• Akmaev, R. A., , and H.-M. H. Juang, 2008: Using enthalpy as a prognostic variable in atmospheric modeling with variable composition. Quart. J. Roy. Meteor. Soc., 134, 21932197.

    • Search Google Scholar
    • Export Citation
  • Arakawa, A., , and V. R. Lamb, 1977: Computational design of the basic dynamical processes of the UCLA general circulation model. Methods in Computational Physics, Vol. 17, Academic Press, 173–265.

    • Search Google Scholar
    • Export Citation
  • Asselin, R. A., 1972: Frequency filter for time integration. Mon. Wea. Rev., 100, 487490.

  • Benjamin, S. G., , G. A. Grell, , J. M. Brown, , and T. G. Smirnova, 2004: Mesoscale weather prediction with the RUC hybrid isentropic-terrain following coordinate model. Mon. Wea. Rev., 132, 473494.

    • Search Google Scholar
    • Export Citation
  • Bleck, R., 2002: An oceanic general circulation model framed in hybrid isopycnic-Cartesian coordinates. Ocean Modell., 37, 5588.

  • Haltiner, G. J., , and R. T. Williams, 1980: Numerical Predictions and Dynamical Meteorology. 2nd ed. John Wiley and Sons, 477 pp.

  • Hirschfelder, J. O., , C. F. Curtiss, , and R. B. Bird, 1964: Molecular Theory of Gases and Liquids. John Wiley & Sons, 1280 pp.

  • Hoskins, B. J., , and A. J. Simmons, 1975: A multi-layers spectral model and the semi-implicit method. Quart. J. Roy. Meteor. Soc., 101, 637655.

    • Search Google Scholar
    • Export Citation
  • Johnson, D. R., , and Z. Yuan, 1998: The development and initial tests of an atmospheric model based on a vertical coordinate with a smooth transition from terrain following to isentropic coordinates. Adv. Atmos. Sci., 15, 283299.

    • Search Google Scholar
    • Export Citation
  • Juang, H.-M. H., 2000: The NCEP Mesoscale Spectral Model: A revised version of the nonhydrostatic regional spectral model. Mon. Wea. Rev., 128, 23292362.

    • Search Google Scholar
    • Export Citation
  • Juang, H.-M. H., 2005: Discrete generalized hybrid vertical coordinates by a mass, energy, and angular momentum conserving finite-difference scheme. NCEP Office Note 455, 35 pp.

    • Search Google Scholar
    • Export Citation
  • Konor, C. S., , and A. Arakawa, 1997: Design of an atmospheric model based on a generalized vertical coordinate. Mon. Wea. Rev., 125, 16491673.

    • Search Google Scholar
    • Export Citation
  • Robert, A. J., 1969: The integration of a spectral model of the atmosphere by the implicit method. Proc. WMO/IUGG Symp. on Numerical Weather Prediction, Tokyo, Japan, Japan Meteorological Agency, VII-19–VII-24.

    • Search Google Scholar
    • Export Citation
  • Robert, A. J., , J. Henderson, , and C. Turnbull, 1972: An implicit time integration scheme for baroclinic models of the atmosphere. Mon. Wea. Rev., 100, 329335.

    • Search Google Scholar
    • Export Citation
  • Sela, J. G., 1982: The NMC spectral model. NOAA Tech. Rep. NWS 30, Silver Spring, MD, 36 pp.

  • Simmons, A. J., , and D. M. Burridge, 1981: An energy and angular-momentum conserving vertical finite-difference scheme and hybrid vertical coordinates. Mon. Wea. Rev., 109, 758766.

    • Search Google Scholar
    • Export Citation
  • Simmons, A. J., , B. J. Hoskins, , and D. M. Burridge, 1978: Stability of the semi-implicit time scheme. Mon. Wea. Rev., 106, 405412.

  • Zhu, Z., , T. Thuburn, , B. J. Hoskins, , and P. Haynes, 1992: A vertical finite-difference scheme based on a hybrid σ-θ-ρ coordinate. Mon. Wea. Rev., 120, 851862.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 27 27 2
PDF Downloads 20 20 1

A Multiconserving Discretization with Enthalpy as a Thermodynamic Prognostic Variable in Generalized Hybrid Vertical Coordinates for the NCEP Global Forecast System

View More View Less
  • 1 Environmental Modeling Center, NOAA/NWS/NCEP, Camp Springs, Maryland
© Get Permissions
Restricted access

Abstract

A new vertical discretization used in the atmospheric dynamics of the National Centers for Environmental Prediction (NCEP) Global Forecast System (GFS) is illustrated, with enthalpy as the thermodynamic prognostic variable to reduce computation in thermodynamic equations while concerning all gas tracers in the model. Mass, energy, entropy, and angular momentum conservations are utilized as constraints to discretize the vertical integration with a finite-difference scheme. A specific definition of a generalized hybrid vertical coordinate, including sigma, isobaric, and isentropic surfaces, is introduced to define pressure at the model levels. Vertical fluxes are obtained by the equation of local changes in variables defined for vertical coordinates at all model layers. The forward-weighting semi-implicit time scheme is utilized to eliminate computational noise for stable integration. Because of time splitting between the dynamic and physics processes, the vertical advection is required both in the model dynamics and model physics, and the semi-implicit time scheme is used both in dynamics and after physics computation.

Three configurations—sigma, sigma pressure, and sigma entropy—from the specific hybrid vertical coordinates with layer definition similar to NCEP operational GFS have been implemented in the NCEP GFS. Results from the sigma-isentropic coordinate show the largest anomaly correlation and the smallest root-mean-square error in tropical wind among all results at all layers, especially the upper layers. The scores from a period of daily forecast up to 5 days with the sigma-isentropic coordinate show the same level of skill as compared to the NCEP operational GFS. The results from the hurricane tracks for the fall of 2005 with sigma-isentropic coordinates show better scores compared with the operational GFS.

Corresponding author address: Dr. Hann-Ming Henry Juang, NOAA Science Center, Room 207, 5200 Auth Road, Camp Springs, MD 20746. E-mail: henry.juang@noaa.gov

Abstract

A new vertical discretization used in the atmospheric dynamics of the National Centers for Environmental Prediction (NCEP) Global Forecast System (GFS) is illustrated, with enthalpy as the thermodynamic prognostic variable to reduce computation in thermodynamic equations while concerning all gas tracers in the model. Mass, energy, entropy, and angular momentum conservations are utilized as constraints to discretize the vertical integration with a finite-difference scheme. A specific definition of a generalized hybrid vertical coordinate, including sigma, isobaric, and isentropic surfaces, is introduced to define pressure at the model levels. Vertical fluxes are obtained by the equation of local changes in variables defined for vertical coordinates at all model layers. The forward-weighting semi-implicit time scheme is utilized to eliminate computational noise for stable integration. Because of time splitting between the dynamic and physics processes, the vertical advection is required both in the model dynamics and model physics, and the semi-implicit time scheme is used both in dynamics and after physics computation.

Three configurations—sigma, sigma pressure, and sigma entropy—from the specific hybrid vertical coordinates with layer definition similar to NCEP operational GFS have been implemented in the NCEP GFS. Results from the sigma-isentropic coordinate show the largest anomaly correlation and the smallest root-mean-square error in tropical wind among all results at all layers, especially the upper layers. The scores from a period of daily forecast up to 5 days with the sigma-isentropic coordinate show the same level of skill as compared to the NCEP operational GFS. The results from the hurricane tracks for the fall of 2005 with sigma-isentropic coordinates show better scores compared with the operational GFS.

Corresponding author address: Dr. Hann-Ming Henry Juang, NOAA Science Center, Room 207, 5200 Auth Road, Camp Springs, MD 20746. E-mail: henry.juang@noaa.gov
Save