At ECMWF, two nonhydrostatic dynamical cores are available: a nonhydrostatic spectral transform, which extends the hydrostatic spectral formulation used in the operational Integrated Forecasting System (IFS), and a grid-point dynamical core based on the finite volume method, designed for scalability at high resolutions. This study focuses on the spectral nonhydrostatic dynamical core (NH‑IFS), originally developed for the ALADIN model and later extended for the ARPEGE model by Météo-France. ECMWF shares this component of the model code with its Member States. NH‑IFS uses finite element discretisation in the vertical to ensure full compatibility with its hydrostatic counterpart (HY‑IFS).
It is generally accepted that nonhydrostatic (NH) effects become relevant at horizontal grid spacings finer than 10 km, and models at 1 km grid spacing or finer must use NH dynamics to maintain physical realism. The EU’s Destination Earth (DestinE) initiative, which is partly implemented by ECMWF, aims to push global numerical weather prediction (NWP) toward these horizontal scales. Therefore, the significance of NH effects must be tested experimentally within the full framework of the spectral IFS to determine the grid spacing at which they become essential for accurate medium-range weather forecasting.
Ensuring consistent comparisons
To ensure a fair and consistent comparison between HY-IFS and NH‑IFS, the following key improvements have been introduced into NH‑IFS:
- Stabilizing model time-stepping and improving its accuracy: NH‑IFS required modifications to its time integration scheme to maintain numerical stability and improve its accuracy. This was achieved by ensuring full consistency between the nonlinear and linear parts of the dynamics, improving the coupling of the iterative time-stepping scheme with physics, adapting NH‑IFS for single-precision computations, and suppressing numerical noise through slight first- or second-order decentering.
- Ensuring NH dynamics is an extension of HY dynamics: NH‑IFS is now formulated as a direct extension of HY‑IFS. To ensure consistency, all terms common to both models employ identical numerical methods. As a result, NH‑IFS solutions match HY‑IFS outputs at scales where the hydrostatic approximation holds.
- Switch to a unified NH/HY vertical finite element (VFE) scheme: ECMWF is the first centre performing such a comparison with a VFE scheme; other partners use a finite difference scheme version of NH dynamics.
Case studies and systematic verification
We compare NH‑IFS with HY‑IFS at 9 km, 4.4 km, 2.8 km, and 1.4 km grid spacings using cubic spectral truncation. The goal is to assess the impact of nonhydrostatic effects across different scales, focusing on two phenomena where such effects are theoretically expected to appear:
- gravity wave propagation over complex terrain during strong near-surface flows
- tropical cyclones, where large-scale convection dominates.
Nonhydrostatic effects primarily influence the dispersion properties of small-scale gravity waves (GWs), affecting the characteristics of mountain-induced waves above major mountain ranges. While the HY-IFS model restricts wave propagation predominantly to the vertical, NH-IFS supports more dispersive wave dynamics, including significant horizontal propagation and the vertical trapping of small-scale modes. This increased dispersion tends to limit the upward transmission of wave energy, resulting in fewer waves reaching the upper troposphere and stratosphere, depending on background atmospheric conditions. These waves can generate clear-air turbulence, and momentum deposited by such waves can influence jet streams in the troposphere and stratosphere.
For this evaluation, January and February 2022 were selected – a period characterised by persistent strong near-surface winds above the Himalayas. The first figure shows that, under such conditions, NH effects are evident in +96 h forecasts, and the root-mean-square wind error at 100 hPa is significantly reduced. NH‑IFS propagates less gravity wave energy associated with mountain waves into these regions of the atmosphere, consistent with established theory. Such signals can be seen only in the stratosphere above the Himalaya region in the winter period.
The influence of NH effects on tropical cyclones was also investigated. However, no significant impact was found when analysing maximum wind speeds and minimum surface pressure.
The second figure illustrates how model resolution affects the manifestation of NH effects. The kinetic energy spectra, representing energy associated with various horizontal scales at model level 50 hPa, show that differences begin to appear at a grid spacing of 2.8 km for horizontal scales shorter than 20 km.
Conclusion
Recent advances in nonhydrostatic modelling at ECMWF have made the NH-IFS stable at horizontal grid spacings down to 1.4 km. This opens up opportunities to investigate the role of nonhydrostatic processes at the scales targeted by the DestinE initiative. However, studies have demonstrated that, at the 4.4 km grid spacing currently used in the DestinE operational suite, it is not essential to consider nonhydrostatic dynamics. Given that NH‑IFS is approximately 2.5 times more expensive in terms of computational resources compared to HY‑IFS, its use must be justified by compelling evidence. Systematic evaluation of its added value will continue, including verification against high-resolution observational data.