yoichi ishikawa 1, toshiyuki awaji 1,2, teiji in 3, satoshi nakada 2, tsuyoshi wakamatsu 1,...
TRANSCRIPT
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
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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
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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
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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
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x L = M L x0Lb
( )
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x H = M H x0Lb
( )
€
β =H '⋅M H x0Lb
( ) −H⋅M L x0Lb
( )
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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.