi1,Yuji Sasaki1
1DrC, JAMSTEC
2Kyoto University
3Japan Marine Science Foundation
Introduction
 4DVAR data assimilation system with
Eddy-Resolving OGCM have been
successfully developed (e.g. Ishikawa
et al., 2009)
 Strong Western Boundary Currents,
meso-scale eddies, strong flows
through narrow channels.
 Estimate initial conditions with
1month assimilation window
Introduction
 Eddy resolving/permitting OGCM with 1/6x1/8 resolution
 limitation of computational resources
 limitation of available observation data
 Resolution is not enough for
 detailed processes for eddy activities, detachment, junction,
deformation, etc.
 detailed processes associated with narrow channel, Tsushima
strait, Tsugaru strait.
 Higher resolution is required but cannot execute.
 Down scaling approach is often adopted.
Introduction
 Downscaling approach is very effective to obtain high-
resolution data set.
 Initial & boundary conditions are realistic because they are
taken from reanalysis dataset.
 However, the quality of downscaled dataset is not guaranteed
 different physical processes, different topography, different
parameterization
 There differences sometimes leads serious biases downscaling
dataset
 To obtain realistic high-resolution dataset, data assimilation
and downscaling systems are integrated.
 make reanalysis dataset suitable for downscaling.
Kyoto Univ. Ocean General Circulation Model
OGCM & data assimilation system is based on
Ishikawa et al., 2009.
σ-z hybrid vertical coordinate
Equation of Motion
Takano-Onishi scheme (Ishizaki and Motoi, 1999)
Equation of Tracer
Mixed layer sheme based on turbulence closure(Noh, 2005)
Isopycnal diffusion and eddy parameterization
(Gent and McWillams, 1990; Griffies, 1998)
3rd-Order advection scheme (Hasumi, 2000)
Configuration of system
1/6x1/8 deg. Parent model
1/18x1/24 deg child model
Observation data
•Sea surface temperature :OSTIA (Operational Sea
Surface Temperature and Sea Ice Analysis) by NCOF,
1/20deg.
•Sea surface height : Ssalto/Ducacus grided absolute
dynamic topography by AVISO, 1/3 deg.
•In-situ data : GTSPP (global temperature-salinity profile
program) XBT and CTD data by NOAA/NODC.
Variational adjoint method
Cost function : constraint for observational data and intial
guess of control variables

J  x0  x0

b T
B
1


x 0  x 0  Hx  y  R 1 Hx  y 
b
T
Control variables : initial conditions of model variables
Gradient descent method :Popular scheme (Fujii and
Kamachi, 2003), which can utilize non-diagonal part of the
error covariance matrix for initial guess.
This method is modified in this study
for combining downscaling system
Assimilation & downscaling
Classical framework
Low resolution Parent model:

J  x x
L
0
Lb
0
 
T
B
1
x x
L
0
Lb
0

x L  M L x0L 
 Hx  y R1Hx L  y
x M
High resolution child model

T
L
H
H
x
H
0
;x
La

High resolution data assimilation in future
 x H  M H x H 
High resolution model
0

J  x x
H
0
 
T
f
H
0
B
1
x x
H
0
Hf
0

 H' x  y  R 1H' x H  y 
H
T
Assimilation & downscaling
new approach in this study
Low resolution Parent model:

J  x x
L
0
Lb
0
 
T
B
1
x x
L
0
Lb
0
High resolution child model


x L  M L x0L 
 H' x  y  R1H' x H  y 
H
T
 
x H  M H xL
Solving optimization problems to minimize the difference
between
& observation data by
estimating the initial condition
 of
Incremental approach
x  x  x
Make new formulation using increment:
x L  ML  x 0L
H
H
L
x  M  x 0
parent model:
Child model:
Outer Loop:
J  x 
B
L T
0
1
L
0
x

L
0
L
0
Lb
0
1
H
L

H'

M
x

y
R
H'

M
x
 
 
0  y 
H
L
0
T

Inner Loop:
Approximate:
H' x H  HML x 0L  
  H'MH  HML x0L
Bias (Constant in Inner Loop):
J  x  B
L T
0
1
x  H M
L
0

L
x    y  R 1 H M L x 0L    y 
L
0
T
Calculation Procedure
1.
forecast Parent & Child model
x M
L
2.
L
calculate bias
x 
Lb
0
x M
H
 
b

x 
Lb
0
 
  H' M H x 0L  H M L x 0L
3.
H
b
optimized initial condition


 

J  x x
B x  x  Hx    y R1Hx L    y

4. forecast Parent & Child model
Lb
0
L
0
T
x M
L
1
L
L
0
x 
La
0
Lb
0
T
L
x M
H
H
x 
La
0
Experimental setting
 Assimilation period: 28day
 observation data are averaged every 1day
 Start from Jan.5 2011
 currently, 1 year integration
 Compare new approach with classical downscaling
Snapshot of SST Apr. 1st, 2011
Classical Downscaling
New incremental 4DVAR
Observation data
Reduce warm biases
appears in classical
Downscaling
RMSD with observation of SST
Classical Downscaling
New incremental 4DVAR
Time series of RMSD of SST
Classical Downscaling
New incremental 4DVAR
Seasonal change of RMSD is due to the change of mixed layer depth.
Summer: thin mixed layer & heat flux is effective
Winter: thick mixed layer & advection is effective
Vertical profile of RMSD
Classical Downscaling
New incremental 4DVAR
SST and surface velocity
Classical Downscaling
New incremental 4DVAR
Temperature at 100m depth
Classical Downscaling
New incremental 4DVAR
Velocity at 100m
Classical Downscaling
New incremental 4DVAR
Tsushima strait (child model)
Classical Downscaling
New incremental 4DVAR
Tsushima strait (parent model)
Classical Downscaling
New incremental 4DVAR
Tsugaru strait (child model)
Classical Downscaling
New incremental 4DVAR
Tsugaru strait (parent model)
Classical Downscaling
New incremental 4DVAR
Along 41N
Classical Downscaling
New incremental 4DVAR
Along 40.5N
Classical Downscaling
New incremental 4DVAR
Summary
 To obtain high resolution analysis, incremental approach is
introduced in 4DVAR system, considering the biases in
downscaling.
 Associating strong flows through the narrow channel,
significant improvement can be recognized.
 Topographic effect and nonlinear behavior is important.
 Configuration of Inner-Outer loop will be examined for
better estimation.