# Presentation: 534418

## Bias: the unmentionable problem in ocean data assimilation*

Jim Carton and Gennady Chepurin 
(UMD)

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

- Support: JCSDA Grant “Improving analysis of tropical upper ocean conditions for forecasting”

- Bias in ocean data assimilation
- Two-stage bias correction algorithm
- SODA
- GODAS
- 					*{but, of course I’m going to talk about it}

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

## Forecast Bias

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

- <**.**>
- Time-mean
- Annual harmonic
- ENSO-related
- etc.

## Bias in the ocean state estimate affects its thermodynamic influence on the atmosphere

- October

- Frey et al., 1997

- Climatological SST from _ECHO2_ coupled model

- Cold bias

## Bias in ECMWF ENSO forecasts(1987-1999)

- David B. Stephenson, http://www.met.rdg.ac.uk/home/swr01cac/public_html/talks/bayes3.pdf

- Bias in ECMWF ENSO forecasts(1987-1999)

## SODA grid

- (actual resolution is 4x)

## 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

## SODA flow-dependent background error

**Notes:**
Region 2 picture is screwed up

## Gulf Stream in SODA 

- Hydro
- Observations

- Sea level

## RMS sea level variability

- Altimeter

- SODA

- GFDL

## SODA  zonal vel. 0N, 140W

**SODA**  zonal vel. 0N, 140W

- SODA

- OBS

- 10m

- 50m

- 100m

- 150m

## SODA  meridional vel. 0N, 140W

**SODA**  meridional vel. 0N, 140W

- SODA

- OBS

## Time-mean bias along equator

**20C**

- “Cold tongue is too cold, while the thermocline in the central basin is too diffuse”

## Annual cycle bias in the mixed layer 

- Annual cycle bias in the mixed layer

- June

- Dec

- Histogram of
- In the North Pacific

- “The summer mixed layer is too cold, the winter mixed layer is too warm”

- Annual cycle of ML bias

- amp

- phase

## Time-evolution of forecast error along equator 

- “Forecast error is episodic, linked to ENSO”

-  D20

- Time 

- Mixed layer T

## 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*; *D’Andrea and Vautard, 2000; Griffith and Nichols 1996, 2000*
- This follows: *Friedland (1969) , Dee and daSilva (1998)*

## Three-term bias forecast model

**Time-mean bias**

**Annual cycle bias**

**ENSO-linked bias**

## Correcting time-mean bias

- along Pacific Eq

- This is business as usual

- This is what results when time-mean bias is modeled

**20C**

**20C**

## Correcting time-mean bias

- along Pacific Eq

- This is business as usual

- This is what results when time-mean bias is modeled

**20C**

**20C**

## Correcting time-mean bias

- Corr time-mean bias

## Correcting time-mean bias

- Corr time-mean bias

## Correcting annual cycle bias

- Business as usual

- Annual cycle bias correction

- June

- Dec

## Correcting annual cycle bias

- Business as usual

- Annual cycle bias correction

- June

- Dec

## Annual cycle of forecast error before correction

## Annual cycle of forecast error after correction

- Before

- After

## Correcting ENSO bias

- before

- after

- CorEOF1,SOI = 0.7

## Correcting ENSO bias

- before

- after

- CorEOF1,SOI = 0.7

## Summary of the impact of bias correction

- time mean

- +annual cycle

- +ENSO variability

- RMS (fcst-obs)

- ML temp

- Thermocline depth

## RMS (fcst – obs)

## 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.

- 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/~carton/bias}

- Summary

## NCEP GODAS

- Global
- MOM v.3

- Data
- Assimilation
- 3D VAR

- Observations:
- XBTs
- TAO
- P-Floats
- Altimetry

- Analyzed
- Fields:
- Temperature
- Salinity

- Oceanic I.C.for
- Coupled Model

- Statistical Models
- CCA, Markov

- ENSO
- Monitoring

- Surface
- Fluxes:
- Momentum
- Heat
- E - P

***From Dave & Jiande***

## 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.

## Data coverageinhomogeneities,differences

## Zonal velocity at 0N, 110W

**SODA**

**GFDL**

## Temperature – salinity characteristics

**NCEP** may have some problems with AAIW

## <Tf – To> {mean}at three depths

- GODAS

## <Tf – To> {mean} along Equator

- <Tf – To> {mean} along Equator

- Errors in forcing  

## Annual cycle of <Tf – To> at depth = 5m

## Annual cycle of <Tf – To> at depth = 100 m

## Annual cycle of <Tf – To> along equator

## 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 won’t be done ‘from scratch’}*

## Then the state analysis cost function becomes:

- where:

*{From a programming point of view all of this is already in place.}*

## Some conclusions

- <date/time>

*Some conclusions*

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

## The End