Yoichi Ishikawa1, Toshiyuki Awaji1,2, Teiji In3,

Satoshi Nakada2, Tsuyoshi Wakamatsu1, Yoshimasa Hiyoshi1, Yuji Sasaki1

1DrC, JAMSTEC2Kyoto University

3Japan Marine Science Foundation

Development of an incremental 4D-VAR system for ocean model downscaling

Introduction4DVAR 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

IntroductionEddy resolving/permitting OGCM with

1/6x1/8 resolutionlimitation of computational resourceslimitation 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.

IntroductionDownscaling 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

guaranteeddifferent physical processes, different topography,

different parameterizationThere differences sometimes leads serious biases

downscaling datasetTo obtain realistic high-resolution dataset, data

assimilation and downscaling systems are integrated.make reanalysis dataset suitable for downscaling.

Kyoto Univ. Ocean General Circulation Model

σ-z hybrid vertical coordinate

Takano-Onishi scheme (Ishizaki and Motoi, 1999)Equation of Motion

Equation of TracerMixed 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)

OGCM & data assimilation system is based on Ishikawa et al., 2009.

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

€

J = x0 − x0b

( )TB−1 x0 − x0

b( ) + Hx − y( )

TR−1 Hx − y( )

Cost function : constraint for observational data and intial guess of control variables

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

€

J = x0L − x0

Lb

( )T

B−1 x0L − x0

Lb

( ) + HxL − y( )TR−1 Hx L − y( )

€

x L = M L x0L

( )Low resolution Parent model:

€

x H = M H x0H ;x L

a

( )High resolution child model

Classical framework

€

J = x0H − x0

H f

( )T

B−1 x0H − x0

H f

( ) + H ' x H − y( )TR−1 H ' x H − y( )

High resolution data assimilation in future

€

x H = M H x0H

( )High resolution model

Assimilation & downscaling

€

J = x0L − x0

Lb

( )T

B−1 x0L − x0

Lb

( ) + H ' x H − y( )TR−1 H ' x H − y( )

€

x L = M L x0L

( )Low resolution Parent model:

€

x H = M H x L( )High resolution child model

new approach in this study

Solving optimization problems to minimize the difference between high resolution model & observation data by estimating the initial condition of low resolution model

Incremental approach

€

Δx L =ML ⋅ Δx0L

€

Δx0L = x0

L − x0LbMake new formulation using

increment:parent model:

€

Δx H =MH ⋅ Δx0LChild model:

Outer Loop:

€

J = Δx0L

( )TB−1 Δx0

L( ) + H'⋅MHΔx0

L − Δy( )TR−1 H'⋅MHΔx0

L − Δy( )

Inner Loop:

€

J = Δx0L

( )TB−1 Δx0

L( ) + H⋅MLΔx0

L + β − Δy( )TR−1 H⋅MLΔx0

L + β − Δy( )€

H'Δx H =HMLΔx0L + βApproximat

e:

€

β = H'MH −HML( )Δx0

LBias (Constant in Inner Loop):

Calculation Procedure1. forecast Parent & Child model

2. calculate bias

3. optimized initial condition

4. forecast Parent & Child model

€

x L = M L x0Lb

( )

€

x H = M H x0Lb

( )

€

β =H '⋅M H x0Lb

( ) −H⋅M L x0Lb

( )

€

x L = M L x0La

( )

€

x H = M H x0La

( )€

J = x0L − x0

Lb

( )T

B−1 x0L − x0

Lb

( ) + HxL + β − y( )TR−1 Hx L + β − y( )

Experimental settingAssimilation period: 28day

observation data are averaged every 1dayStart from Jan.5 2011

currently, 1 year integrationCompare 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

Seasonal change of RMSD is due to the change of mixed layer depth.Summer: thin mixed layer & heat flux is effectiveWinter: thick mixed layer & advection is effective

Classical DownscalingNew incremental 4DVAR

Vertical profile of RMSD

Classical DownscalingNew incremental 4DVAR

SST and surface velocityClassical Downscaling

New incremental 4DVAR

Temperature at 100m depthClassical Downscaling

New incremental 4DVAR

Velocity at 100mClassical 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

SummaryTo 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.