Advantages of data assimilation in coastal ocean circulation models: Oregon perspective

Alexander L. Kurapov, J. S. Allen, G. D. Egbert, R. N. Miller COAS/Oregon State University

In cooperation with P. M. Kosro, M. D. Levine, T. Boyd, J. A. Barth, J. N. Moum, P. T. Strub, S. Erofeeva29 January 2004, AGU/Ocean Scienceshttp://www.coas.oregonstate.edu/po/research/kurapov/main.html

wind stress (upwelling favorable) is dominant forcingstrong effects of flow-topography interactionsenergetic internal tide Summer circulation on the Oregon shelf: Summer 2001: DA system is implemented with data from COAST observational program Data assimilation: improves prediction of the ocean state, provides solution error estimates, is used as a tool for data synthesis, helps to design an observational system (e.g., suggests optimal observational locations)

Dual approach:Objectives:to develop practical, but still nearly optimal methods for the assimilation of data into coastal circulation modelsto apply these methods to measurements from the Oregon shelfto utilize DA to increase scientific understanding of shelf circulation

Variational(generalized inverse)DA method Simpler, sequential(optimal interpolation)Linearized Dynamics Fully non-linearInternal tides Application Wind-driven circulation

Model of of M2 internal tide [Kurapov et al., JPO 33, 2003] - linearized, primitive eqns, 3D, periodic in time [~exp(iwt)]- terrain following coordinatese.g., momentum equations:HF (P. M. Kosro)HFADPModel domain: 40 60 km, Dx=1 km, 21 s-layers Zone of coverage of 2 HF radars (May-July 1998) Efficient model solver (direct factorization of the model operator) Address open boundary issuesMost internal tide comes from outside the computational domainDA: corrects open boundary baroclinic flux

Generalized Inverse Method (GIM):Solution minimizes a cost function:Cost Function = || Model error ||2 + || BCond error ||2 + || Obs error ||2 min

Explicit statistical assumptions about errors in the inputs Statistics in the output (prior model and inverse solutions) are computed [Bennett, 1992, 2002]State vector: v = {velocity, sea surface elevation, density}Model+BCond: S v = f + emData: L v = d + ederrors in model forcing and dataspecified prior to assimilation

Use of Representers: Model+BCond: S v = f + emData: L v = d + edAdjoint solverFwd solverReduce burden of representer computation with: reduced basis representer approach indirect representer approach [Egbert et al., JGR, 1994] HF radars: K=900 locations where radial velocity components are available Standard feature in Inverse Ocean Modeling system [IOM, Chua and Bennett, Ocean Modeling, 2001]voStrongly constrained dynamics:

Solution sensitivity to the choice of model error covariance COB (in an experiment with synthetic data)-true solution: forced at open boundary (OB) with a significantly baroclinic fluxsynthetic data (velocity harmonic constants) are sampled from true solution prior model: forced with depth-averaged OB current DA: corrects OB baroclinic fluxes Depth-ave RMS error with respect to true solutionPriorDA, COB (Type I)DA, COB (Type II)these two solutions allow for OB b/clinic correction of the same magnitude (but different correlation structure)

DA COB (Type I) is obtained by nesting approach:In a large domain, compute representers for small domain boundary datathen sample these representers along the OB of small domain COB (covariance for the errors on the OB of the small domain, with a dynamically consistent spatial structure)

COB controls radiation at an open boundary representer column of prior solution error covariance matrixCOB (Type II): our best guess w/out nesting

A series of M2 tidal solutions, May-July 1998Internal tide intermittence: analysis in 2-week overlapping time windowsDA: in each time windowValidation ADPDA solutionNo DAdeviations from depth-ave. (CW)depth-ave (rotating CCW)Assimilation of HF surface currents improves prediction at depthTidal ellipses of horizontal currents at ADP location, vs depth: (a) observed, (b) prior model, (c) DA.ADP

M2 tidal ellipses on the surface: internal tide velocities can be twice as large as barotropic tidal velocitiesCCW rotationCW rotationDepth-aveDeviations from depth-ave (time window centered on day 139)

Energy balance is closed : Data assimilation corrects only boundary inputs40 W m-1Most baroclinic signal comes into the computational domain from outsideSome persistent features are found: e.g., baroclinic phase and energy propagation is from NW.Terms in the baroclinic energy equation (time and space averaged)Baroclinic energy flux (depth-integrated and time-ave.)

Baroclinic KE averaged over a series of days 139-167: a) surface, b) bottom, c) cross-section north of Stonewall Bank, d) cross-section through Stonewall Bank.Zones of higher KE variability are aligned along the coast, consistent with energetic of a internal Poincare waveinteraction with bathymetryDominance of 1st baroclinic modebeams over Stonewall BA series of tidal solutions (constrained by HF radar data) provides a uniquely detailed description of spatial and temporal variability of M2 internal tide

Model of wind-driven circulation:Princeton Ocean Model: 220350 km, periodic OB conditions (south-north), Dx~2 km, 31 s-layersForcing: alongshore wind stress, heat flux

Data assimilation: Optimal Interpolation

Initial implementation (summer 1998): assimilation of HF radar data improves modeled circulation at depth [Oke et al., JGR-Oceans, 2002]

Data from COAST program (summer 2001): assimilate moored ADP currents

Optimal Interpolation (3DVAR):matrix matching observations to state vector ||Error||Timemodel w/out DADAforecastanalysisForecast error covariance (stationary in OI): Pf = Pm F (lagged Pm, Cd) where Pm is the covariance of errors in the model solution not constrained by the data (in contrast, Pf is conditioned upon previously assimilated data) [Kurapov et al., Mon. Wea Rev., 2002] Pf has a shorter horizontal scale in the alongshore direction than Pm (effect of propagation) Pm: could be obtained as representer calculation, if an adjoint model were available Presently, Pm is computed from an ensemble of model solutionsIncremental approach: correction is applied gradually over the analysis time window (1/4 of inertial period)

Spatial structure of Pf:NMS, 12m SSB, 16m [cm2 s-2]

Time- and depth-ave terms in the momentum eqn. (along-jet direction) no DADA (ADPs in south)Dominant dynamical balance is preservedSmooth, large scale correction (in this case, DA tends to reduce upwelling intensity)

Assimilation of moored ADP velocities (May-Aug 2001):90 kmCentral part of model domain with mooring locations, Bathymetry each 100 m (black) and 10 m (half-tone, from 0 to 200 m)Moorings: Lines N and S COAST (Kosro, Levine, Boyd), NH10 GLOBEC (Kosro)Study is focused on: Distant effect of data assimilation Multivariate capabilities (effect on SSH, isopycnals, temperature, salinity transport, turbulent dissipation rate)

Case 1: assimilate currents at Northern Line improve currents at NH10, SSB

Correction can be advected by a predominantly southward current90 kmADP sites, May-Aug 2001Assimilated ADP sitesSites where DA is better than model only solution (smaller model-data rms error, larger correlation) NH10SSBrmse: 7.8 5.8 cm s1, corr: 0.18 0.71rmse: 9.6 7.1 cm s1, corr: 0.36 0.70Alongshore depth-ave current: obs, no DA, DA

Case 2: assimilate ADP currents at Southern Line improve currents up North

Correction can be propagated northward with coastal trapped wavesNMSNH10rmse: 11.3 7.9 cm s1, corr: 0.46 0.79rmse: 7.8 6.9 cm s1, corr: 0.18 0.63Alongshore depth-ave current: obs, no DA, DA

Posterior error statistics analysisE.g., compare expected and actual analysis rms error as a consistency test for Pf Expected performancediag (Pm) and (Pa) are compared, where Pa = Pf G H Pf is the analysis error covarianceActual performanceDiscrepancy between expected and actual outcome when assimilating inner-shelf data : artificially large decorrelation scale in Pf inclusion of a more realistic spatially varying wind stress is a necessity

Multivariate capabilitiesno DADA (South)SeaSoar measurements (Barth et al.)e.g., effect on SSH (validation - tide gauge data):effect on isopycnal slope:Model-data Corr.: 0.51 0.78, rmse: 5.4 3.8 cmSSH: obs, model only, DA (Lines N+S)(white contours are measured sq= 24, 25, and 26 kg m-3) + improvement in temperature correlations, surface salinity transport

Turbulent Dissipation rate (e): Microstructure data [J. Moum, A. Perlin]No DADA (North)12 transects on Line Nyearday, 2001 Time series of e averaged near bottom (in box area)DA correction in near-bottom velocity field yields improvement in eAnalysis of BBL dynamics is extended for the whole study period presentation OS52I-08

http://www.coas.oregonstate.edu/po/research/kurapov/main.htmlSUMMARY: Progress has been made on both aspects of the dual approach to coastal ocean DALinearized dynamics, variational DA (internal tides)has provided unique information on spatial and temporal variability of internal tide from HF radar measurements of surface currentshas given us experience in open boundary DANonlinear dynamics, sequential OI DA (wind-driven circulation)- has shown the value of assimilation of currents from HF radar and from moored ADPs (distant effect, multivariate capabilities, BBL analysis)has provided information on optimal ADP mooring locations and on effective alongshore scales of ADP current measurementsIn both cases, formulation of error hypotheses is the science and art of DA DA is utilized to increase scientific understanding of shelf circulation

PLANNED RESEARCH:Merger of approaches: use tangent linear and adjoint codes for a fully non-linear ocean circulation model (ROMS)Use data assimilation to help provide open boundary conditions for high-resolution limited-area coastal modelsTidal research: study effect of wind-forced subinertial flows on internal tide propagationStudy of wind-forced upwelling circulation: analyze cross-shelf transport, bottom boundary layer processes, dynamical balances