in collaboration with: J. S. Allen, G. D. Egbert, R. N. Miller and COAST investigators

1. Assimilation of moored ADP currents into a model of wind-driven circulation off Oregon Alexander L. Kurapov 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

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. Data:COAST observational program, May-Aug 2001 • Mooring locations: • Lines N and S: ADP, T, S (COAST - Kosro, Levine & Boyd) • NH10: ADP (GLOBEC - Kosro) NSB NMS NIS NH-10 • 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 90 km SSB SMS SIS Vectors: Depth- and time-aver model v

5. Model set-up: • POM (hydrostatic; primitive eqns; prognostic for u, SSH, T, S, q2, q2L; turbulence parameterization) • 220350 km, periodic OB conditions (south-north) • - Dx~2 km, 31 s-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 Alongshore wind stress (NMS site):

6. Optimal interpolation (OI): tf (a): forecast (analysis) state obst: 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) G = Pf HT (HPfHT+ C)1 C: data error covariance Pf: forecast error covariance (stationary estimate) Note: for OI, only Pf HTis needed

7. Forecast error covariance, Pf is computed using Pm, the estimate of the errors in the model, not constrained by data [Kurapov et al. MWR, 2002] Pm – including lagged model error covariances (to account for the effect of previously assimilated data) Pm – 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 (ntrue is replaced by the time-ave nm) • The resulting Pm is the mean of the correlations for 9 summers scaled by StD for year 2001. Theoretical models: propagating modes affect spatial structure of Pf Pf  aPm

8. NH10 Corr: 0.18 0.74 RMS: 7.8  5.5cm s-1 SSB Corr: 0.35 0.73 RMS: 9.5  6.6 cm s-1 SMS SIS 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. Distant effect of assimilating ADP currents (“Case 2”): Depth-ave alongshore current: Obs, no DA, DA NSB - Assimilate SSB & SMS - Improvement at Line N, NH10 Corr: 0.45 0.82 RMS: 6.7  5.05cm s-1 NMS Corr: 0.46 0.79 RMS: 11.3  7.9cm s-1 NIS Corr: 0.55 0.71 RMS: 13.5  10.8cm s-1 NH10 Corr: 0.18 0.63 RMS: 7.8  6.9cm s-1

10. Effect of assimilating ADP data on nearshore SSH Low pass filtered SSH at South Beach, OR (44o37.5’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 (sq): Cross-sections near Line S of moorings DA (SSB, SMS, SIS) SeaSoar (Barth et al.) no DA

12. MEAN Obs, no DA, DA (N ADPs), DA (SSB+SMS) Obs, no DA, DA (N ADPs) RMS diff Transect 10 Dissipation rate (e): model vs. microstructure data [Moum & A. Perlin] Plotted is log10(e)  Transect 10

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

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

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

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, sqslope, e • 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