The authors gratefully acknowledge the continuous support by the managers—Hubert Allard, Michel Béland, Peter Chen, Pierre Dubreuil, Louis Lefaivre, Réal Sarrazin, Angèle Simard, and David Steenbergen—of both the Meteorological Research Branch of the Climate and Atmospheric Research Directorate and the Canadian Meteorological Centre, during the development phase of the project described herein.
Many of the authors’ colleagues made very valuable technical contributions to the development of the GEM model. Particular thanks are due to James Caveen, Yves Chartier, Gabriel Lemay, Judy St. James, Joseph-Pierre Toviessi, and Michel Valin.
Thanks are also due to Pierre Gauthier, Stéphane Laroche, Josée Morneau, Saroja Polavarapu, Judy St. James, and Monique Tanguay for their work, briefly summarized here and to be described in detail by them elsewhere, on the complementary data assimilation aspects of the project.
Finally, the authors wish to thank the anonymous reviewers for their comments, which led to substantial improvements in the presentation of the material.
Alpert, P., S. O. Krichak, T. N. Krishnamurti, U. Stein, and M. Tsidulko, 1996: The relative roles of lateral boundaries, initial conditions, and topography in mesoscale simulations of lee cyclogenesis. J. Appl. Meteor.,35, 1091–1099.
Anthes, R. A., 1983: Regional models of the atmosphere in middle latitudes. Mon. Wea. Rev.,111, 1306–1335.
Arakawa, A., 1984: Boundary conditions in limited-area models. Proceedings of the Workshop on Limited-Area Numerical Weather Prediction Models for Computers of Limited Power, Short- and Medium- Range Weather Prediction Research Publication Series No. 13 (WMO/TD No. 19), World Meteorological Organization, Geneva, Switzerland, 403–436.
——, and V. R. Lamb, 1977: Computational design of the basic dynamical processes of the UCLA general circulation model. Methods in Comput. Phys., Vol. 17, Academic Press, 174–265.
Barros, S. R. M., D. Dent, L. Isaksen, and G. Robinson, 1995: The IFS model overview and parallel strategies. Parallel Supercomputing in Atmospheric Science: Sixth ECMWF Workshop on the Use of Parallel Processors in Meteorology. World Scientific, 303–318.
——, ——, ——, and ——, 1996: A parallel spectral model. Research activities in atmospheric and oceanic modelling. CAS/JSC WGNE Rep. No. 23 (WMO/TD - No. 734), World Meteorological Organization, I.2–I.4.
Bartello, P., and S. J. Thomas, 1996: The cost-effectiveness of semi-Lagrangian advection. Mon. Wea. Rev.,124, 2883–2897.
Bates, J. R., 1991: Comments on “Noninterpolating semi-Lagrangian advection schemes with minimized dissipation and dispersion errors.” Mon. Wea. Rev.,119, 230.
——, 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.
Baumhefner, D. P., and D. J. Perkey, 1982: Evaluation of lateral boundary errors in a limited-domain model. Tellus,34, 409–428.
Bélair, S., P. Lacarrère, J. Noilhan, V. Masson, and J. Stein, 1998: High-resolution simulation of surface and turbulent fluxes during HAPEX-MOBILHY. Mon. Wea. Rev., in press.
Benoit, R., M. Desgagné, P. Pellerin, S. Pellerin, Y. Chartier, and S. Desjardins, 1997: The Canadian MC2: A semi-Lagrangian, semi-implicit wideband atmospheric model suited for finescale process studies and simulation. Mon. Wea. Rev.,125, 2382–2415.
Bermejo, R., and A. Staniforth, 1992: The conversion of semi-Lagrangian advection schemes to quasi-monotone schemes. Mon. Wea. Rev.,120, 2622–2632.
Bougeault, P., 1997: Physical parameterization for limited area models: some current problems and issues. Meteor. Atmos. Phys.,63, 71–88.
Bubnova, R., G. Hello, P. Bénard, and J.-F.Geleyn, 1995: Integration of the fully elastic equations cast in hydrostatic pressure terrain-following coordinate in the framework of the ARPEGE/Aladin NWP system. Mon. Wea. Rev.,123, 515–535.
Caian, M., and J.-F. Geleyn, 1997: Some limits to the variable mesh solution and comparison with the nested LAM one. Quart. J. Roy. Meteor. Soc.,123, 743–766.
Chen, M., and J. R. Bates, 1996a: Forecast experiments with a global finite-difference semi-Lagrangian model. Mon. Wea. Rev.,124, 1992–2007.
——, and ——, 1996b: A comparison of climate simulations from a semi-Lagrangian and an Eulerian GCM. J. Climate,9, 1126–1149.
Chouinard, C., J. Mailhot, H. L. Mitchell, A. Staniforth, and R. Hogue, 1994: The Canadian regional data assimilation system: operational and research applications. Mon. Wea. Rev.,122, 1306–1325.
Concus, P., G. H. Golub, and D. P. O’Leary, 1976. A generalized conjugate gradient method for the numerical solution of partial differential equations. Sparse Matrix Computations, R. Bunch and D. J. Rose, Eds., Academic Press, 309–322.
Côté, J., 1988: A Lagrange multiplier approach for the metric terms of semi-Lagrangian models on the sphere. Quart. J. Roy. Meteor. Soc.,114, 1347–1352.
——, M. Roch, A. Staniforth, and L. Fillion, 1993: A variable-resolution semi-Lagrangian finite-element global model of the shallow-water equations. Mon. Wea. Rev.,121, 231–243.
——, J.-G. Desmarais, S. Gravel, A. Méthot, A. Patoine, M. Roch, and A. Staniforth, 1998: The operational CMC–MRB Global Environmental Multiscale (GEM) model. Part II: Results. Mon. Wea. Rev.,126, 1397–1418.
Courtier, P., and J.-F. Geleyn, 1988: A global numerical weather prediction model with variable resolution: Application to the shallow-water equations. Quart. J. Roy. Meteor. Soc.,114, 1321–1346.
——, C. Freydiet, J.-F. Geleyn, F. Rabier, and M. Rochas, 1991: The Arpege project at Météo France. Proc. Numerical Methods in Atmospheric Models, European Centre for Medium-Range Weather Forecasts, 193–231.
——, J.-N. Thépaut, and A. Hollingsworth, 1994: A strategy for operational implementation of 4D-Var, using an incremental approach. Quart. J. Roy. Meteor. Soc.,120, 1367–1388.
Cullen, M. J. P., 1993: The unified forecast/climate model. Meteor. Mag.,122, 81–94.
——, T. Davies, M. H. Mawson, J. A. James, and S. C. Coulter, 1997:An overview of numerical methods for the next generation UK NWP and climate model. The André J. Robert Memorial Volume, Canadian Meteorological and Oceanographic Society, 425–444.
Daley, R., 1991: Atmospheric Data Analysis. Cambridge Atmospheric and Space Science Series, Vol. 2, Cambridge University Press, 457 pp.
Daley, R. W., 1988: The normal modes of the spherical non-hydrostatic equations with applications to the filtering of acoustic modes. Tellus,40A, 96–106.
Dastoor, A. P., and J. Pudykiewicz, 1996: A numerical global meteorological sulfur transport model and its application to arctic air pollution. Atmos. Environ.,30, 1501–1522.
Davies, H. C., 1976: A lateral boundary formulation for multi-level prediction models. Quart. J. Roy. Meteor. Soc.,102, 405–418.
——, 1983: Limitations of some common lateral boundary schemes used in regional NWP models. Mon. Wea. Rev.,111, 1002–1012.
Déqué, M., and J. P. Piedelievre, 1995: High resolution climate simulation over Europe. Climate Dyn.,11, 321–339.
Dickinson, A., P. Burton, J. Parker, and R. Baxter, 1995: Implementation and initial results from a parallel version of the Meteorological Office atmosphere prediction model. Parallel Supercomputing in Atmospheric Science: Sixth ECMWF Workshop on the Use of Parallel Processors in Meteorology. World Scientific, 177–194.
Dietachmayer, G. S., 1990: Comments on “Noninterpolating semi-Lagrangian advection schemes with minimized dissipation and dispersion errors.” Mon. Wea. Rev.,118, 2252–2253.
DiMego, G. J., K. E. Mitchell, R. A. Petersen, J. E. Hoke, J. P. Gerrity, J. C. Tuccilo, R. L. Wobus, and H. H. Juang, 1992: Changes to NMC’s Regional Analysis and Forecast System. Wea. Forecasting,7, 185–198.
Drake, J. B., I. T. Foster, J. G. Michalakes, B. Toonen, and P. H. Worley, 1995: Design and performance of a scalable parallel community climate model. Parallel Comput.,21, 1571–1592.
Edouard, S., B. Legras, F. Lefèvre, and R. Eymard, 1996: The effect of mixing on ozone depletion in the Arctic. Nature,384, 444–447.
Errico, R., and D. Baumhefner, 1987: Predictability experiments using a high-resolution limited-area model. Mon. Wea. Rev.,115, 488–504.
——, T. Vukicevic, and K. Raeder, 1993: Comparison of initial and lateral boundary condition sensitivity for a limited-area model. Tellus,45A, 539–557.
Estrade, J. F., and D. Birman, 1995: Adapting parallel IFS/ARPEGE to METEO-FRANCE implementation. Parallel Supercomputing in Atmospheric Science: Sixth ECMWF Workshop on the Use of Parallel Processors in Meteorology. World Scientific, 206–222.
Fillion, L., H. L. Mitchell, H. Ritchie, and A. Staniforth, 1995: The impact of a digital filter finalization technique in a global data assimilation system. Tellus,47A, 304–323.
Fox-Rabinovitz, M., G. Stenchikov, M. Suarez, and L. Takacs, 1997:A finite-difference GCM dynamical core with a variable resolution stretched grid. Mon. Wea. Rev.,125, 2943–2968.
Gates, W. L., 1992: AMIP: The Atmospheric Model Intercomparison Project. Bull. Amer. Meteor. Soc.,73, 1962–1970.
——, ed. 1995: The Proceedings of the First International AMIP Scientific Conference. WCRP-92, WMO/TD-No. 732, World Climate Research Programme, World Meteorological Organisation, 532 pp.
Gauthier, P., L. Fillion, P. Koclas, and C. Charette, 1996: Implementation of a 3D variational analysis at the Canadian Meteorological Centre. Preprints, 11th Conf. on Numerical Weather Prediction, Norfolk, Virginia, American Meteor. Soc. 232–234.
Gravel, S., and A. Staniforth, 1992: Variable resolution and robustness. Mon. Wea. Rev.,120, 2633–2640.
——, ——, and J. Côté, 1993: A stability analysis of a family of baroclinic semi-Lagrangian forecast models. Mon. Wea. Rev.,121, 815–826.
Gustafsson, N., 1990: Sensitivity of limited area model data assimilation to lateral boundary condition fields. Tellus,42A, 109–115.
——, and A. McDonald, 1996: A comparison of the HIRLAM gridpoint and spectral semi-Lagrangian models. Mon. Wea. Rev.,124, 2008–2022.
Hack, J. J., J. M. Rosinski, D. L. Williamson, B. A. Boville, and J. E. Truesdale, 1995: Computational design of the NCAR community climate model. Parallel Comput.,21, 1545–1569.
Hammond, S. W., R. D. Loft, J. M. Dennis, and R. K. Sato, 1995: Implementation and performance issues of a massively parallel atmospheric model. Parallel Comput.,21, 1593–1610.
Hardiker, V., 1997: A global numerical weather prediction model with variable resolution. Mon. Wea. Rev.,125, 59–73.
Harrison, E. J., and R. L. Elsberry, 1972: A method of incorporating nested finite grids in the solution of systems of geophysical equations. J. Atmos. Sci.,29, 1235–1245.
Held, I. M., and M. J. Suarez, 1994: A proposal for the intercomparison of the dry dynamical cores of atmospheric general circulation models. Bull. Amer. Meteor. Soc.,75, 1825–1830.
Henderson, T., C. Baillie, S. Benjamin, M. Govett, L. Hart, A. Marroquin, B. Rodriguez, T. Black, R. Bleck, G. Carr, and J. Middlecoff, 1995: Progress toward demonstrating operational capability of massively parallel processors at the Forecast Systems Laboratory. Parallel Supercomputing in Atmospheric Science: Sixth ECMWF Workshop on the Use of Parallel Processors in Meteorology. World Scientific, 162–176.
Héreil, P., and R. Laprise, 1996: Sensitivity of internal gravity waves to the time step of a semi-implicit semi-Lagrangian nonhydrostatic model. Mon. Wea. Rev.,124, 972–999.
Imbard, M., A. Craplet, P. Degardin, Y. Durand, A. Joly, N. Marie, and J.-F. Geleyn, 1987: Fine-mesh limited area forecasting with the French operational Peridot system. Proc., The Nature and Prediction of Extra-tropical Weather Systems. Vol. II, European Centre for Medium-Range Weather Forecasts, Shinfield Park, Reading, United Kingdom, 231–269.
Isaksen, L., and S. R. M. Barros, 1995: IFS 4d-variational analysis overview and parallel strategy. Parallel Supercomputing in Atmospheric Science: Sixth ECMWF Workshop on the Use of Parallel Processors in Meteorology, World Scientific, 337–351.
Jones, R. G., J. M. Murphy, and M. Noguer, 1995: Simulation of climate change over Europe using a nested regional-climate model. I: Assessment of control climate, including sensitivity to location of lateral boundaries. Quart. J. Roy. Meteor. Soc.,121, 1413–1449.
——, ——, ——, and A. B. Keen, 1997: Simulation of climate change over Europe using a nested regional-climate model. II: Comparison of driving and regional model responses to a doubling of carbon dioxide. Quart. J. Roy. Meteor. Soc.,123, 265–292.
Kalnay de Rivas, E., 1972: On the use of nonuniform grids in finite-difference equations. J. Comput. Phys.,10, 202–210.
Kasahara, A., 1974: Various vertical coordinate systems used for numerical weather prediction. Mon. Wea. Rev.,102, 509–522.
Kreiss, H, and J. Oliger, 1973: Methods for the Approximate Solution of Time Dependent Problems. GARP Publ. Series, No. 10, World Meteorological Organization, 107 pp. [Available from World Meteorological Organization, Case Postale 2300, CH-1211 Geneva 2, Switzerland.].
Kurihara, Y., and R. E. Tuleya, 1974: Structure of a tropical cyclone developed in a three-dimensional numerical simulation model. J. Atmos. Sci.,31, 893–919.
Laprise, R., 1992: The Euler equations of motion with hydrostatic pressure as independent variable. Mon. Wea. Rev.,120, 197–207.
Leslie, L. M., and G. S. Dietachmayer, 1997: Comparing schemes for integrating the Euler equations. Mon. Wea. Rev.,125, 1687–1691.
Lynch, P., and X.-Y. Huang, 1994. Diabatic initialization using recursive filters. Tellus,46A, 583–597.
Mailhot, J., R. Sarrazin, B. Bilodeau, N. Brunet, and G. Pellerin, 1997: Development of the 35-km version of the operational regional forecast system. Atmos.–Ocean,35, 1–28.
McFarlane, N. A., G. J. Boer, J.-P. Blanchet, and M. Lazare, 1992: The Canadian Climate Centre second-generation general circulation model and its equilibrium climate. J. Climate,5, 1013–1044.
Mesinger, F., 1973: A method for construction of second-order accuracy difference schemes permitting no false two-grid-interval wave in the height field. Tellus,25, 444–458.
Michalakes, J., T. Canfield, R. Nanjundiah, S. Hammond, and G. Grell, 1995: Parallel implementation, validation, and performance of MM5. Parallel Supercomputing in Atmospheric Science: Sixth ECMWF Workshop on the Use of Parallel Processors in Meteorology. World Scientific, 266–276.
Mitchell, H. L., C. Chouinard, C. Charette, R. Hogue, and S. J. Lambert, 1996: Impact of a revised analysis algorithm on an operational data assimilation system. Mon. Wea. Rev.,124, 1243–1255.
Miyakoda, K., and A. Rosati, 1977: One-way nested grid models: the interface conditions and the numerical accuracy. Mon. Wea. Rev.,105, 1092–1107.
Moncrieff, M. W., S. K. Krueger, D. Gregory, J.-L. Redelsperger, and W.-K. Tao, 1997: GEWEX Cloud System Study (GCSS) Working Group 4: precipitating convective cloud systems. Bull. Amer. Meteor. Soc.,78, 831–845.
Moorthi, S., 1997: NWP experiments with a gridpoint semi-Lagrangian semi-implicit global model at NCEP. Mon. Wea. Rev.,125, 74–98.
——, R. W. Higgins and J. R. Bates, 1995: A global multilevel atmospheric model using a vector semi-Lagrangian finite-difference scheme. Part II: Version with physics. Mon. Wea. Rev.,123, 1523–1541.
Murphy, J. M., 1995: Transient response of the Hadley Centre coupled ocean–atmosphere model to increasing carbon dioxide. Part I: Control climate and flux adjustment. J. Climate,8, 36–56.
——, and J. F. B. Mitchell, 1995: Transient response of the Hadley Centre coupled ocean–atmosphere model to increasing carbon dioxide. Part II: Spatial and temporal structure of response. J. Climate,8, 57–80.
Oliger, J., and A. Sundström, 1978: Theoretical and practical aspects of some initial boundary value problems in fluid dynamics. S.I.A.M. J. Appl. Math.,35, 419–446.
Paegle, J., 1989: A variable resolution global model based upon Fourier and finite element representation. Mon. Wea. Rev.,117, 583–606.
——, Q. Yang, and M. Wang, 1997: Predictability in limited area and global models. Meteor. Atmos. Phys.,63, 53–69.
Parrish, D. F., and J. C. Derber, 1992: The National Meteorological Center’s spectral statistical-interpolation analysis system. Mon. Wea. Rev.,120, 1747–1763.
Perkey, D. J., and C. Kreitzberg, 1976: A time-dependent lateral boundary scheme for limited-area primitive equation models. Mon. Wea. Rev.,104, 744–755.
Phillips, N. A., 1957: A coordinate system having some special advantages for numerical forecasting. J. Meteor.,14, 184–185.
——, and J. Shukla, 1973: On the strategy of combining coarse and fine grid meshes in numerical weather prediction. J. Appl. Meteor.,12, 763–770.
Pinty, J.-P., R. Benoit, E. Richard, and R. Laprise, 1995: Simple tests of a semi-implicit semi-Lagrangian model on 2D mountain wave problems. Mon. Wea. Rev.,123, 3042–3058.
Polavarapu, S., and M. Tanguay, 1998: Linearising iterative processes for four-dimensional data assimilation. Quart. J. Roy. Meteor. Soc., in press.
——, ——, R. Ménard, and A. Staniforth, 1995: The tangent linear model for semi-Lagrangian schemes—Linearizing the process of interpolation. Tellus,47A, 74–95.
Priestley, A., 1993: A quasi-conservative version of the semi-Lagrangian advection scheme. Mon. Wea. Rev.,121, 621–629.
Purser, R. J., and L. M. Leslie, 1994: An efficient semi-Lagrangian scheme using third-order semi-implicit time integration and forward trajectories. Mon. Wea. Rev.,122, 745–756.
Ritchie, H., and C. Beaudoin, 1994: Approximations and sensitivity experiments with a baroclinic semi-Lagrangian spectral model. Mon. Wea. Rev.,122, 2391–2399.
——, C. Temperton, A. Simmons, M. Hortal, T. Davies, D. Dent, and M. Hamrud, 1995: Implementation of the semi-Lagrangian method in a high-resolution version of the ECMWF forecast model. Mon. Wea. Rev.,123, 489–514.
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.
Robert, A., 1981: A stable numerical integration scheme for the primitive meteorological equations. Atmos.–Ocean,19, 35–46.
——, 1982: A semi-Lagrangian and semi-implicit numerical integration scheme for the primitive meteorological equations. J. Meteor. Soc. Japan,60, 319–325.
——, and E. Yakimiw, 1986: Identification and elimination of an inflow boundary computational solution in limited area model integrations. Atmos.–Ocean,24, 369–385.
——, T. L. Yee, and H. Ritchie, 1985: A semi-Lagrangian and semi-implicit numerical integration scheme for multilevel atmospheric models. Mon. Wea. Rev.,113, 388–394.
Rogers, E., T. L. Black, D. G. Deaven, G. J. DiMego, Q. Zhao, M. Baldwin, N. W. Junker, and Y. Lin, 1996: Changes to the operational “Early” Eta analysis/forecast system at the National Centers for Environmental Prediction. Wea. Forecasting,11, 391–413.
Rood, R. B., 1996: Three dimensional transport models. Global Tracer Transport Models, WMO/TD-No. 770, World Meteorological Organization. 152–156.
Schmidt, F., 1977: Variable fine mesh in the spectral global models. Beitr. Phys. Atmos.,50, 211–217.
Semazzi, F. H. M., J.-H. Qian, and J. S. Scroggs, 1995: A global nonhydrostatic semi-Lagrangian atmospheric model. Mon. Wea. Rev.,123, 2534–2550.
Sharma, O. P., H. Upadhyaya, Th. Braine-Bonnaire, and R. Sadourny, 1987: Experiments on regional forecasting using a stretched coordinate general circulation model. Short- and Medium- Range Numerical Weather Prediction, Proc. WMO/IUGG NWP Symposium, Tokyo, Japan, Met. Soc. Japan, 263–271.
Skamarock, W. C., P. K. Smolarkiewicz, and J. B. Klemp, 1997: Preconditioned conjugate-residual solvers for Helmholtz equations in nonhydrostatic models. Mon. Wea. Rev.,125, 587–599.
Smith, B., P. Bjorstad, and W. Gropp, 1996. Domain Decomposition:Parallel Multilevel Methods for Elliptic Partial Differential Equations. Cambridge University Press, 224 pp.
Staniforth, A., 1987: Review—Formulating efficient finite-element codes for flows in regular domains. Int. J. Numer. Methods Fluids,7, 1–16.
——, 1997: Regional modeling: A theoretical discussion. Meteor. Atmos. Phys.,63, 15–29.
——, and J. Côté, 1991: Semi-Lagrangian integration schemes for atmospheric models—A review. Mon. Wea. Rev.,119, 2206–2223.
Sundström, A., and T. Elvius, 1979: Computational problems related to limited-area modeling. Numerical Methods Used in Atmospheric Models, Vol. II, GARP Series No. 17, World Meteorological Organization, 379–416. [Available from World Meteorological Organization, Case Postale 2300, CH-1211 Geneva 2, Switzerland.].
Tanguay, M., A. Simard, and A. Staniforth, 1989: A three-dimensional semi-Lagrangian scheme for the Canadian regional finite-element forecast model. Mon. Wea. Rev.,117, 1861–1871.
——, A. Robert, and R. Laprise, 1990: A semi-implicit semi-Lagrangian fully compressible regional forecast model. Mon. Wea. Rev.,118, 1970–1980.
——, S. Polavarapu, and P. Gauthier, 1997: Temporal accumulation of first-order linearization error for semi-Lagrangian passive advection. Mon. Wea. Rev.,125, 1296–1311.
Verseghy, D., 1991: CLASS—A Canadian land surface scheme for GCMs. I: Soil model. Int. J. Climatol.,11, 111–113.
——, 1993: CLASS—A Canadian land surface scheme for GCMs. II: Vegetation model and coupled runs. Int. J. Climatol.,13, 343–370.
Vichnevetsky, R., 1986: Invariance theorems concerning reflection at numerical boundaries. J. Comput. Phys.,63, 268–282.
——, 1987: Wave propagation and reflection in irregular grids for hyperbolic equations. Appl. Numer. Math.,2, 133–166.
——, and L. H. Turner, 1991: Spurious scattering from discontinuously stretching grids in computational fluid dynamics. J. Appl. Math.,8, 315–328.
von Laszewski, G., M. Seablom, M. Makivic, P. Lyster, and S. Ranka, 1995: Design issues for the parallelization of an optimal interpolation algorithm Parallel Supercomputing in Atmospheric Science: Sixth ECMWF Workshop on the Use of Parallel Processors in Meteorology, World Scientific, 290–302.
Vukicevic, T., and R. Errico, 1990: The influence of artificial and physical factors upon predictability estimates using a complex limited-area model. Mon. Wea. Rev.,118, 1460–1482.
Walsh, K., and J. L. McGregor, 1995: January and July climate simulations over the Australian region using a limited area model. J. Climate,8, 2387–2403.
Weisman, M. L., W. C. Skamarock, and J. B. Klemp, 1997: The resolution dependence of explicitly modeled convective systems. Mon. Wea. Rev.,125, 527–548.
Williamson, D. L., and G. L. Browning, 1974: Formulation of the lateral boundary conditions for the NCAR limited area model. J. Appl. Meteor.,13, 8–16.
——, and J. G. Olson, 1994: Climate simulations with a semi-Lagrangian version of the NCAR CCM2. Mon. Wea. Rev.,122, 1594–1610.
——, and ——, 1998: A comparison of semi-Lagrangian and Eulerian polar climate simulations. Mon. Wea. Rev.,126, 991–1000.
——, ——, and B. A. Boville, 1998. A comparison of semi-Lagrangian and Eulerian tropical climate simulations. Mon. Wea. Rev.,126, 1001–1012.
Wolters, L., R. van Engelen, G. Cats, N. Gustafsson, and T. Wilhelmsson, 1995: A data parallel HIRLAM forecast model. Parallel Supercomputing in Atmospheric Science: Sixth ECMWF Workshop on the Use of Parallel Processors in Meteorology, World Scientific, 49–62.
Yakimiw, E., and A. Robert, 1990: Validation experiments for a nested grid-point regional forecast model. Atmos.–Ocean, 466–472.
Yanenko, N. N., 1971. The Method of Fractional Steps. Springer, 160 pp.
Yessad, K., and P. Bénard, 1996: Introduction of a local mapping factor in the spectral part of the Météo France global variable mesh numerical forecast model. Quart. J. Roy. Meteor. Soc.,122, 1701–1719.
Zhang, D.-L., H.-R. Chang, N. L. Seaman, T. T. Warner, and J. M. Fritsch, 1986: A two-way interactive nesting procedure with variable terrain resolution. Mon. Wea. Rev.,114, 1330–1339.
Zupanski, M., 1993: Regional four-dimensional variational data assimilation in a quasi-operational forecasting environment. Mon. Wea. Rev.,121, 2396–2408.