Yoichi Ishikawa1, Toshiyuki Awaji1,2, Teiji In3, Satoshi Nakada2, Tsuyoshi Wakamatsu1, Yoshimasa Hiyoshi1, Yuji Sasaki11DrC, JAMSTEC2Kyoto University3Japan 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 windowIntroductionEddy resolving/permitting OGCM with 1/6x1/8 resolutionlimitation of computational resourceslimitation of available observation dataResolution 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-z hybrid vertical coordinateTakano-Onishi scheme (Ishizaki and Motoi, 1999)Equation of MotionEquation 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., 2009.5Configuration of system

1/6x1/8 deg. Parent model

1/18x1/24 deg child model6Observation dataSea 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 variablesControl variables : initial conditions of model variablesGradient 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 systemAssimilation & downscaling

Low resolution Parent model:

High resolution child modelClassical framework

High resolution data assimilation in future

High resolution modelAssimilation & downscaling

Low resolution Parent model:

High resolution child modelnew 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 modelIncremental approach

Make new formulation using increment:parent model:

Child model:Outer Loop:

Inner Loop:

Approximate:

Bias (Constant in Inner Loop):Calculation Procedureforecast Parent & Child model

calculate bias

optimized initial condition

forecast Parent & Child model

Experimental settingAssimilation period: 28dayobservation data are averaged every 1dayStart from Jan.5 2011currently, 1 year integrationCompare new approach with classical downscaling

Snapshot of SST Apr. 1st, 2011

Classical DownscalingNew incremental 4DVARObservation dataReduce warm biases appears in classical Downscaling RMSD with observation of SST

Classical DownscalingNew incremental 4DVARTime 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 effectiveClassical DownscalingNew incremental 4DVARVertical profile of RMSD

Classical DownscalingNew incremental 4DVARSST and surface velocity

Classical DownscalingNew incremental 4DVARTemperature at 100m depth

Classical DownscalingNew incremental 4DVARVelocity at 100m

Classical DownscalingNew incremental 4DVARTsushima strait (child model)

Classical DownscalingNew incremental 4DVARTsushima strait (parent model)

Classical DownscalingNew incremental 4DVARTsugaru strait (child model)

Classical DownscalingNew incremental 4DVARTsugaru strait (parent model)

Classical DownscalingNew incremental 4DVARAlong 41N

Classical DownscalingNew incremental 4DVARAlong 40.5N

Classical DownscalingNew incremental 4DVARSummaryTo 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.