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
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)]([)(}{ 1 priordk Lb qdCRb
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priornew b rqq
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ttttdtdtJ eCeeCeeCeq 1
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kr
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00)0( eqq prior
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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)
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
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