Atmospheric dynamics deals with motion in the atmosphere and its thermodynamic state. Our research on this subject aims to improve the mathematical equations, numerical methods, and the dynamical core of the forecast model, as well as technical aspects such as implementation on high-performance computers.

The dynamical core in the forecast model discretises the Euler equations of motion, resolving flow features to approximately 4-6 grid-cells at the nominal resolution. The subgrid-scale features and unresolved processes are described by atmospheric physics parametrizations.

The Integrated Forecasting System (IFS)

The dynamical core of IFS is hydrostatic, two-time-level, semi-implicit, semi-Lagrangian and applies spectral transforms between grid-point space (where the physical parametrizations and advection are calculated) and spectral space. In the vertical the model is discretised using a finite-element scheme. A reduced Gaussian grid is used in the horizontal.

The IFS also has extra configurations available for research experiments that are not used operationally. An example is the non-hydrostatic dynamical core. 

Official IFS documentation


The IFS hydrostatic dynamical core is described in more detail in:

  • Hortal, M. (2002). The development and testing of a new two-time-level semi-Lagrangian scheme (SETTLS) in the ECMWF forecast model. Q. J. R. Meteorol. Soc, 128, 1671–1687.
  • Hortal, M. and Simmons, A. J. (1991). Use of reduced Gaussian grids in spectral models. Mon. Wea. Rev., 119, 1057–1074.
  • Ritchie, H., Temperton, C., Simmons, A., Hortal, M., Davies, T., Dent, D. and Hamrud, M. (1995). Implementation of the semi-Lagrangian method in a high-resolution version of the ECMWF forecast model. Mon. Wea. Rev., 123, 489–514.
  • Simmons, A. J. and Burridge, D. M. (1981). An energy and angular momentum conserving vertical finite difference scheme and hybrid vertical coordinates. Mon. Wea. Rev., 109, 758–766.
  • Simmons, A. J., Burridge, D. M., Jarraud, M., Girard, C. and Wergen, W. (1989). The ECMWF medium-range prediction models: development of the numerical formulations and the impact of increased resolution. Meteorol. Atmos. Phys., 40, 28–60.
  • Temperton, C. (1991). On scalar and vector transform methods for global spectral models. Mon. Wea. Rev., 119, 1303–1307.
  • Temperton, C., Hortal, M. and Simmons, A. (2001), A two-time-level semi-Lagrangian global spectral model. Q.J.R. Meteorol. Soc., 127: 111–127.
  • Untch, A. and Hortal, M. (2004). A finite-element scheme for the vertical discretisation of the semi-Lagrangian version of the ECMWF forecast model. Q. J. R. Meteorol. Soc., 130, 1505–1530.
  • Wedi, N.P. and P.K. Smolarkiewicz (2009). A framework for testing global nonhydrostatic models, Q.J.R. Meteorol. Soc. 135, 469-484.


Other relevant papers:

  • Bénard, P., J. Vivoda, J. Mašek, P. Smolíková, K. Yessad, C. Smith, R. Brožková, and J.-F. Geleyn, (2010) Dynamical kernel of the Aladin-NH spectral limited-area model: Revised formulation and sensitivity experiments. Quart. J. Roy. Meteor. Soc., 136, 155–169.
  • Bubnová, R., G. Hello, P. Bénard, J.-F. Geleyn, (1995) Integration of the Fully Elastic Equations Cast in the Hydrostatic Pressure Terrain-Following Coordinate in the Framework of the ARPEGE/Aladin NWP System. Mon. Wea. Rev., 123, 515–535.

Hydrostatic and non-hydrostatic dynamics

Hydrostatic equilibrium describes the atmospheric state in which the upward directed pressure gradient force (the decrease of pressure with height) is balanced by the downward-directed gravitational pull of the Earth. On average the Earth’s atmosphere is always close to hydrostatic equilibrium. This has been used to approximate the Euler equations underlying weather prediction models and successfully applied in NWP and climate prediction. Non-hydrostatic dynamical effects start to become important below horizontal scales of about 10km.

The current ECMWF model uses a hydrostatic dynamical core for all forecasts. A non-hydrostatic version developed by the ALADIN modelling consortium, made available by Météo-France through the IFS/ARPEGE collaboration, is in use at ECMWF for research purposes. The PantaRhei project (see below) is an alternate approach to represent non-hydrostatic effects.

Current research

PantaRhei: multi-scale fluid flow

ECMWF hosts the PantaRhei project, the development of an interdisciplinary forecasting system for simulating multi-scale fluid flows (funded by the European Research Council). The project explores a hybrid approach for forecasting global weather and climate that combines the strengths of established and efficient (at large hydrostatic scales) structured grid numerical weather prediction (NWP) and climate models with control-volume (small-scale) edge-based codes, originating from other computational fluid dynamics (CFD) disciplines. The work will synthesise the complementary skills of two exceptionally successful modelling systems: ECMWF's Integrated Forecasting System (IFS) and the nonhydrostatic research model EULAG. The essence of the proposal is a pioneering numerical approach, where a nonhydrostatic global model is conditioned by global hydrostatic solutions within a single code framework. The new model will prepare ECMWF for predicting with greater fidelity extreme weather events that are critical to the protection of society. Moreover, it is envisaged that the next generation forecasting system will be one of the most advanced computing tools available to the European community for operations, research and education.

For more information see PantaRhei project page.


Future high performance computer (HPC) architectures will continue the trend of increasing numbers of computer cores, as well as use of co-processors (such as GPUs). To ensure IFS performs efficiently on current and future HPC platforms is a challenge and ECMWF conducts research in new programming concepts and alternative numerical algorithms in all areas of the IFS.

The EU-funded CRESTA project has contributed ECMWF efforts in the area of scalability.

For more information see section on Scalability on the project page.