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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

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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  1. 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

  2. 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).

  3. Introduction • Assimilation system combines all sources of information: • Observations - yo • Background field - xb • Estimate of observation/background errors. • Laws of physics.

  4. 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.

  5. 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.

  6. Implementation Cold-Start Mode

  7. 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.

  8. 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

  9. 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).

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

  11. Correlation between pressure increment and ‘‘balanced’’ pressure

  12. Sinlaku

  13. 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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