# Presentation: 863629

## WRF 4D-VarHans Huang, MMM/NCAR

- A short introduction to WRF 4D-Var
- The current status: The basic system
- The structure function: single ob exp
- Results from cold-start experiments
- Results from cycling experiments
- Our first radar data assimilation experiments
- Summary

## WRF 4D-Var developers 

- Xiang-Yu Huang,
- Qingnong Xiao, Dale Barker, Xin Zhang, John Michalakes, Wei Huang, John Bray, Zaizhong Ma, Tom Henderson, Jimy Dudhia, Xiaoyan Zhang, Duk-Jin Won, Yongsheng Chen, Yongrun Guo, Juanzhen Sun, Hui-Chuan Lin, Ying-Hwa Kuo

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

## 4D-Var: 4-Dimensional Variation 

- 4D-Var: 4-Dimensional Variation
- 				data assimilation

- (new)

- (initial condition for NWP)

- (old forecast)

## WRF 4D-Var: J=Jo +Jb +Jc 	

## Why 4D-Var?

- Use observations over a time interval, which suits most asynoptic data and use tendency information from observations.
- Use a forecast model as a constraint, which enhances the dynamic balance of the analysis.
- Implicitly use flow-dependent background errors, which ensures the analysis quality for fast developing weather systems.
- NOT easy to build and maintain!

## 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
- Xu, et al. (2005); NAVDAS-AR
- Gauthier, et al. (2007); MSC
- Operation: ECMWF, Meteo France, JMA, UKMO, MSC.
- Pre-operation: HIRLAM, NAVDAS-AR

## 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.
-           JcDF
- 2007: The WRF 4D-Var basic system.				2.5 FTE

## Basic system: 3 exes, disk I/O, parallel, full dyn, 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

## 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**  **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)

## Real Case: Typhoon HaitangExperimental Design (Cold-Start)

- Domain configuration: 91x73x17, 45km
- Observations from Taiwan CWB operational database.
- 5 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 WRF-Var3d using FGS as background
- FGAT - forecast from WRF-Var3dFGAT using FGS as background
- 4DVAR – forecast from WRF-Var4d using FGS as background

## Observations used in a 4D-Var experiment

## Typhoon Haitang 20052005.07.16.00Z

## Typhoon Haitang 2005

## A KMA Heavy Rain Case 

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

## Observations used in 3D-Var

## Observations used in 4D-Var

## Observations Verification

## Precipitation Verification

## Observation Verification: Precipitation, CSI

## Observation Verification: Precipitation, BIAS

## First radar data assimilation experiment using WRF 4D-Var Yong-Run Guo and Juanzhen Sun

## The OSSE setup

** ****12/4-km WRFV2.2 run**
-  Initial and boundary conditions: Eta 3-hly analysis starting at 2002061212Z
-  Domain size: 271x241x31 (12-km) and 325x280x31 (4km)
- The control experiment with the domain2 (325x280x31):

- 061212Z			         061300Z			        061312Z

- 4DVAR time window

## Domain settings

**height**

**landuse**

## Hourly rainfall forecast from the control run starting from 2002061212Z

**Hourly rainfall forecast from the control run starting from 2002061212Z**

## Slide 30

## Slide 31

## Physics option as the control run (truth)
Initial time for Experiments at 2002061301Z (the 13-h forecast starting from 2002061212Z)
Domain size: 151x118x31, covered the convective cells. 
Grid size: 4-km, Time step: 20 seconds
First guess from NCEP GFS analysis
Time window for WRF 4DVar: 
0.25-h, 45 steps
		0.5-h, 90 steps (?)
Forecast length: 11-h.
BES interpolated from 12km IHOP BES (Hongli Wang)

- Initial time for Experiments at 2002061301Z (the 13-h forecast starting from 2002061212Z)
- Domain size: 151x118x31, covered the convective cells.
- Grid size: 4-km, Time step: 20 seconds
- First guess from NCEP GFS analysis
- Time window for WRF 4DVar:
- 0.25-h, 45 steps
- 		0.5-h, 90 steps (?)
- Forecast length: 11-h.
- BES interpolated from 12km IHOP BES (Hongli Wang)

**WRF 4D-Var Experiment design**

## Control run 4-km domain

- WRF 4DVar Exp 4-km Domain

**Control run 4-km domain**

**325**

**280**

**151**

**118**

## OSSE Radar data generation

- Gaussian random perturbation (0,1), *X**pert*, added to truth
- The truth is obtained by using *iowrf* utility to extract a box-domain <x121to 271, y94to211> from the 4-km control run <325x280> domain.
- Soichiro Sugimoto’s code as the reference
- The Radius of Radar OBS: 200km
- When Rain water mixing ratio > 1.e-7, the reflectivity truth will be computed as *X**t**dbz*
- It is regarded as ***clear air*** when *X**o**dbz* < 5, no clear air radar obs considered.
- When the bean angle > 20o, no radar obs
- The radial velocity data are generated in the same way as reflectivity

## Rain water mixing ratio every 5 minutes from 130100  to 130130

- 	130100		    130105	         130110		130115

- 	130120		    130125	          130130

## OSSE Radar data coverage

- 10 NEXRAD Radar sites
- over the Exp. Domain

-  at 0100 UTC 13 June 20

## Experiment design

**TRUTH** ----- *Initial condition from TRUTH (13-h forecast initialized at 2002061212Z from AWIPS 3-h analysis) run cutted by ndown****,*** boundary condition from NCEP GFS data.
**NODA** ----- Both initial condition and boudary condition from NCEP GFS data.
**3DVAR** ----- 3DVAR analysis at 2002061301Z used as the initial condition, and boundary condition from NCEP GFS. Only Radar radial velocity at 2002061301Z assimilated (total # of data points = 65,195).
**4DVAR** ----- 4DVAR analysis at 2002061301Z used as initial condition, and boundary condition from NCEP GFS. The radar radial velocity at 4 times: 200206130100, 05, 10, and 15, are assimilated (total # of data points = 262,445).

## INCREMENTS (A-B): B is the NCEP GFS analysis at 2002061301Z

- Truth Temperature/wind at lowest  level

- (3DVAR-FG) Temperature/wind
- at lowest  level

**INCREMENTS (A-B):**** ****B is the NCEP GFS analysis at 2002061301Z**

## Hourly precipitation ending at 01-h forecast

## Hourly precipitation ending at 03-h forecast

## Hourly precipitation ending at 06-h forecast

**TRUTH**

## Summary

- A short introduction to WRF 4D-Var
- The current status: The basic system
- The structure function: single ob exp
- A cold-start experiment
- A cycling experiment
- First radar data assimilation experiment