# Presentation: 351554

## WRF 4D-VarWhere we are and where we go

- Xiang-Yu Huang
- National Center for Atmospheric Research, Boulder, Colorado

## WRF 4D-Var developers

- Xiang-Yu Huang1, Qingnong Xiao1, Xin Zhang2, John Michalakes1, Wei Huang1, Dale M. Barker1, John. Bray1, Zaizhong Ma1, Tom Henderson1, Jimy Dudhia1, Xiaoyan Zhang1, Duk-Jin Won3, Yongsheng Chen1, Yongrun Guo1, Hui-Chuan Lin1, Ying-Hwa Kuo1
- 1National Center for Atmospheric Research, Boulder, Colorado, USA
- 2University of Hawaii, Hawaii, USA
- 3Korean Meteorological Administration, Seoul, South Korea

*Acknowledgments. *The WRF 4D-Var development has been primarily
- supported by the Air Force Weather Agency. The Korean Meteorological
- Administration also funded some 4D-Var tasks.

## Outline 

- Introduction
- WRF 4D-Var
- Current status of WRF 4D-Var
- Single ob experiments
- Noise control
- Meteorological tests
- Work plan
- Summary

## A short 4D-Var review

- The idea: Le Dimet and Talagrand (1986); Lewis and Derber (1985)
- Implementation examples:
- Courtier and Talagrand (1990); a shallow water model
- Thepaut and Courtier (1991); a multi-level primitive equation model
- Navon, et al. (1992); the NMC global model
- Zupanski M (1993); the Eta model
- Zou, et al. (1995); the MM5 model
- Sun and Crook (1998); a cloud model
- Rabier, et al. (2000); the ECMWF model
- Huang, et al. (2002); the HIRLAM model
- Zupanski M, et al. (2005); the RAMS model
- Ishikawa, et al. (2005); the JMA mesoscale model
- Huang, et al. (2005); the WRF model
- Operation: ECMWF, Meteo France, JMA, UKMO, MSC.
- Pre-operation: HIRLAM

## Why 4D-Var?

- Use observations over a time interval, which suits most asynoptic data.
- Use a forecast model as a constraint, which ensures the dynamic balance of the analysis.
- Implicitly use flow-dependent background errors, which ensures the analysis quality for fast developing weather systems.

## Variational methods

- (old forecast)

- (new)

- (initial condition for NWP)

## Necessary components of 4D-Var

*H* observation operator, including the tangent linear operator **H** and the adjoint operator **H****T**.
*M* forecast model, including the tangent linear model **M** and adjoint model **M****T**.
**B** background error covariance (N*N matrix).
**R** observation error covariance, which includes the representative error (K*K matrix).

## WRF 4D-Var milestones

- 2003: WRF 4D-Var project.						??  FTE
- 2004: WRF SN (simplified nonlinear model).		1.5 FTE
- 			  Modifications to WRF 3D-Var.
- 2005: TL and AD of WRF dynamics.				1.5 FTE
-           WRF TL and AD framework.
-           WRF 4D-Var framework.
- 2006: The WRF 4D-Var prototype.					2.5 FTE
-           Single ob and real data experiments.
-           Parallelization of WRF TL and AD.
-           Simple physics TL and AD.
-           JcDFI
- 2007: The WRF 4D-Var basic system.				2.5 FTE
- 			 Here we are!

## The WRF 4D-Var basic system 

- WRF, VAR and WRF+ parallelized in WRF Software Framework
- WRF TL/AD (dyn + vdiff + lsc) produced using TAF (_[www.](http://www.fastopt.com/)__[fastopt](http://www.fastopt.com/)__[.com](http://www.fastopt.com/)_)
- Parallel versions from hand-parallelized TAF output
- MPMD execution on processors sets under IBM load-leveler/LSF
- Coupling (coordination and exchange) among WRF, VAR and WRF+ through files

## Basic system: 3 exes, disk I/O, parallel, simple phys, JcDF

- NL(1),...,NL(K)

- TL(1),...,TL(K)

- AD00

- call

- call

**R**
**y**1
- ...
**y**K

**x**b

- I/O

- WRFBDY

**B**

-     WRF+

- BS(0),...,BS(N)

**x**n

## Wall clock of 6 hours integration

-  (IBM power 5+)

## Single observation experiment

- The idea behind single ob tests:
- The solution of 3D-Var should be

- Single observation

- 3D-Var  4D-Var: **H**  **HM; H***T*  **M***T***H***T*
- The solution of 4D-Var should be

- Single observation, solution at observation time

## Analysis increments of 500mb 

- 4D-Var

- Analysis increments of 500mb 
-  from 3D-Var at 00h and from 4D-Var at 06h
- due to a 500mb T observation at 06h

- +

- +

## 500mb  increments at 00,01,02,03,04,05,06h to a 500mb T ob at 06h

## 500mb  difference at 00,01,02,03,04,05,06h from two nonlinear runs (one from background; one from 4D-Var)

## 500mb  difference at 00,01,02,03,04,05,06h from two nonlinear runs (one from background; one from FGAT)

## JcDF in WRF-Var4dWeak constraint for noise control 	

- Before: *J=J**o**+J**b*

- After: *J=J**o **+J**b **+J**c*

## Performance of JcDF

## 3-hour Surface Pressure Tendency

## Meteorological tests 

- Typhoon Haitang
- KMA Heavy Rain (KMA funded project)

## Real Case: Typhoon HaitangExperimental Design

- Domain configuration: 91x73x17, 45km
- Observations from Taiwan CWB operational database.
- Experiments are conducted before Haitang’s landfall at 0000 UTC 18 July 2005.
- FGS – forecast from the background [The background fields are 6-h WRF forecasts from National Center for Environment Prediction (NCEP) GFS analysis.]
- AVN- forecast from the NCEP AVN analysis
- 3DVAR – forecast from cycling WRF-Var3d
- 4DVAR – forecast from cycling WRF-Var4d
- NOBOGUS - 4D-Var, but withheld BOUGS data

## Observations used in a 4D-Var experiment

## Typhoon track verification

## The track error in km averaged over 48 h

## Typhoon Track Verification

## Intensity error in hPa averaged over 48 h

## Typhoon Intensity Verification

## Summary of 

- Typhoon Haitang Experiments

- Better track forecasts from 4D-Var (compared to those from 3D-Var)
- Comparable central pressure forecasts
- Bogus data are important

## Real Case: KMA Heavy Rain 

- Period: 12 UTC 4 May - 00 UTC 7 May, 2006
- Assimilation window: 6 hours
- Cycling
- All KMA operational data
- Grid : 60x54x31
- Resolution : 30km
- Domain size: the same as the
- KMA perational 10km domain.
- (from the KMA project)

## Observations used in 3D-Var

## Observations used in 4D-Var

## Observations Verification

## Precipitation Verification

## Summary of 

- the Heavy Rain Experiments

- T: 3D-Var better
- u,v: comparable
- Precipitation: 4D-Var significantly better

## Work plan for 2007

- Multi-incremental formulation
- Optimization
- Convection
- Meteorological tests
- Lateral boundary control
- Analysis on C-grid

## Summary 

- Introduction
- WRF 4D-Var
- Current status of WRF 4D-Var
- Single ob experiments
- Noise control
- Meteorological tests
- Work plan
- Summary