Variational Assimilation of HF Radar Variational Assimilation of HF Radar Surface Currents into the Coastal Ocean Surface Currents into the Coastal Ocean

Circulation Model off Oregon Circulation Model off Oregon

Peng YuPeng Yu

in collaboration with Alexander Kurapov, in collaboration with Alexander Kurapov, Gary Egbert, John S. Allen, P. Michael KosroGary Egbert, John S. Allen, P. Michael Kosro

College of Oceanic and Atmospheric SciencesCollege of Oceanic and Atmospheric SciencesOregon State UniversityOregon State University

Supported by ONR

Complicated dynamics on the shelf in the coastal transition zone (CTZ):

-Strong upwelling season-Modeling sensitive to many factors (model resolution, horizontal eddy viscosity, bathymetry, boundary conditions, forcing) -Use data assimilation to improve prediction, forecasting, and scientific understanding of shelf and CTZ flows 6-km, visc=10 m2/s

Model details:

Regional Ocean Modeling System (ROMS)

- 6km horizontal resolution and 15 vertical level- NOOA -NAM wind & heat flux- NCOM-CCS boundary conditions (Shulman et al., NRL)

(shown: SST Jul. 20, 2008)

Summer 2008: available observations

- HF radar surface velocities (daily maps, provided by PM Kosro, OSU)Combination of several standard and long-range radar provides time-series info about shelf,

slope and CTZ flows

- SSH along track altimetry (Jason, Envisat)

- satellite SST maps (D. Folley, NOAA CoastWatch)

- gliders (T and S sections, once every 3 days, J Barth and R. K. Shearman, OSU) – 3D information

Bathymetric contours: 1000 and 200 m)

How does each of these data types contribute to data assimilation?

Variational (representer-based) data assimilationin a series of 3-day time windows, June 1– July 30, 2008:

In each window, (1)correct initial conditions (use tangent linear &adjoint codes AVRORA, developed at OSU, Kurapov et al., Dyn. Atm. Oceans, 2009)(2)run the nonlinear ROMS for 6 days (analysis + forecast)

assim (TL&ADJ AVRORA)forecast (NL ROMS)

prior

analysisforecast

The representer-based DA systemThe representer-based DA system

T

kk tttdtt 0

111 )(),(][ λCrqAr

)0()0( 0λCr k

)]([)(}{ 1 priordk Lb qdCRb

k kk

priornew b rqq

ddd

TT

ttttdtdtJ eCeeCeeCeq 1

0100221

11

0

2

0

1 )(),()()(

kr

efqq

priorNt

)(

00)0( eqq prior

dL edq )(

the representer function

)(, jiji L rR

• Indirect method is Indirect method is computationally more efficientcomputationally more efficient

• Conjugate Gradient methodConjugate Gradient method

• Preconditioned Conjugate Preconditioned Conjugate GradientGradient

Indirect method (Egbert et al. 1994; Chua and Indirect method (Egbert et al. 1994; Chua and Bennett, 2001)Bennett, 2001)

hqdbCR ))(()( priord L

))(min( 21 hbbCRb d

Forecast model

Adjoint model

Tangent Linear model….

1r

MrkrPrecondition

AR

….

Conjugate Gradient (5-10 steps)

b

T

T

NCCA

211112121

2111|RRRR

RRRRR (Egbert, 1997)

Task Parallel

Initial Condition Error Covariance (Dynamically balanced):

multivariateu, v, SSH, T, S – geostrophy, thermal-wind

Implement the balance operator A (Weaver et al. 2005):

)0()0(0 TSAACC

univariate covariance for mutually uncorrelated fields s

Adj solution at ini time

A: Uncorrelated fields: error in T and depth-integrated transport (uH, vH)

S (using constant T-S relationships) horizontal density gradients vertical shear in u, v (thermal wind balance) SSH (2nd order ellipitic eqn.) u, v (surface current in geostrophic balance with SSH)

Observed and prior model SST and surface currents

Initial test with one 3-day assimilation window Initial test with one 3-day assimilation window (balanced covariances better in SST forecast)(balanced covariances better in SST forecast)

RMSE

Correlation

Surface Velocity SST (not assimilated)

Analysis Forecast Analysis Forecast

SST data provided by D. Foley, NOAA CoastWatch

Same experiment: extend the forecast to 15days

SST (not assimilated)Surface Velocity

RMSE

Correlation

Analysis Forecast Analysis Forecast

SST RMSE and correlation are improved for 15 days, after the 1st assimilation cycle

Balanced better

60-day assimilation (June 1-July 30, 2008; 20 assimilation 60-day assimilation (June 1-July 30, 2008; 20 assimilation windows): Both Surface velocity and SST are improvedwindows): Both Surface velocity and SST are improved

RMSE

Correlation

Surface Velocity SST (not assimilated)

Model data comparison: Surface currents (assimilated) and SST (not assimilated)

Assimilation of HF radar surface currents improves the geometry of the upwelling SST front

The time-averaged sea surface currents field: more uniform cross-shore transport than in prior

Observation Prior Forecast Analysis

The mean and variance ellipses of the model-data difference

Mean: Obs-Prior

Variances Mean: Obs-Forecast

Mean: Obs-Analysis

Variances Variances

Verification SSH, prior, HF radar velocity assimilation

Assimilation of HFR data improves SSH, compared to along-track altimetry (not assimilated) in the area covered by the HF Radar

Data coverage

Cont. (another pass)

Data coverage

Verification SSH, prior, HF radar velocity assimilation

Observation PriorAnalysis

(balanced)Analysis

(Imbalanced)

Comparison against Hydrographic data

-The assimilation of the HF Radar surface currents data improves the density structure in the hydrographic sections south of Cape Blanco in the separation zone

Data provided by Bill Peterson and Jay Peterson)

NH

CC

RR

Summary• The representer-based data assimilation system

improves the forecast of the model variables (e.g. SST, surface currents, SSH, density)

• The assimilation of unique set of long-range HF radar observations has a positive impact on the area of the shelf, slope and part of the open ocean

• Assimilation of the HF Radar radial component might be advantageous

• A combination of different types of observations is being pursued