A three dimensional variational data assimilation system for mm5 implementation and initial results
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D. M. Barker, W. Huang, Y.-R. Guo, A. J. Bourgeois, and Q. N. Xiao Mon. Wea. Rev., 132, 897-914 PowerPoint PPT Presentation


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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 :

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D. M. Barker, W. Huang, Y.-R. Guo, A. J. Bourgeois, and Q. N. Xiao Mon. Wea. Rev., 132, 897-914

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A three dimensional variational data assimilation system for mm5 implementation and initial results

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

Introduction

Goals of 3DVAR for MM5 :

  • Release as a research community data assimilation system.

  • Implementation in the Advanced Operational Aviation 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).


Introduction1

Introduction

  • Assimilation system combines all sources of information:

    • Observations - yo

    • Background field - xb

    • Estimate of observation/background errors.

    • Laws of physics.


Introduction2

Introduction

Main feature :

  • Observations are assimilated to provide analysis increments.

  • Analysis increments computed on an unstaggered 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.


Introduction3

Introduction

Main feature :

  • Control variables include streamfunction, velocity 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 theNational Meteorological Center (NMC) method.


Implementation

Implementation

Cold-Start Mode


Implementation1

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.


Implementation2

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


Implementation3

Implementation

  • The horizontal transform Uhis 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

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


D m barker w huang y r guo a j bourgeois and q n xiao mon wea rev 132 897 914

Correlation between pressure increment and ‘‘balanced’’ pressure


D m barker w huang y r guo a j bourgeois and q n xiao mon wea rev 132 897 914

Sinlaku


D m barker w huang y r guo a j bourgeois and q n xiao mon wea rev 132 897 914

  • 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.


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