Abstract
The operational numerical weather prediction system established by the China Meteorological Administration (CMA), based on the Global/Regional Assimilation and Prediction System (GRAPES) model, adopts the classical semi-implicit semi-Lagrangian (SISL) time integration algorithm. This paper describes a major upgrade to the dynamical core of the CMA global forecast system (CMA-GFS), which was successfully incorporated into operation in 2020. In the upgrade, the classical SISL is further developed into a predictor–corrector scheme, a three-dimensional (3D) reference profile instead of the original isothermal reference profile is applied when implementing the semi-implicit algorithm, and a hybrid terrain-following vertical coordinate system is also applied. The new version of the dynamical core greatly improves the model performance, the time integration reaches second-order accuracy, the time step can be extended by 50%, and the efficiency is greatly improved (by approximately 30%). Atmospheric circulation simulation is systematically improved, and deviations in temperature, wind, and humidity are reduced. The new version of the dynamical core provides a solid foundation for further development of the entire operational system of the CMA.
This is a preview of subscription content, access via your institution.
References
Asselin, R., 1972: Frequency filter for time integrations. Mon. Wea. Rev., 100, 487–490, doi: https://doi.org/10.1175/1520-0493(1972)100<0487:FFFTI>2.3.CO;2.
Bates, J. R., S. Moorthi, and R. W. Higgins, 1993: A global multilevel atmospheric model using a vector semi-Lagrangian finite-difference scheme. Part I: Adiabatic formulation. Mon. Wea. Rev., 121, 244–263, doi: https://doi.org/10.1175/1520-0493(1993)121<0244:AGMAMU>2.0.CO;2.
Beljadid, A., A. Mohammadian, M. Charron, et al., 2014: Theoretical and numerical analysis of a class of semi-implicit semi-Lagrangian schemes potentially applicable to atmospheric models. Mon. Wea. Rev., 142, 4458–4476, doi: https://doi.org/10.1175/MWR-D-13-00302.1.
Bénard, P., 2003: Stability of semi-implicit and iterative centered-implicit time discretizations for various equation systems used in NWP. Mon. Wea. Rev., 131, 2479–2491, doi: https://doi.org/10.1175/1520-0493(2003)131<2479:SOSAIC>2.0.CO;2.
Chen, J., and X. L. Li, 2020: The review of 10 years development of the GRAPES global/regional ensemble prediction. Adv. Meteor. Sci. Technol., 10, 9–18, 29, doi: https://doi.org/10.3969/j.issn.2095-1973.2020.02.003. (in Chinese)
Clancy, C., and J. A. Pudykiewicz, 2013: A class of semi-implicit predictor–corrector schemes for the time integration of atmospheric models. J. Comput. Phys., 250, 665–684, doi: https://doi.org/10.1016/j.jcp.2012.08.032.
Cordero, E., N. Wood, and A. Staniforth, 2005: Impact of semi-Lagrangian trajectories on the discrete normal modes of a non-hydrostatic vertical-column model. Quart. J. Roy. Meteor. Soc., 131, 93–108, doi: https://doi.org/10.1256/qj.04/34.
Davies, T., M. J. P. Cullen, A. J. Malcolm, et al., 2005: A new dynamical core for the Met Office’s global and regional modelling of the atmosphere. Quart. J. Roy. Meteor. Soc., 131, 1759–1782, doi: https://doi.org/10.1256/qj.04.101.
Diamantakis, M., T. Davies, and N. Wood, 2007: An iterative time-stepping scheme for the Met Office’s semi-implicit semi-Lagrangian non-hydrostatic model. Quart. J. Roy. Meteor. Soc., 133, 997–1011, doi: https://doi.org/10.1002/qj.59.
Durran, D. R., and P. A. Reinecke, 2004: Instability in a class of explicit two-time-level semi-Lagrangian schemes. Quart. J. Roy. Meteor. Soc., 130, 365–369, doi: https://doi.org/10.1256/qj.03.14.
Durran, D. R., and P. N. Blossey, 2012: Implicit–explicit multistep methods for fast-wave–slow-wave problems. Mon. Wea. Rev., 140, 1307–1325, doi: https://doi.org/10.1175/MWR-D-11-00088.1.
Gal-Chen, T., and R. C. J. Somerville, 1975: On the use of a coordinate transformation for the solution of the Navier-Stokes equations. J. Comput. Phys., 17, 209–228, doi: https://doi.org/10.1016/0021-9991(75)90037-6.
Gospodinov, I. G., V. G. Spiridonov, and J.-F. Geleyn, 2001: Second-order accuracy of two-time-level semi-Lagrangian schemes. Quart. J. Roy. Meteor. Soc., 127, 1017–1033, doi: https://doi.org/10.1002/qj.49712757317.
Gravel, S., A. Staniforth, and J. Côté, 1993: A stability analysis of a family of baroclinic semi-Lagrangian forecast models. Mon. Wea. Rev., 121, 815–824, doi: https://doi.org/10.1175/1520-0493(1993)121<0815:ASAOAF>2.0.CO;2.
Hortal, M., 2002: The development and testing of a new two-time-level semi-Lagrangian scheme (SETTLS) in the ECMWF forecast model. Quart. J. Roy. Meteor. Soc., 128, 1671–1687, doi: https://doi.org/10.1002/qj.200212858314.
Huang, L. P., D. H. Chen, L. T. Deng, et al., 2017: Main technical improvements of GRAPES_Meso V4.0 and verification. J. Appl. Meteor. Sci., 28, 25–37, doi: https://doi.org/10.11898/1001-7313.20170103. (in Chinese)
Husain, S. Z., C. Girard, A. Qaddouri, et al., 2019: A new dynamical core of the Global Environmental Multiscale (GEM) model with a height-based terrain-following vertical coordinate. Mon. Wea. Rev., 147, 2555–2578, doi: https://doi.org/10.1175/MWR-D-18-0438.1.
Jablonowski, C., P. Lauritzen, R. Nair, et al., 2008: Idealized Test Cases for the Dynamical Cores of Atmospheric General Circulation Models: A Proposal for the NCAR ASP 2008 Summer Colloquium. NCAR ASP Summer Colloquium, Boulder, Colorado, USA, 74 pp.
Kar, S. K., 2012: An explicit time-difference scheme with an Adams–Bashforth predictor and a trapezoidal corrector. Mon. Wea. Rev., 140, 307–322, doi: https://doi.org/10.1175/MWR-D-10-05066.1.
Kurihara, Y., 1965: On the use of implicit and iterative methods for the time integration of the wave equation. Mon. Wea. Rev., 93, 33–16, doi: https://doi.org/10.1175/1520-0493(1965)093<0033: OTUOIA>2.3.CO;2.
McDonald, A., 1997: Lateral Boundary Conditions for Operational Regional Forecast Models: A Review. HIRLAM Tech. Rep., Kuopio, Finland, 31 pp.
McDonald, A., and J. R. Bates, 1987: Improving the estimate of the departure point position in a two-time level semi-Lag-rangian and semi-implicit scheme. Mon. Wea. Rev., 115, 737–739, doi: https://doi.org/10.1175/1520-0493(1987)115<0737:ITEOTD> 2.0.CO;2.
Regan, H., C. Lique, C. Talandier, et al., 2020: Response of total and eddy kinetic energy to the recent spinup of the Beaufort Gyre. J. Phys. Oceanogr., 50, 575–594, doi: https://doi.org/10.1175/JPO-D-19-0234.1.
Ritchie, H., and M. Tanguay, 1996: A comparison of spatially averaged Eulerian and semi-Lagrangian treatments of mountains. Mon. Wea. Rev., 124, 167–181, doi: https://doi.org/10.1175/1520-0493(1996)124<0167:ACOSAE>2.0.CO;2.
Rivest, C., A. Staniforth, and A. Robert, 1994: Spurious resonant response of semi-Lagrangian discretizations to orographic forcing: Diagnosis and solution. Mon. Wea. Rev., 122, 366–376, doi: https://doi.org/10.1175/1520-0493(1994)122<0366:SRROSL>2.0. CO;2.
Shen, X. S., Y. Su, J. L. Hu, et al., 2017: Development and operation transformation of GRAPES global middle-range forecast system. J. Appl. Meteor. Sci., 28, 1–10. (in Chinese)
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, 758–766, doi: https://doi.org/10.1175/1520-0493(1981)109<0758:AEAAMC>2. 0.CO;2.
Simmons, A. J., and C. Temperton, 1997: Stability of a two-time-level semi-implicit integration scheme for gravity wave motion. Mon. Wea. Rev., 125, 600–615, doi: https://doi.org/10.1175/1520-0493(1997)125<0600:SOATTL>2.0.CO;2.
Simmons, A. J., B. J. Hoskins, and D. M. Burridge, 1978: Stability of the semi-implicit method of time integration. Mon. Wea. Rev., 106, 405–412, doi: https://doi.org/10.1175/1520-0493(1978)106<0405:SOTSIM>2.0.CO;2.
Su, Y., X. S. Shen, and Q. Zhang, 2016: Application of the correction algorithm to mass conservation in GRAPES_GFS. J. Appl. Meteor. Sci., 27, 666–675. (in Chinese)
Su, Y., X. S. Shen, Z. T. Chen, et al., 2018: A study on the three-dimensional reference atmosphere in GRAPES_GFS: Theoretical design and ideal test. Acta Meteor. Sinica, 76, 241–254. (in Chinese)
Su, Y., X. S. Shen, H. L. Zhang, et al., 2020: A study on the three-dimensional reference atmosphere in GRAPES_GFS: Constructive reference state and real forecast experiment. Acta Meteor. Sinica, 78, 962–971. (in Chinese)
Tanguay, M., E. Yakimiw, H. Ritchie, et al., 1992: Advantages of spatial averaging in semi-implicit semi-Lagrangian schemes. Mon. Wea. Rev., 120, 113–123, doi: https://doi.org/10.1175/1520-0493(1992)120<0113:AOSAIS>2.0.CO;2.
Temperton, C., M. Hortal, and A. Simmons, 2001: A two-time-level semi-Lagrangian global spectral model. Quart. J. Roy. Meteor. Soc., 127, 111–127, doi: https://doi.org/10.1002/qj.49712757107.
Ullrich, P. A., C. Jablonowski, J. Kent, et al., 2013: Dynamical Core Model Intercomparison Project (DCMIP) Test Case Document. DCMIP Summer School, Boulder, Colorado, USA, 83 pp.
Wang, J. Z., J. Chen, Z. R. Zhuang, et al., 2018: Characteristics of initial perturbation growth rate in the regional ensemble prediction system of GRAPES. Chinese J. Atmos. Sci., 42, 367–382. (in Chinese)
Xue, J. S., and Y. Liu, 2007: Numerical weather prediction in China in the new century—Progress, problems and prospects. Adv. Atmos. Sci., 24, 1099–1108, doi: https://doi.org/10.1007/s00376-007-1099-1.
Xue, J. S., and D. H. Chen, 2008: The Scientific Design and Application of GRAPES. Science Press, Beijing, 400 pp.
Zhang, J., S. H. Ma, D. H. Chen, et al., 2017: The improvements of GRAPES_TYM and its performance in northwest Pacific Ocean and South China Sea in 2013. J. Trop. Meteor., 33, 64–73, doi: https://doi.org/10.16032/j.issn.1004-4965.2017.01.007. (in Chinese)
Zhang, L., Y. Z. Liu, Y. Liu, et al., 2019: The operational global four-dimensional variational data assimilation system at the China Meteorological Administration. Quart. J. Roy. Meteor. Soc., 145, 1882–1896, doi: https://doi.org/10.1002/qj.3533.
Zheng, Y. J., Z. Y. Jin, and D. H. Chen, 2008: Kinetic energy spectrum analysis in a semi-implicit semi-Lagrangian dynamical framework. Acta Meteor. Sinica, 66, 143–157. (in Chinese)
Author information
Authors and Affiliations
Corresponding author
Additional information
Supported by the National Natural Science Foundation of China (42090032 and 42275168).
Rights and permissions
About this article
Cite this article
Shen, X., Su, Y., Zhang, H. et al. New Version of the CMA-GFS Dynamical Core Based on the Predictor–Corrector Time Integration Scheme. J Meteorol Res 37, 273–285 (2023). https://doi.org/10.1007/s13351-023-3002-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13351-023-3002-0