# Presentation: 850096

## NOAA THORPEX PI WORKSHOPJanuary 17-19, 2006, Camp Springs, MD Assimilation of real observations using the GFS model and the Maximum Likelihood Ensemble Filter Milija Zupanski and Arif AlbayrakCooperative Institute for Research in the AtmosphereColorado State UniversityFort Collins, CO 80523-1375E-mail: ZupanskiM@CIRA.colostate.edu

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## Outline

**Maximum Likelihood Ensemble Filter (MLEF)**
**Hessian preconditioning**
**THORPEX related research**
**Details of algorithm implementation on the NCEP computers**
**Preliminary results with GFS T62L28 and real observations**
**Future**

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## Maximum Likelihood Ensemble Filter (MLEF)(Zupanski 2005, MWR; Zupanski and Zupanski 2006, MWR)

- Estimate of the ***conditional mode*** of the posterior PDF
- Ensembles used to estimate the ***uncertainty*** of the conditional mode
***Non-differentiable*** minimization with Hessian preconditioning:
- 	(Generalized conjugate-gradient and BFGS quasi-Newton algorithms)
- Augmented control variable: ***initial conditions***, ***model bias***, ***empirical parameters***, ***boundary conditions***
***Not*** sample based
- Becomes the Reduced-Rank KF for linear operators and Gaussian PDF
- Error covariances computed from minimization, not from a sample

***MLEF currently implemented with:***
-  Carbon and biosphere transport models: **LPDM**, **PCTM**, **SIB** (D. Zupanski)
-  **GEOS-5** column model (D. Zupanski)
-  **RAMS** CSU non-hydrostatic model: Mesoscale, LES (D. Zupanski)
-  CSU **Shallow-water **model (M. Zupanski)
-  NCEP **GFS** model (M. Zupanski)
-  **Ensemble Cloud** Model (NASA) + Super Parameterization (M. Zupanski)

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## Forecast (prior) error covariance

**Control vector is the *****most likely***** forecast**
**Square-root used in the algorithm **(full covariance can be calculated)
**No sampling of error covariance**
**Provides dynamic continuity between the analysis and forecast**

**Ensemble size**

**State-space dimension**

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## MLEF Analysis Step

**Minimize cost function in the subspace *****spanned by ensemble perturbations***

**Similar to variational, however:**** **
**Non-differentiable iterative minimization with superior preconditioning**
**Solution in ensemble subspace (reduced rank)**
**Analysis uncertainty estimate**

**Analysis increment is a linear combination of  *****p****f*** ****vectors**

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## Hessian preconditioning in MLEF

**Change of variable (Hessian preconditioning)**

*k* – iteration index

**Use ETKF transformation in Hessian preconditioning**

- Ensemble-size matrix

- Background (first guess)

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## Analysis (posterior) error covariance

**Analysis error covariance estimated from minimization algorithm**
**At the minimum: *****Inverse Hessian = Analysis error covariance***

- Analysis (minimizer)

***Conjugate-gradient algorithm:***

***Quasi-Newton algorithm:***

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## THORPEX related research

**MLEF with T62L28 GFS and real observations**
-  Code development completed and debugged
-  GFS model + interpolation from model to observations (using the SSI code)
-  Currently tested PREPBUFR observations, will include satellite/radar/lidar
**Compare MLEF with other EnKF methods**
-  Evaluate if dynamical localization holds
-  Ensemble size, robustness of the algorithm
-  Code efficiency: script driven algorithm, exploits the NCEP code structure
**Dual-resolution MLEF**
-  Control forecast in operational resolution, ensembles in coarse resolution
-  Save computational time, possible practical advantages
-  Test this capability, using two GFS resolutions (T62, T126)
-  Evaluate the ensemble size issue

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## Implementation on the NCEP computers (IBM SP - snow)

**MLEF Driving Script**
***Parallel programming***
***MLEF programs***
***Column matrix representation***
***On-the-fly LoadLeveler script submission for***** *****ensemble runs in parallel***
***Continuous data flow using observation dates***

**GFS model**
***Single script ***
***(ensemble or control)***

**Observation operator**
***SSI interpolation to observation location***
***QC obs: Setuprhsall.f90 ***

**Interface**

**Keep the original GFS and SSI directories, compilation separate from the MLEF**

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## Practical implementation issues

**MLEF is script driven (UNIX)**
-  Allows quick adjustment to the upgraded codes of GFS and SSI (GSI)
-  Minimal adjustment of the operational GFS and SSI scripts
-  Separate directories, original compilation
**Parallel ensemble runs**
-  Defined *number of ensembles* and *number of CPUs*
-  On-the-fly LL script optimally combines ensembles in groups
-  Run scripts in parallel, check when done
**Quality Control (QC) of observations**
-  SSI has a quality control of observations: Reject, Keep, Change obs error
-  Each ensemble run has its own QC, thus not necessarily the same outcome as the control
-  Critically important to keep track of the QC-ed obs in calculation

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## MLEF with GFS model and real observations: Preliminary Results

** ****Cold start on January 7, 2004, 06 UTC**
** ****4 data assimilation cycles**
** ****6-hour cycle**
** ****200 ensembles**
** *****Ensemble initiation*****: Random perturbation of spectral coefficients**
** *****Observations***** from NCEP operational file: **
**surface pressure, winds, temperature ~ 360,000 obs per cycle**
** ****Control variables: spectral coefficients -  T, *****ln(*****ps), div, vort**
** ****GFS T62L28 model**

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## Innovation vector frequency histogram

-  Insufficient width => overestimation of ***P****f ** *or* ****R ***?
* *Width improves* *with cycles (only 4 cycles at present, however)
-  Close to the Gaussian distribution *N*(0,1) => Adequate PDF assumptions, MLEF does not show divergence -  need more cycles

**Cycles 1-4**

## INFORMATION (TRANSFORM) MATRIX SPECTRUM

**Cycles 1-4: Eigenvalues **

-  Each cycle benefits from observations (*eigenvalues *< 1)
* *Similar, steady improvement in cycles 2-4 => expected to continue

## Future

**Complete GFS + MLEF + real observations experiments**
-  Explore the need for error covariance localization
-  Ensemble initiation techniques
-  SSI observation error compatibility: disproportionate cost function decrease
**Comparison operational analysis and other EnKF  **
-  Adopt the common post-processing and evaluation programs
**Prepare for dual-resolution MLEF **
-  T126 control, T62 ensembles
-  Adjust control forecast script
-  Interpolation from T126 to T62
**Add all operational observations**
-  Algorithmically simple, just change the observation masks
-  Special attention to specific humidity and ozone: Gaussian PDF?

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