# Presentation: 536279

## The GMAO Ocean EnKF and Application to the Assimilation of Altimetry Data  Christian Keppenne1, Michele Rienecker, Jossy Jacob1, Robin Kovach1, Chaojiao2 Sun, Shu-Chih Yang3, Yelena Marshak Global Modeling and Assimilation OfficeNASA Goddard Space Flight CenterGreenbelt, MD 207711SAIC 2University of Maryland Baltimore County3University of Maryland  College Park JCSDA Science Meeting, May 1-2, 2007

## GMAO Ocean Data Assimilation System (ODAS-1)

**Algorithms:**
**- ****Univariate optimal interpolation (UOI): functional error covariances**
**- Multivariate OI (MvOI): steady-state ensemble based error representation **
**- Multivariate EnKF**
**Model:**
**- Poseidon v4 OGCM ****(Schopf and Loughe, 1995)**** :**
**Quasi-isopycnal vertical coordinate**
**Prognostic variables are *****h*****, *****t*****, *****s*****,***** u***** and *****v***
**Sea surface height (SSH) is diagnostic: ******** = ********i****buoyancy(t****i****, s****i****)h****i****/g **
**538 x 572 x L27 ((1/3° x 5/8° x L27): ****About 30 million prognostic variables**
**Observations:**
**- UOI: T, S **
**- MvOI: T, S, SSH**
**- EnKF: T, S, SSH**
** **

**ODAS-2**
**Algorithms:**
**- ****UOI: tested **
**- MvOI: tested**
**- EnKF: upcoming**
**Models:**
**- Poseidon v5: tested**
**- MOM v4: development**
**- MITGCM: upcoming**
**Why a new system?:**
**- Adherence to ESMF gridded component paradigm  **
**- Model independent & enhanced portability**
**- Main new features: **
**Faster analysis**
**Analysis conducted at any arbitrary resolution**
**Supports multi-model, multi-resolution ensembles**
**OMF calculation at observation time**
**4-D (x, y, z, 1/t) error-covariance specification**
**No code changes required to include new data types**

## Ocean EnKF (MWR 130, 2951-2965, 2002; JMS  40-41, 363-380, 2003; NPG 12, 491-503, 2005)

** ****Multivariate compactly supported background covariances: updates T, S, u & v**
** ****Massively parallel**
** ****System noise representation: **
** ****Random linear combinations of model-state EOFs to simulate model errors**
** ****Forcing perturbations to simulate forcing errors (colored spectrum in space and time)**
** ****Online bias correction (used in SSH assimilation)**

**Challenge****: ****Transit EnKF from R&D status to a production application**
**  ****Match the performance/outperform production ODAS**
**  ****Good performance with very small ensembles**

**EnKF validation experiments**
**Assimilate T/P SSH anomalies + TAO & XBT temperature profiles 1/1/2001-12/31/2001**
**Online bias estimation in SSH assimilation**
**4 runs: 9, 17, 33 & 65 member EnKF**
**Compare with **
**no-assimilation control**
**Production ODAS (temperature OI + S(T) correction)**

## First attempt to assimilate T/P anomalies with ENKF (2001)

**First attempt to assimilate T/P anomalies with ENKF (2001)**

## Improving the performance for small ensembles

**Spatio-temporal filtering of background-error covariances**
** ****Temporal filter applied to X****f**** integration (exponential moving average)**
** ****Spatial filter applied to (X****f**** -<X>) deviations (Gaussian filter)**

**Time filter:**

**Compactly supported EnKF (bias estimation omitted)**

## Effect of spatial filtering

** ****Example of marginal Kalman gain: T obs @(0n,156E,150m) on 12/31/01**
** ****horizontal section through <T’,T’> covariances**

## Effect of spatial filtering

** ****Example of marginal Kalman gain: T obs @(0n,156E,150m) on 12/31/01**
** ****horizontal section through <T’,T’> covariances**

** ****Filtering increases correlation of Kalman gain with corresponding raw (no filter, globally supported) gain from EnKF-65 run**
** ****Especially for very small ensembles, the filter “simulates” the covariances one would get from a larger ensemble**

## Temporal evolution of Kalman gain for T obs.

**EnKF-33: filter**
**Schur(C,P) @(0N,156E,150m)**

**Temporal evolution of Kalman gain for T obs.**

## Temporal evolution of Kalman gain for SSH obs.

**EnKF-33: filter**
**Schur(C,P) @(0N,156E,150m)**

## SSH passive

**SSH passive**

## Validation with December 2001 ADCP zonal currents

**Validation with December 2001 ADCP zonal currents**

## Impact of assimilation on CGCM hindcast skill
17-member EnKF
Assimilate T + SSH for February-April of each year from 1993 to 2002
Couple OGCM to AGCM & LSM after running ODAS
12-month May start CGCM hindcasts initialized with ocean from EnKF runs
	(to save CPU time, EnKF-initializedCGCM hindcasts have only 5 ensemble member) 

Assess impact of assimilation on SST hindcast skill
Compare to history of production May-start hindcasts

**17-member EnKF**
**Assimilate T + SSH for February-April of each year from 1993 to 2002**
**Couple OGCM to AGCM & LSM after running ODAS**
**12-month May start CGCM hindcasts initialized with ocean from EnKF runs**
**	****(to save CPU time, EnKF-initializedCGCM hindcasts have only 5 ensemble member) **
**Assess impact of assimilation on SST hindcast skill**
**Compare to history of production May-start hindcasts**
**	**

## May start Niño-3.4 SST hindcasts

## May start SSH hindcasts

**May start SSH hindcasts**

## Conclusions

**Analysis speed up makes it practically feasible to use the EnKF in the production forecast initialization **
**	****Small ensemble EnKF can outperform production system provided background covariances are appropriately preconditioned**

**Ongoing work**
**More hindcast experiments with EnKF and Poseidon v4 (Robin Kovach)**
**ODAS-2 testing and development: towards multi-model multi-resolution EnKF**
**Investigating use of bred vectors (Shu-Chih Yang): **
**- in lieu of model EOFs in MvOI**
**- in EnKF system noise model and initialization **