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 R1Hx 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 1H' 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 R1H' 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 R1Hx 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.