A multi-scale three-dimensional variational data assimilation scheme

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A multi-scale three-dimensional variational data
assimilation scheme

• Zhijin Li, , Yi Chao (JPL)
• James C. McWilliams (UCLA), Kayo Ide (UMD)

The 8th International Workshop on Adjoint Model
Applications in Dynamic Meteorology May 18-22,
2009, Tannersville, PA
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Outline

• Motivations
• A multi-scale three-dimensional variational data
  assimilation (MS-3DVAR) scheme
• Applications and evaluations
• Summary

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Data Assimilation and Forecast Cycle
Time scales comparable with those of the
atmosphere
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Observations and Data assimilation

• T/S profiles from gliders
• Ship CTD profiles
• Aircraft SSTs
• AUV sections
• HF radar velocities

AOSN-II
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TEMP(C)
Glider temperature/salinity profiles
(Chao et al., 2009, DSR)
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Challenge An Example with SCCOOS
Model domain, the resolution of 1km
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Southern California Coastal Ocean Observing
System (SCCOOS)
Aug 2008, simulation without DA
SIO Glider Tracks
Challenge How to assimilate sparse vertical
profiles along with high resolution observations
for a very high resolution model
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Data Assimilation Formulation
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Error Covariance and correlations
Correlations are the vehicle for spreading out
information of observations Correlation scales
are about 15-30km
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Forecast Error Covariance BSingle Observation
Experiment
(increment)

One single observation of SSH
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Southern California Coastal Ocean Observing
System (SCCOOS)
SIO Glider Tracks
Motivation assimilating sparse vertical profiles
along with high resolution observations for a
very high resolution model
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Multi-Scale Data Assimilation Concept
SCCOOS Glider Tracks
(Boer, 1983, MWR)
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Multi-Scale Data Assimilation Scheme
Low Resolution (LR)
SCCOOS Glider Tracks
Sparse Obs
High Resolution (HR)
High resolution HF radar
High Resolution Obs
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Work Flowchart of MS-3DVAR
Satellite SST/SSH
HF Radar
Glider/Argo/Mooring
Smoothed
LR-3DVAR
HR-3DVAR
End
Smoothed
Forecast
Increment
Start
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Glider Observations vs Analyses
Aug 2008
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CALCOFI Observations
(not assimilated)
Aug 14-30, 2008
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Monthly Means
Aug, 2008
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Analysis vs HF Radar Observations
Taylor diagram
(Taylor, 2001, JGR)
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Forecasts vs Analyses
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Summary

• A multi-scale 3DVAR (MS-3DVAR) scheme has been
  formulated and developed.
• It has been implemented in support of SCCOOS and
  AOOS-PWS.
• The scheme has demonstrated the capability of
  assimilating sparse and high resolutions
  observations simultaneously, effectively and
  reliably.

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Alaska Ocean Observing System -Prince William
SoundAOOS-PWS
3 nested levels L0 / L1 / L2. Resolution 10km
/ 3.6km / 1.2 km (L2 Prince William Sound)
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Oil Spill 1989 Exxon Tanker Wreck Prince
William Sound, Alaska
March 24, 1989
From USGS
Today
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Decomposition of Large and Small Scalesand
Estimation of Error Covariance

• Generate perturbations difference between 24h
  and 48h forecasts, valid at the same time.
• Decompose perturbations
• Large scales smoothed fields, with weight
  of
• where L25km, which is the decorrelation
  length scale from Russs estimation
• Small scales the residuals

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Observational Errors Representativeness Errors

• Large scale observations T/S vertical profiles
  from SIO, mooring and Argo
• Observational errors at the depth of z
• Tentative values briefly and empirically
• estimated from the RMS profile of the small
• scale components

For temperature
For salinity
CALCOFI Section
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Future Coastal Observing System
(National Research Council, 2003)

• Buoy and glider profiles are sparse, with
  distances between profiles
• larger than decorrelation scales
• Radar and satellite measurements may have very
  high resolutions,
• as high as the model resolution

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Glider Temperature and Salinity Profiles
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Surface Tidal Current Comparison (M2)
Length of Major Axis (cm/s)
Corr. RMS Mean Sept. 0.43
3.6 6.6 Oct. 0.44 3.8
6.6 Nov. 0.51 3.7 6.3
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A There-Dimensional Variational Data Assimilation
(3DVAR)

• Real-time capability
• Implementation with sophisticated and high
  resolution model configurations
• Flexibility to assimilate various observation
  simultaneously
• Development for more advanced scheme

(Li et al., 2006, MWR Li et al., 2008, JGR, Li
et al., 2008, JAOT)