Linearly implicit time stepping methods for numerical weather prediction

Abstract. We present a nonhydrostatic finite-volume global atmospheric model formulation for numerical weather prediction with the Integrated Forecasting System (IFS) at ECMWF and compare it to the established operational spectral-transform formulation. The novel Finite-Volume Module of the IFS (henceforth IFS-FVM) integrates the fully compressible equations using semi-implicit time stepping and non-oscillatory forward-in-time (NFT) Eulerian advection, whereas the spectral-transform IFS solves the hydrostatic primitive equations (optionally the fully compressible equations) using a semi-implicit semi-Lagrangian scheme. The IFS-FVM complements the spectral-transform counterpart by means of the finite-volume discretization with a local low-volume communication footprint, fully conservative and monotone advective transport, all-scale deep-atmosphere fully compressible equations in a generalized height-based vertical coordinate, and flexible horizontal meshes. Nevertheless, both the finite-volume and spectral-transform formulations can share the same quasi-uniform horizontal grid with co-located arrangement of variables, geospherical longitude–latitude coordinates, and physics parameterizations, thereby facilitating their comparison, coexistence, and combination in the IFS. We highlight the advanced semi-implicit NFT finite-volume integration of the fully compressible equations of IFS-FVM considering comprehensive moist-precipitating dynamics with coupling to the IFS cloud parameterization by means of a generic interface. These developments – including a new horizontal–vertical split NFT MPDATA advective transport scheme, variable time stepping, effective preconditioning of the elliptic Helmholtz solver in the semi-implicit scheme, and a computationally efficient implementation of the median-dual finite-volume approach – provide a basis for the efficacy of IFS-FVM and its application in global numerical weather prediction. Here, numerical experiments focus on relevant dry and moist-precipitating baroclinic instability at various resolutions. We show that the presented semi-implicit NFT finite-volume integration scheme on co-located meshes of IFS-FVM can provide highly competitive solution quality and computational performance to the proven semi-implicit semi-Lagrangian integration scheme of the spectral-transform IFS.

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Semi-implicit semi-Lagrangian modelling of the atmosphere: a Met Office perspective

Communications in Applied and Industrial Mathematics ◽

10.1515/caim-2016-0020 ◽

2016 ◽

Vol 7 (3) ◽

pp. 4-25 ◽

Cited By ~ 1

Author(s):

Tommaso Benacchio ◽

Nigel Wood

Keyword(s):

Numerical Weather Prediction ◽

Prediction Models ◽

Weather Prediction ◽

Time Integration ◽

Implicit Time ◽

Good Representation ◽

Solution Approach ◽

Numerical Weather ◽

Geostrophic Balance ◽

The Impact

Abstract The semi-Lagrangian numerical method, in conjunction with semi-implicit time integration, provides numerical weather prediction models with numerical stability for large time steps, accurate modes of interest, and good representation of hydrostatic and geostrophic balance. Drawing on the legacy of dynamical cores at the Met Office, the use of the semi-implicit semi-Lagrangian method in an operational numerical weather prediction context is surveyed, together with details of the solution approach and associated issues and challenges. The numerical properties and performance of the current operational version of the Met Office’s numerical model are then investigated in a simplified setting along with the impact of different modelling choices.

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FVM 1.0: A nonhydrostatic finite-volume dynamical core formulation for IFS

10.5194/gmd-2018-237 ◽

2018 ◽

Author(s):

Christian Kühnlein ◽

Willem Deconinck ◽

Rupert Klein ◽

Sylvie Malardel ◽

Zbigniew P. Piotrowski ◽

...

Keyword(s):

Finite Volume ◽

Numerical Weather Prediction ◽

Weather Prediction ◽

Integration Scheme ◽

The Novel ◽

Advective Transport ◽

Numerical Weather ◽

Time Stepping ◽

Spectral Transform ◽

Volume Integration

Abstract. We present a nonhydrostatic finite-volume global atmospheric model formulation for numerical weather prediction with the Integrated Forecasting System (IFS) at ECMWF, and compare it to the established operational spectral-transform formulation. The novel Finite-Volume Module of IFS (henceforth IFS-FVM) integrates the fully compressible equations using semi-implicit time stepping and non-oscillatory forward-in-time (NFT) Eulerian advection, whereas the spectral-transform IFS solves the hydrostatic primitive equations (optionally the fully compressible equations) using a semi-implicit semi-Lagrangian scheme. The IFS-FVM complements the spectral-transform counterpart by means of the finite-volume discretisation with a local communication footprint, fully conservative and monotone advective transport, all-scale deep-atmosphere fully compressible equations in a generalised height-based vertical coordinate, applicable on flexible meshes. Nevertheless, both the finite-volume and spectral-transform formulations can share the same quasi-uniform horizontal grid with co-located arrangement of variables, geospherical longitude-latitude coordinates, and physical parametrisations, thereby facilitating their comparison, coexistence and combination in IFS. We highlight the advanced semi-implicit NFT finite-volume integration of the fully compressible equations of the novel IFS-FVM considering comprehensive moist-precipitating dynamics with coupling to the IFS cloud parametrisation by means of a generic interface. These developments – including a new horizontal-vertical split NFT MPDATA advective transport scheme, variable time stepping, effective preconditioning of the elliptic Helmholtz solver in the semi-implicit scheme, and a computationally efficient coding implementation – provide a basis for the efficacy of IFS-FVM and its application in global numerical weather prediction. Here, numerical experiments focus on relevant dry and moist-precipitating baroclinic instability at various resolutions. We show that the presented semi-implicit NFT finite-volume integration scheme on co-located meshes of IFS-FVM can provide highly competitive solution quality and computational performance to the proven semi-implicit semi-Lagrangian integration scheme of the spectral-transform IFS.

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Mixed Parallel–Sequential-Split Schemes for Time-Stepping Multiple Physical Parameterizations

Monthly Weather Review ◽

10.1175/mwr2893.1 ◽

2005 ◽

Vol 133 (4) ◽

pp. 989-1002 ◽

Cited By ~ 14

Author(s):

Mark Dubal ◽

Nigel Wood ◽

Andrew Staniforth

Keyword(s):

Numerical Weather Prediction ◽

Climate Models ◽

Weather Prediction ◽

Finite Difference Schemes ◽

Time Step ◽

Splitting Technique ◽

Numerical Weather ◽

Advantages And Disadvantages ◽

Time Stepping ◽

Physical Parameterizations

Split schemes for time-stepping physical parameterizations in numerical weather prediction and climate models are investigated within the context of simplified model equations. A symmetrized-splitting technique is applied to various parameterized systems containing fast and slow physics processes. The physics processes are represented by time-dependent forcing terms and linear damping/oscillatory terms. Finite-difference schemes, obtained from the splitting procedures, are examined to determine their stability properties, degree of splitting error, and truncation error. This analysis provides insight into the advantages and disadvantages of different splitting procedures across a range of possible parameterization scenarios. Many schemes obtained via splitting have time-step-dependent splitting errors, which can lead to inaccurate solutions when fast processes are present and the time step is large. Some splitting combinations, however, are more useful than others. The symmetrized-splitting procedure considered in this paper can produce stable first- and second-order accurate schemes, which have either no significant splitting errors or acceptably small errors relative to a steady-state solution. The consequences of this analysis for physics coupling strategies in realistic numerical weather prediction and climate models are noted.

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Implementation of a semi-Lagrangian fully-implicit time integration of the unified soundproof system of equations for numerical weather prediction

Monthly Weather Review ◽

10.1175/mwr-d-20-0291.1 ◽

2021 ◽

Author(s):

Abdessamad Qaddouri ◽

Claude Girard ◽

Syed Zahid Husain ◽

Rabah Aider

Keyword(s):

Numerical Weather Prediction ◽

Weather Prediction ◽

Time Integration ◽

Implicit Time ◽

System Of Equations ◽

Dynamical Core ◽

Vertical Coordinate ◽

Numerical Weather ◽

Fully Implicit ◽

Computational Performance

AbstractAn alternate dynamical core that employs the unified equations of A. Arakawa and C.S. Konor (2009) has been developed within Environment and Climate change Canada’s GEM (Global Environmental Multiscale) atmospheric model. As in the operational GEM dynamical core, the novel core utilizes the same fully-implicit two-time-level semi-Lagrangian scheme for time discretization while the log-pressure-based terrain-following vertical coordinate has been slightly adapted. Overall, the new dynamical core implementation required only minor changes to the existing informatics code of the GEM model and from a computational performance perspective, the new core does not incur any significant additional cost. A broad range of tests – that include both two-dimensional idealized theoretical cases and three-dimensional deterministic forecasts covering both hydrostatic and non-hydrostatic scales–have been carried out to evaluate the performance of the new dynamical core. For all the tested cases, when compared to the operational GEM model, the new dynamical core based on the unified equations has been found to produce statistically equivalent results. These results imply that the unified equations can be adopted for operational numerical weather prediction that would employ a single soundproof system of equations to produce reliable forecasts for all meteorological scales of interest with negligible changes for the computational overhead.

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