A Three-Dimensional Variational Data Assimilation System for MM5 : Implementation and Initial Results

D. M. Barker, W. Huang, Y.-R. Guo, A. J. Bourgeois, and Q. N. Xiao

Mon. Wea. Rev., 132, 897-914

Introduction

Goals of 3DVAR for MM5 :• Release as a research community data assimil

ation system.• Implementation in the Advanced Operational A

viation Weather System (AOAWS) of the Taiwan Civil Aeronautics Administration (CAA).

• Replacement of the multivariate optimum interpolation (MVOI) system in the operational, multitheater MM5-based system run by the U.S. Air Force Weather Agency (AFWA).

Introduction

Assimilation system combines all sources of information:

– Observations - yo

– Background field - xb

– Estimate of observation/background errors.– Laws of physics.

Introduction

Main feature :• Observations are assimilated to provide analysis

increments.• Analysis increments computed on an unstaggere

d grid. The unstaggered wind analysis increments are interpolated to the staggered grid of MM5/WRF, combined with the background field and output.

• Analysis vertical levels are those of the input background forecast.

Introduction

Main feature : • Control variables include streamfunction, velocit

y potential,‘‘unbalanced’’ pressure, and a humidity variable.

• the horizontal component of background error is via horizontally isotropic and homogeneous recursive filters.

• The vertical component of background error is climatologically averaged eigenvectors of vertical error estimated via the National Meteorological Center (NMC) method.

Implementation

Cold-Start Mode

Implementation

• analysis xa is minimum x of cost-function

y = H(x). H is the nonlinear “observation operator”. Error covariances:

B = Background (previous forecast) errors.

E = Observation (instrumental) errors.

F = Representivity (observation operator) errors.

)()()(2

1)()(

2

1 11 oTobTb EJ yyFyyxxBxxx

Implementation

• Define analysis increments: x’ = x-xb=UpUvUhv

where y’ = Hx’, yo’ = yo - y.

Up: physical variable transformation

Uv: vertical transform

Uh: horizontal transform v : control variable

)(1)()(2

112

1 oEToTJ y'y'Fy'y'x'Bx'x'

Implementation

• The horizontal transform Uh is performed using recursive filters. The background error length scales is estimated using the NMC method’s accumulated forecast difference data.

• The vertical transform Uv is applied via an empirical orthogonal function (EOF) decomposition of background error Bv (via the NMC method).

Impact of truncating 3DVAR’s responsible for only 0.1% of error variance.

Variance # psi mode

# chi

mode

# pu

mode

# q mode

n Its Final J

(x104)

CPU (s)

Mem

(Mb)

99.9% 17 17 10 22 438438 25 1.33 251 220

100% 31 31 31 31 823723 24 1.32 420 316

Correlation between pressure increment and ‘‘balanced’’ pressure

][2 'fpb vkvvvv

Sinlaku

• The resulting analysis central pressure is given by

• Using yb = 991 hPa, y0 = 955 hPa, σb =1 hPa (derived from the NMC statistics) and σ0= 1 hPa, leads to y = 973 hPa. Using the PBogus2 value of σ0= 2 hPa gives y = 984 hPa.

)/()( 20

220

02 bb

b yyy