1. in collaboration with: J. S. Allen, G. D. Egbert, R. N. Miller and COAST investigators P. M. Kosro, M. D. Levine, T. Boyd, J. A. Barth, J. Moum, et al. College of Oceanic and Atmospheric Sciences Oregon State University Assimilation of moored ADP currents into a model of wind-driven circulation off Oregon Alexander L. Kurapov

2. Dual approach: - A model based on fully non-linear dynamics is applied with a suboptimal, sequential DA scheme Example: POM + optimal interpolation (OI), applied with HF radar surface velocity data [ Oke et al. JGR 2002 ] - Dynamical models based on simplified (linearized) dynamics are applied with rigorous (variational) DA methods Example: linear model + representer method, HF radar surface velocity data [ Kurapov et al. JPO 2003 ]

3. Data assimilation (DA): a tool for data synthesis Model is used as a dynamically based interpolator between data, both in space and time -Constrain model solution (model errors) with available observations (3D + Time) - Provide extensive validation against data that are not assimilated - Provide accurate description of spatial and temporal variability of physical (and in perspective, biological) fields

4. 90 km NSB NMS NIS SSB SMS SIS NH-10 Data: COAST observational program, May-Aug 2001 Our objectives: - Assimilate ADP: distant effect - Multivariate capabilities (e.g., effect on SSH, T, isopycnals, dissipation rate) - Variability near bottom (currents, stress) - Estimates of cross-shelf transport Mooring locations: -Lines N and S: ADP, T, S (COAST - Kosro, Levine & Boyd) -NH10: ADP (GLOBEC - Kosro) Vectors: Depth- and time-aver model v

5. Model set-up: Alongshore wind stress (NMS site): - POM (hydrostatic; primitive eqns; prognostic for u, SSH, T, S, q 2, q 2 L; turbulence parameterization) - 220  350 km, periodic OB conditions (south-north) -  x~2 km, 31  -layers - Initial conditions: T, S from NH line 45 nm offshore, ave for June, 1961-71 [ Huyer et al.] - Forcing (low pass filtered) : alongshore wind stress (spatially uniform), heat flux

6. Optimal interpolation (OI): t f (a) : forecast (analysis) state obs t : the vector of observations at time t H: maps the state vector to obs G: the gain matrix (stationary in OI) - Incremental approach: correction is applied gradually over the analysis time window (1/4 inertial period) C : data error covariance P f : forecast error covariance (stationary estimate) Note: for OI, only P f H T is needed G = P f H T (H P f H T + C)  1

7. Forecast error covariance, P f is computed using P m, the estimate of the errors in the model, not constrained by data [ Kurapov et al. MWR, 2002 ] P m – including lagged model error covariances (to account for the effect of previously assimilated data) P m – can be estimated, e.g., if TL and ADJ codes were available, based on assumptions of error covariances of inputs (wind stress) This implementation: - Compute an ensemble of 9 summer runs (forced w/ observed winds for different years, seasonal heat flux) - For each year, assume model error correlation = model variable correlation ( true is replaced by the time-ave m ) - The resulting P m is the mean of the correlations for 9 summers scaled by StD for year 2001. Theoretical models: propagating modes affect spatial structure of P f P f   P m

8. NH10 SSB SMS SIS Corr: 0.18  0.74 RMS: 7.8  5.5 cm s -1 Corr: 0.35  0.73 RMS: 9.5  6.6 cm s -1 Distant effect of assimilating ADP currents (“Case 1”) - Assimilate NSB, NMS, NIS - Improvement at NH10, SSB Depth-ave alongshore current: Obs, no DA, DA

9. Corr: 0.45  0.82 RMS: 6.7  5.05 cm s -1 Corr: 0.46  0.79 RMS: 11.3  7.9 cm s -1 Corr: 0.55  0.71 RMS: 13.5  10.8 cm s -1 Corr: 0.18  0.63 RMS: 7.8  6.9 cm s -1 Distant effect of assimilating ADP currents (“Case 2”): - Assimilate SSB & SMS - Improvement at Line N, NH10 NSB NMS NIS NH10 Depth-ave alongshore current: Obs, no DA, DA

10. Effect of assimilating ADP data on nearshore SSH 12 Low pass filtered SSH at South Beach, OR (44 o 37.5’N): observed (NOAA tide gauge) and modeled (no DA and DA Cases 1 (assim N ADPs) and 2 (S ADPs)). Time-ave are subtracted from each time series. Obs – corrected for barometric p. Model-data Corr.: 0.41  0.71, 0.79 RMS diff: 6.0  3.8, 3.3 cm

11. Effect of assimilating ADP currents on isopycnal structure    Cross-sections near Line S of moorings no DA DA (SSB, SMS, SIS) SeaSoar (Barth et al.)

12. Dissipation rate (  )  model vs. microstructure data [ Moum & A. Perlin ] Plotted is log 10 (  )  Transect 10 Obs, no DA, DA (N ADPs), DA (SSB+SMS) MEAN RMS diff Obs, no DA, DA (N ADPs) Transect 10

13. Model-obs temperature correlation vs. depth, at COAST mooring sites No DA, DA Case 2 (vert. axis tickmarks are each 10 m) NSB NMSNIS SSB SMSSIS

14. Time-averaged current and   near bottom Variance ellipses of bottom current ( days 146-191 ) no DA DA (assim SSB+SMS) 5 cm s -1 kg m -3 Also looking at: surface current, SST, bottom stress, cross-shore transport…

15. Model sensitivity to assimilation of data from 1 mooring Actual performance: Expected (compare diag (P m ) and (P a ), where P a = P f – G H P f ): DA is better than model only solution DA is worse than model only solution

16. Summary: - A data assimilative model is suggested as a tool for data synthesis - Assimilation of ADP currents from a line of moorings: currents improved at an alongshore dist. of 90 km, both to N and S - Assimilate ADP velocities: improve SSH, variability in T,    slope,  - DA affects: surface currents, BBL processes, cross-shelf transport - Need for model improvement (open boundaries): remote forcing, spatially varying wind stress - Need for a more advanced DA methodology: make explicit assumptions about errors (wind forcing, open boundaries), provide an improved, dynamically balanced solution - Theoretical studies: role of OB error covariance http://www.oce.orst.edu/po/research/kurapov/main.html