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

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]

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

90 k

m

NSB NMS NISNSB NMS NIS

SSB SMS SISSSB SMS SIS

NH-10NH-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

Model set-up:

Alongshore wind stress (NMS site):

- POM (hydrostatic; primitive eqns; prognostic for u, SSH, T, S, q2, q2L; turbulence parameterization)

- 220350 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

Optimal interpolation (OI):

,a ft t t POMν ν

( )a f ft t t t ν ν G obs Hν

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)

C: data error covariance

Pf: forecast error covariance (stationary estimate)

Note: for OI, only Pf HT is needed

G = Pf HT (H Pf HT + C)1

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 (true is replaced by the time-ave m)

- 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 Pm

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

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

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 11 (assim N ADPs) and 2 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

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.)

Dissipation rate () model vs. microstructure data [Moum & A. Perlin]

32 3

2

POM:

(m s ),16.6

where is TKE 2

is turb. length scale

q

L

q

L

Plotted is log10() Transect 10

Obs, no DA, DA (N ADPs), DA (SSB+SMS)

MEAN

RMS diff

3 3 (m s )

min 30 m, / 2

H

Hdz

H

Obs, no DA, DA (N ADPs)

Transect 10

Model-obs temperature correlation vs. depth, at COAST mooring sites

No DA, DA Case 2(vert. axis tickmarks are each 10 m)

NSB NMS NIS SSB SMS SIS

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-3Also looking at:

surface current, SST, bottom stress, cross-shore transport…

Model sensitivity to assimilation of data from 1 mooring

Actual performance:

Expected (compare diag (Pm) and (Pa), where Pa = Pf – G H Pf):

DA is better than model only solutionDA is worse than model only solution

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