NOPP Project: Boundary conditions, data assimilation, and predictability in coastal ocean models

1. NOPP Project: • Boundary conditions, data assimilation, and predictability in coastal ocean models • OSU: R. M. Samelson (lead PI), J. S. Allen, G. D. Egbert, A. Kurapov, R. N. Miller • NRL: J. C. Kindle • NCAR: C. Snyder • Objectives: • Determine impact of open ocean boundary conditions from GODAE Pacific Ocean models on Oregon coastal ocean models by comparison with in situ measurements • Determine impact on Oregon coastal ocean simulations of assimilating satellite remote sensing observations • Quantify uncertainty and predictability in coastal ocean simulations • + Interactions with ongoing ONR, CIOSS, and GLOBEC funded projects on coastal ocean/atmosphere modeling and data assimilation

2. Spatial variability and flow-topography interactions in coastal flows: AVHRR Satellite SST (24 Aug. 2003) Isobaths: 100 and 200 m. Coastal Model daily ave. surface T, velocities (7 Sept. 2005). Using ROMS at 2 km resolution, forced with output from atmospheric ETA model Stronger interactions between coastal and interior oceanic flows in the observed fields than in the coastal model Improvements in coastal transition zone (CTZ) modeling require nesting in larger scale models

3. Interaction of the shelf flows and interior ocean seen in model SSH The SSH snapshot from the 1/12o resolution Pacific HYCOM (15 July 2001) [J. Metzger, NRL]. The boundary of the regional West Coast HYCOM (also NCOM-CCS) ROMS-based Oregon coastal model in white

4. GLOBEC study: analysis of CCS model simulation Model solution for 2000 provided by E. Curchitser, currently being analyzed by CIOSS-supported post-doc B. J. Choi Model SST and surf. currents (August 2000): Coastal ocean interacts with interior ocean Separation near Heceta Bank, Cape Blanco Upwelling is weaker than observed (should be improved using higher resolution winds) Model improvement in the CTZ should also result from assimilation of SSH, SST, and long-range HF radar data

5. Location of time series observations to be used for assimilation and validation Daily ave. HF radar surface currents, (courtesy of P. M. Kosro at OSU). Blackcontours: H= 100, 200, and 1000 m

6. Development of DA methods for the Coastal Ocean (research supported by ONR) “Dual Approach” • Linearized models + rigorous (variational) DA • Theoretical models: help formulate model error statistics for practical applications [Scott et al., JPO, 2000, Kurapov et al., Mon. Wea Rev., 2002] • Internal tide, HF radar surface velocity data [Kurapov et al., JPO, 2003] Fully nonlinear model + suboptimal, sequential DA (Optimal Interpolation) 1) HF radar surface velocity data [Oke et al., JGR, 2002] 2) moored ADP velocities [Kurapov et al., JGR, 2005a, 2005b, JPO, 2005] Present focus: merger of these approaches: Application of tangent linear and adjoint ROMS for variational DA Barotropically unstable jet in a channel[Kurapov and Di Lorenzo, 2005] Forced-dissipative flows in the nearshore: ongoing research Three-dimensional, stratified flows on shelf: ongoing research

7. Advantages of variational DA: the study of M2 internal tide off Oregon • HF radar data for summer 1998 (provided by P. M. Kosro) are assimilated in a linear frequency-domain model[Kurapov et al. JPO, 2003] • DA corrects open boundary (OB) baroclinic tidal currents • Inverse solution minimizes penalty function: J(u)= || OB error ||2 + || data error ||2 Tidal ellipses of the horizontal current (for a series of overlapped 2-week time windows) Representer-based minimization optimally projects surface observational information to 3D (Improvement is verified to be obtained at ADP site) depth-ave ADP HF Deviations from depth-ave Validation ADP no DA Day, 1998 HF Depth DA

8. Inverse solutions provide a uniquely detailed picture of the spatial and temporal variability of the M2 internal tide Surface tidal ellipses Day 139 Time-ave baroclinic KE: Bottom Surface lat 45.65N lat 45.55N Depth-ave (white ellipses rotate CCW) Deviations from depth-ave (gray ellipses rotate CW)

9. Experience assimilating data into the fully nonlinear, primitive eqn. model of wind-driven shelf circulation (studies of summer upwelling) Dynamics: Princeton Ocean Model (free surface, nonlinear, primitive eqn., w/ turbulence parameterization [Mellor & Yamada 1982]) -Realistic bathymetry -Boundary conditions: periodic (south to north) -Forcing: alongshore wind stress and heat flux HF radars (Kosro) Moorings (ADP, T, S: Levine, Kosro, Boyd)

10. Optimal Interpolation (OI) Data assimilation: - sequential, optimal interpolation (OI) - correction is added in small increments every time step model w/out DA ||Error|| forecast DA analysis Time-invariant gain matrix matrix matching observations to state vector Time - correction only to u: -correction term is present in momentum equations -however, equations for T, S, q2, q2l are dynamically balanced (which facilitates their term balance analysis) - Approximate gain matrix obtained from an ensemble of model runs

11. Effects of DA: improvement in near-bottom currents alongshore velocity at NH10 mooring [Kosro] close to surface close to bottom model-data corr.: 0.52 (no DA)  0.83 (DA) rms error: 8.1 (no DA)  4.4 cm s-1 (DA) Assimilation sites:

12. Effects of ADP velocity DA: improvement in near-shore SSH time series comparison with coastal tide gauge data near Newport obs, no DA, DA SSH, surf v, no DA SSH, surf v, DA surf v, HF radar [Kosro] Flow control over Stonewall Bank (Day 166, 2001) Assimilation of velocity observations in shelf circulation models can improve accuracy of SSH maps in the coastal zone, where altimetry is not available

13. Optimal Interpolation: limitations OI corrects the ocean state, not forcing  limited control over source of error OI assumes time-invariant forecast error covariance, used to compute the gain matrix. State-dependent covariance is needed to predict events. Observations (such as satellite SSH, SST, HF radar) will generally have to be processed into maps (without spatial or temporal gaps) before using OI-DA Variational, representer based, generalized inverse method (GIM) GIM has potential of resolving these and some other deficiencies of OI. Methodology has been developed for using GIM efficiently with nonlinear oceanic models [Chua and Bennett, 2001]. This technology is yet to be tried in the context of coastal ocean circulation modeling. To use GIM, tangent linear and adjoint models have to be developed. Our ongoing research is focused on GIM assimilation into nonlinear coastal models