**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.

### References

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. -
Diamantakis M., F. Váňa, (2021) A fast converging and concise algorithm for computing the departure points in semi-Lagrangian weather and climate models,

*Quart. J. Roy. Meteor. Soc.*,**148****,**670-684.

## 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 based on the spectral-transform approach for all forecasts. A non-hydrostatic extension developed by the ALADIN modelling consortium, which has been made available by Météo-France through the IFS/ARPEGE collaboration, is in use at ECMWF for research purposes. The IFS-FVM is an alternative non-hydrostatic dynamical core based on a finite-volume discretisation.

## Current research

### IFS-FVM

Even if the accuracy and efficiency of the existing spectral-transform IFS model (IFS-ST) can remain highly competitive compared to other NWP models beyond 2025, it is important for ECMWF to invest in novel technologies to ensure that the high efficacy of its forecast system is maintained in the longer term. Thanks to the finite-volume discretisation, the IFS-FVM complements IFS-ST with a local parallel communication footprint, fully conservative and monotone advective transport, and flexible horizontal and vertical meshes. Despite the different model formulations, IFS-FVM and IFS-ST can share important features, such as the octahedral reduced Gaussian grid and the IFS physics parametrizations. In general, these common features of IFS-FVM and IFS-ST facilitate their coexistence and combination in IFS.

The IFS-FVM development was initiated by the ERC funded PantaRhei project which ended in 2018. More information can be found on the PantaRhei project page.

### From Scalability to Destination Earth

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 ESCAPE-project has contributed to ECMWF efforts in the area of scalability. In 2018 ESCAPE was succeeded by ESCAPE-2 which continues its pioneering work. More information can be found in Scalability in the original project page.

The Scalability Programme matured, passing from research to implementation phase. It helped ECMWF to be a key participant in the ambitious EU initiative Destination Earth which aims to develop a highly accurate digital twin of our planet. The role that scalability played to help the evolution to Destination Earth is summarized in the following newsletter article.