Vol.23, NO.2, 2012
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Wang Ruichun, Gong Jiandong, Zhang Lin. Statistical estimation of dynamic balance constraints in GRAPES variational data assimilation system. J Appl Meteor Sci, 2012, 23(2): 129-138.
Citation: Wang Ruichun, Gong Jiandong, Zhang Lin. Statistical estimation of dynamic balance constraints in GRAPES variational data assimilation system. J Appl Meteor Sci, 2012, 23(2): 129-138.
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Statistical Estimation of Dynamic Balance Constraints in GRAPES Variational Data Assimilation System

  • 1.

    School of Atmospheric Sciences, Nanjing University of Information Science & Technology, Nanjing 210044

  • 2.

    National Meteorological Center, Beijing 100081

  • Received Date: 2011-07-20
  • Rev Recd Date: 2012-01-09
  • Publish Date: 2012-04-30
    Abstract
  • Dynamic balance constraints that govern the atmospheric circulation play very important roles in the analysis of atmospheric state. These constraints indicate how it might be possible to determine one variable from another. As a result, they could help to avoid noise caused by gravity waves, and enable maximum information to be extracted from the observations.The existing GRAPES three-dimensional variational data assimilation system, which is defined on sigma coordinates, uses linear balance equation to ensure that mass and wind analysis increments to be geostrophically coupled. In this formulation, to deal with difficulties in solving the balance equation at sigma levels, analysis variables need to be interpolated to a series of auxiliary isobaric surface to calculate balanced components. A new formulation of estimating dynamic balance constraints is developed in the variation assimilation system. In the new scheme, regression coefficients between stream function and dimensionless pressure (Exner function), instead of the geostrophic balance equation in the original scheme, is used to describe the balance relationship between rotational wind and mass field. In addition, the balance relationship between rotational wind and divergent wind is similarly described by regression coefficients between stream function and velocity potential. Compared to the old scheme, the new formulation avoids repeated interpolations along the vertical direction, which would make the estimation simpler and more accurate.In the new formulation, the balanced coefficients are computed using NMC method, which is found to produce a useful approximation to the true balance constraints in atmosphere. Based on 24 h, 48 h GRAPES forecast differences, linear regression is carried out for each level and for each latitude. By doing this an implied latitude-dependent structure in the dimensionless pressure is directly included in the analysis. Statistical results show that the explained variance of dimensionless pressure is primarily in the extratropics with the variance best explained below 100 hPa in this new formulation. And the explained velocity potential ratio has a maximum in the middle and high latitudes near the surface. Results of randomization and single-observation experiments indicate that, in regions where geostrophic balance is appropriate, the new formulation behaves similarly to the original scheme. However, in regions where geostrophic balance is not appropriate, the new formulation could allow for a smooth decoupling of stream function and dimensionless pressure, while the original scheme can not. Such properties of the new formulation could help variational data assimilation system get more reasonable analysis results in tropics and tropopause. Moreover, by adding the balance relationship between rotational wind and divergent wind, the new formulation could derive a more reasonable wind field in boundary layer.
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  • Fig. 1  Zonal average of the explained variance ratios of velocity potential (a) and dimensionless pressure (b)

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    Fig. 2  Zonal average of simulated background error standard deviations of dimensionless pressure in the original scheme (a) and the new scheme (b)(unit: 10-4)

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    Fig. 3  Zonal average of simulated background error standard deviations of velocity potential (a) and its balance part (b) in the new scheme (unit: 106m2·s-1)

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    Fig. 4  Dimensionless pressure increments generated by a simulated u component wind observation on the 12th model level at 45.5°N, 125.5°E which is 5 m·s-1stronger than background wind (unit: 10-5)

    (a) horizontal distribution of the original scheme, (b) horizontal distribution of the new scheme, (c) meridional section of the original scheme, (d) meridional section of the new scheme

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    Fig. 5  Dimensionless pressure increments generated by a simulated u component wind observation on the 24th model level at 45.5°N, 125.5°E which is 5 m·s-1stronger than background wind (unit: 10-5)

    (a) horizontal distribution of the original scheme, (b) horizontal distribution of the new scheme

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    Fig. 6  Dimensionless pressure increments generated by a simulated u component wind observation on the 12th model level at 5.5°N, 125.5°E which is 5 m·s-1stronger than background wind (unit:10-6)

    (a) horizontal distribution of the original scheme, (b) horizonal distribution of the new scheme

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    Fig. 7  Wind increments generated by a simulated pressure observation on the first model level at 45.5°N, 125.0°E which is 1 hPa higher than the background (unit:m·s-1)

    (a)u increment of the original scheme, (b)u increment of the new scheme, (c)v increment of the original scheme, (d)v increment of the new scheme

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    Table  1  Roughly corresponding pressure values of GRAPES model levels in Dec, Jan and Feb

    模式面 全球平均气压/hPa
    第4层 900
    第8层 740
    第12层 566
    第16层 403
    第20层 262
    第24层 153
    第28层 69
    第32层 26
    第36层 8.8
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    • Received : 2011-07-20
    • Accepted : 2012-01-09
    • Published : 2012-04-30
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