Bias: the unmentionable problem in ocean data assimilation

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Support JCSDA Grant Improving analysis of
tropical upper ocean conditions for forecasting

• Bias the unmentionable problem in ocean data
  assimilation
• Jim Carton and Gennady Chepurin
• (UMD)

• Bias in ocean data assimilation
• Two-stage bias correction algorithm
• SODA
• GODAS
• but, of course Im going to talk about it

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Bias is the difference between the state forecast
and the true state
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Forecast Bias

• Causes
• Errors in forcing
• Errors in initial conditions/data coverage
• Errors in physics parameterizations
• Errors in numerics

lt.gt Time-mean Annual harmonic ENSO-related etc.
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Bias in the ocean state estimate affects its
thermodynamic influence on the atmosphere
Climatological SST from ECHO2 coupled model
October
Cold bias
Frey et al., 1997
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Bias in ECMWF ENSO forecasts(1987-1999)
David B. Stephenson, http//www.met.rdg.ac.uk/home
/swr01cac/public_html/talks/bayes3.pdf
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SODA grid
(actual resolution is 4x)
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Simple Ocean Data Assimilation (SODA)

• Model POP-2
• Grid Global displaced pole with 0.4o x 0.25o
  tropical resolution, 25km resolution in Western
  North Atlantic, 50 levels (5m nearsurface)
• Physics KPP, nonlinear viscosity
• Forcing NCEP/NCAR reanalysis, ECMWF ERA40, GPCP
  precip, WMO river discharge, microwave Sea ice
• Method sequential estimation, flow-dependent
  covariance, explicit bias analysis including bias
  model
• Data
• Hydrography (MBTs, XBTs, CTDs, ARGO, Moored
  thermistor chains, stations, ship intake)
• Altimetry (Geosat, T/P, ERS1/2, Jason)
• Radiance SST
• Period 1940s-pres
• Availability Latest release December 2003

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SODA flow-dependent background error
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Gulf Stream in SODA
Hydro Observations
Sea level
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RMS sea level variability
Altimeter
SODA
GFDL
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SODA zonal vel. 0N, 140W
SODA
10m
OBS
50m
100m
150m
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SODA meridional vel. 0N, 140W
SODA
OBS
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Time-mean bias along equator
Cold tongue is too cold, while the thermocline
in the central basin is too diffuse
20C
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Annual cycle bias in the mixed layer
Histogram of In the North Pacific
Annual cycle of ML bias
amp
June
Dec
phase
The summer mixed layer is too cold, the winter
mixed layer is too warm
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Time-evolution of forecast error along equator
D20
Mixed layer T
Forecast error is episodic, linked to ENSO
Time ?
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Two stage algorithm to correct systematic aspects
of forecast error
Stage I
Stage II

• Alternative approaches Saha, 1992 Thiebaux and
  Morone, 1997 DelSole and Hou, 1999 DAndrea and
  Vautard, 2000 Griffith and Nichols 1996, 2000
• This follows Friedland (1969) , Dee and daSilva
  (1998)

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Three-term bias forecast model
ENSO-linked bias
Annual cycle bias
Time-mean bias
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Correcting time-mean bias
along Pacific Eq
20C
This is business as usual
This is what results when time-mean bias is
modeled
20C
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Correcting time-mean bias
along Pacific Eq
20C
This is business as usual
This is what results when time-mean bias is
modeled
20C
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Correcting time-mean bias
Corr time-mean bias
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Correcting time-mean bias
Corr time-mean bias
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Correcting annual cycle bias
June
Dec
Business as usual
Annual cycle bias correction
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Correcting annual cycle bias
June
Dec
Business as usual
Annual cycle bias correction
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Annual cycle of forecast error before correction
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Annual cycle of forecast error after correction
After
Before
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Correcting ENSO bias
CorEOF1,SOI 0.7
before
after
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Correcting ENSO bias
CorEOF1,SOI 0.7
before
after
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Summary of the impact of bias correction
Thermocline depth
ML temp
time mean
annual cycle
ENSO variability
RMS (fcst-obs)
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RMS (fcst obs)
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Summary

• Half of the forecast observation differences
  in high variability regions are due to bias. The
  largest contribution is time-mean followed by
  annual cycle and interannual variability.
• Two-stage correction works well in addressing
  these.

Manuscript available http//www.atmos.umd.edu/c
arton/bias
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NCEP GODAS
OGCM Global MOM v.3
Data Assimilation 3D VAR
Observations XBTs TAO P-Floats Altimetry
Oceanic I.C.for Coupled Model
Analyzed Fields Temperature Salinity
Surface Fluxes Momentum Heat E - P
Statistical Models CCA, Markov
ENSO Monitoring
From Dave Jiande
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NCEP GODAS products

• An ocean reanalysis extending from 1979 through
  the present has been completed. It is forced by
  daily fluxes from the NCEP Reanalysis 2 and saved
  at 5-day intervals.
• Operational ocean analyses are forced by daily
  fluxes from the NCEP GDAS and saved at daily
  intervals.

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Data coverageinhomogeneities,differences
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Zonal velocity at 0N, 110W
SODA
GFDL
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Temperature salinity characteristics
NCEP may have some problems with AAIW
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ltTf Togt meanat three depths
GODAS
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ltTf Togt mean along Equator

• Errors in forcing ?

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Annual cycle of ltTf Togt at depth 5m
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Annual cycle of ltTf Togt at depth 100 m
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Annual cycle of ltTf Togt along equator
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Developing a cost function for bias analysis
Where, e.g. bias estimate
This will need to be coded, but the code follows
the current 3D-var code, so wont be done from
scratch
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Then the state analysis cost function becomes
where
From a programming point of view all of this is
already in place.
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Some conclusions

• Explore data set differences
• Further algorithm development
• Mixed layers
• Considerable potential for two-stage bias
  correction

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The End