Articles describing the dynamical core of GEM

• Côté, J., S. Gravel, A. Méthot, A. Patoine, M. Roch and A. Staniforth, 1998 a:
  The operational CMC-MRB global environmental multiscale (GEM) model. Part I: Design considerations and formulation. Mon. Wea. Rev., 126, 1373-1395.
• Côté, J., J.-G. Desmarais, S. Gravel, A. Méthot, A. Patoine, M. Roch and A. Staniforth, 1998 b:
  The operational CMC-MRB global environmental multiscale (GEM) model. Part II: Results. Mon. Wea. Rev., 126, 1397-1418.
• Yeh, K.-S., J. Côté, S. Gravel, A. Méthot, A. Patoine, M. Roch and A. Staniforth, 2002:
  The CMC­-MRB Global Environmental Multiscale (GEM) Model. Part III: Nonhydrostatic Formulation. Mon. Wea. Rev., 130, 339­-356. Click on the following link to access the pdf.
• Caya, A., R. Laprise and P. Zwack, 1998:
  Consequences of Using the Splitting Method for Implementing Physical Forcings in a Semi-Implicit Semi-Lagrangian Model. Mon. Wea. Rev. 126(6), 1707-1713.
• Bénard, P., R. Laprise, J. Vivoda, P. Smolíková, 2004:
  Stability of Leapfrog Constant-Coefficients Semi-Implicit Schemes for the Fully Elastic System of Euler Equations: Flat-Terrain Case. Mon. Wea. Rev., 132, 1306-1318.
• Qaddouri, A., and V. Lee, 2011:
  The Canadian Global Environmental Multiscale model on the Yin-Yang grid system, Quart. J. Roy. Meteor. Soc., 137, 660, 1913-1926, DOI: 10.1002/qj.873
• Girard, C., and A. Plante, 2013:
  GEM4.2: A non-hydrostatic atmospheric model (Euler equations) in terrain-following vertical coordinate of the log-hydrostatic-pressure type vertically discretized on a Charney-Phillips grid with simple differences and means, Revision 2. Notes internes. Recherches en prévision numérique, Environment Canada, 59 pp. La version 2011 “GEM4.1 - Revision 1” du document est disponible ici.
• C. Girard, A. Plante et al.:
  Options for Semi-Lagrangian Trajectory Calculations
• Girard, C., Plante, A., Desgagné, M., McTaggart-Cowan, R., Côté, J., Charron, M., Gravel, S., Lee, V., Patoine, A., Qaddouri, A. and Roch, M., 2014.
  Staggered Vertical Discretization of the Canadian Environmental Multiscale (GEM) Model Using a Coordinate of the Log-Hydrostatic-Pressure Type. Monthly Weather Review, 142(3), pp.1183-1196. https://doi.org/10.1175/MWR-D-13-00255.1
  Click on the following link to access the pdf.

Dynamical equations by R. Laprise, UQAM (2015)

• Section 1 : Les équations continues

• Section 1 : Les équations continues Annexes

• Section 2 : Les équations discrètes à la verticale et dans le temps

• Section 2 : Les équations discrètes à la verticale et dans le temps Annexes

Other articles describing dynamics

• 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.

• Laprise, R., 1992:
  The Euler equation of motion with hydrostatic pressure as independent coordinate. Mon. Wea. Rev. 120(1), 197-207.

• Laprise, R., C. Girard, 1990:
  A Spectral Circulation Model Using a Piecewise-Constant Finite-Element Representation on a Hybrid Vertical Coordinate System. J. Climate, 3, 32–52.

• Kasahara, A., 1974:
  Various vertical coordinate systems used for numerical weather prediction. Mon. Wea. Rev. 102, 509-522. See also corrigendum: Mon. Wea. Rev. 103, 664.

Articles describing physics schemes of GEM & CRCM

PDF: Descriptions of GEM physics version 3.6 from 1998

Physics of GEM5:

• McTaggard-Cowen, R. et al., 2019: Modernization of Atmospheric Physics Parameterization in Canadian NWP. JAMES, 11, issue 11, https://doi.org/10.1029/2019MS001781

Li and Barker correlated-k radiation:

• Li, J. and H.W. Barker, 2005: A radiation algorithm with correlated-k distribution. Part I: local thermal equilibrium. J. Atmos. Sci., 62, 286-309.

Kain and Fritsch deep convection:

• Kain, J.S. and J.M. Fritsch, 1990: A one-dimensional entraining/detraining plume model and application in convective parameterization. J. Atmos. Sci., 47, 2784-2802.
• McTaggart-Cowan, R., Vaillancourt, P. A., Zadra, A., Separovic, L., Corvec, S., & Kirshbaum, D. (2019). A lagrangian perspective on parameterizing deep convection. Monthly Weather Review, 147(11), 4127–4149. https://doi.org/10.1175/MWR-D-19-0164.1

Bechtold shallow convection :

• Bechtold, P., Bazile, E., Guichard, F., Mascart, P., & Richard, E. (2001). A mass-flux convection scheme for regional and global models. Quarterly Journal of the Royal Meteorological Society, 127, 869–886. https://doi.org/https://doi.org/10.1002/qj.49712757309

Shallow convection: "ktrsnt":

• Bélair S, Mailhot J, Girard C, Vaillancourt P, 2005: Boundary-layer and shallow cumulus clouds in a medium-range forecast of a large-scale weather system. Mon Weather Rev., 133, 1938-1960

Sundquist condensation:

• Sundqvist, H., E. Berge and J.E. Kristjansson, 1989: Condensation and Cloud Parameterization Studies with a Mesoscale Numerical Weather Prediction Model. Mon. Wea. Rev., 117, 1641-1657.

ISBA, land surface scheme:

• Bélair, S., L-P. Crevier, J. Mailhot, B. Bilodeau, and Y. Delage, 2003: Operational Implementation of the ISBA Land Surface Scheme in the Canadian Regional Weather Forecast Model. Part I: Warm Season Results. J. Hydromet., 4, Issue 2, 352-370
• Bélair, S., R. Brown, J. Mailhot, B. Bilodeau, and L.-P. Crevier, 2003: Operational Implementation of the ISBA Land Surface Scheme in the Canadian Regional Weather Forecast Model. Part II: Cold Season Results. J. Hydromet., 4, Issue 2, 371-386

CLASS, land surface scheme:

• D. L. Verseghy, 1991: CLASS--A Canadian Land Surface Scheme for GCMS: I. Soil Model. International Journal of Climatology IJCLEU, vol. p 111-133, p. 44
• D. L. Verseghy, N. A. McFarlane, and M. Lazare, 1993: CLASS-A Canadian land surface scheme for GCMS, II. Vegetation model and coupled runs. Int. J. Climatol., vol. 13, no. 4, pp. 347-370

• Y. Delage, L. Wen & J.‐M. Bélanger, 1999: Aggregation of parameters for the land surface model CLASS, Atmosphere-Ocean, 37:2, 157-178, DOI: 10.1080/07055900.1999.9649624

• D. L. Verseghy, 2000: The Canadian Land Surface Scheme (CLASS): its history and future. Atmosphere-Ocean, vol. 38, no. 1, pp. 1-1

McFarlane gravity-wave drag:

• McFarlane, N.A., 1987: The effect of orographically excited gravity-wave drag on the circulation of the lower stratosphere and troposphere. J. Atmos. Sci., 44, 1175-1800

Orographic blocking:

• Zadra, A., M. Roch, S. Laroche and M. Charron, 2003: The subgrid scale orographic blocking parametrization of the GEM model. Atmos.-Ocean, 41, 155-170.

Geophysical fields (USGS aka GLC2000):

• E. Bartholomé and A. S. Belward, 2005: GLC2000: a new approach to global land cover mapping from Earth observation data. International Journal of Remote Sensing, 26:9, 1959-1977, DOI: 10.1080/01431160412331291297

CRCM5 evolving towards GEM4:

• Girard, C., A. Plante et al., 2014: Staggered Vertical Discretization of the Canadian Environmental Multiscale (GEM) Model Using a Coordinate of the Log-Hydrostatic-Pressure Type. Monthly Weather Review, DOI: 10.1175/MWR-D-13-00255.1
  Click here to see the paper.

P3 (Prediction Particles Properties):

• Morrison, H. and Milbrandt, J.A., 2015. Parameterization of cloud microphysics based on the prediction of bulk ice particle properties. Part I: Scheme description and idealized tests. Journal of the Atmospheric Sciences, 72(1), pp.287-311.
• Morrison, H., Milbrandt, J.A., Bryan, G.H., Ikeda, K., Tessendorf, S.A. and Thompson, G., 2015. Parameterization of cloud microphysics based on the prediction of bulk ice particle properties. Part II: Case study comparisons with observations and other schemes. Journal of the Atmospheric Sciences, 72(1), pp.312-339.
• Milbrandt, J.A. and Morrison, H., 2016. Parameterization of cloud microphysics based on the prediction of bulk ice particle properties. Part III: Introduction of multiple free categories. Journal of the Atmospheric Sciences, 73(3), pp.975-995.

• Cholette, M., Morrison, H., Milbrandt, J.A. and Thériault, J.M., 2019. Parameterization of the bulk liquid fraction on mixed-phase particles in the predicted particle properties (P3) scheme: Description and idealized simulations. Journal of the Atmospheric Sciences, 76(2), pp.561-582.

• Milbrandt, J.A., Morrison, H., Dawson II, D.T. and Paukert, M., 2021. A triple-moment representation of ice in the Predicted Particle Properties (P3) microphysics scheme. Journal of the Atmospheric Sciences, 78(2), pp.439-458.

Cloud fraction:

• C. Jouan, J. A. Milbrandt, P. A. Vaillancourt, F. Chosson, and H. Morrison, 2020: Adaptation of the Predicted Particles Properties (P3) Microphysics Scheme for Large-Scale Numerical Weather Prediction. Weather and Forecasting, p. 2541-2565, DOI: https://doi.org/10.1175/WAF-D-20-0111.1

TEB (Town Energy Balance):

• Masson, V., 2000. A physically-based scheme for the urban energy budget in atmospheric models. Boundary-layer meteorology, 94, pp.357-397. DOI: https://doi.org/10.1023/A:1002463829265
  
• Masson, V., Grimmond, C.S.B. and Oke, T.R., 2002. Evaluation of the Town Energy Balance (TEB) scheme with direct measurements from dry districts in two cities. Journal of applied meteorology, 41(10), pp.1011-1026. DOI: https://doi.org/10.1175/1520-0450(2002)041<1011:EOTTEB>2.0.CO;2
  
• Leroyer, S., Bélair, S., Souvanlasy, V., Vallée, M., Pellerin, S. and Sills, D., 2022. Summertime Assessment of an Urban-Scale Numerical Weather Prediction System for Toronto. Atmosphere, 13(7), p.1030. DOI: https://doi.org/10.3390/atmos13071030
  

Code repository: Masson, V., Lemonsu, A., Pigeon, G., Schoetter, R., de Munck, C., Bueno, B., Faroux, S., Goret, M., Redon, E., Chancibault, K., Stavropulos-Laffaille, X., Leroyer, S., & Meyer, D. (2021). The Town Energy Balance (TEB) model (4.1.2). Zenodo. https://doi.org/10.5281/zenodo.5775962

FLake:

• Mironov, D., Heise, E., Kourzeneva, E., Ritter, B., Schneider, N. and co-authors., 2010: Implementation of the lake parameterisation scheme FLake into the numerical weather prediction model COSMO. Boreal Environ. Res.15, 218-230.

Moving from GEM4 to GEM5

"Modernisation des paramétrisations de la physique atmosphérique des modèles de PNT canadien"

Partie 1: Introduction, stratégie de développement et description des changements aux schémas de transfert radiatif et de convection (Paul Vaillancourt, 15 janvier 2020)

Partie 2: Changes to the orography, turbulence and surface layer schemes (Ayrton Zadra, 22 janvier 2020)

Partie 3: (Ron McTaggart-Cowen,  29 janvier 2020)

Other references

• Laprise, R.:
  Équations de Navier-Stokes (ou d'Euler). SCA7001, D04, Mouvement 2

• Laprise, R.:
  Coordonnée verticale générale. SCA7001, D09

• Laprise, R., 1991:
  The Euler Equations of Momentum with Hydrostatic Pressure as Independent Variable.