An integrated forecasting and data assimilation system has been and is continuing to be developed by the Meteorological Research Branch (MRB) in partnership with the Canadian Meteorological Centre (CMC) of Environment Canada. Part I of this two-part paper motivates the development of the new system, summarizes various considerations taken into its design, and describes its main characteristics.

https://journals.ametsoc.org/doi/pdf/10.1175/1520-0493%281998%29126%3C1373%3ATOCMGE%3E2.0.CO%3B2

The Operational CMC–MRB Global Environmental Multiscale (GEM) Model. Part I: Design Considerations and Formulation

A computational scheme suitable for numerical weather prediction and climate modelling over a wide range of length scales is described. Its formulation is non-hydrostatic and fully compressible, and shallow atmosphere approximations are not made. Semi-implicit, semi-Lagrangian time-integration methods are used. The scheme forms the dynamical core of the unified model used at the Met Office for all its operational numerical weather prediction and in its climate studies. © Crown copyright, 2005. Royal Meteorological Society

http://www.climateknowledge.org/Advection_subscale_mixing/Davies_Dynamical_Core_QJRMS_2005.pdf

A new dynamical core for the Met Office's global and regional modelling of the atmosphere

A global shallow-water model based on the flux-form semi-lagrangian scheme is described. the mass-conserving flux-form semi-Lagrangian scheme is a multidimensional semi-Lagrangian extension of the higher order Godunov-type finite-volume schemes (e.g., the piece-wise parabolic method). Unlike the piece-wise parabolic methodology, neither directional splitting nor a Riemann solver is involved. A reverse engineering procedure is introduced to achieve the goal of consistent transport of the absolute vorticity and the mass, and hence, the potential vorticity. Gravity waves are treated explicitly, in a manner that is consistent with the forward-in-time flux-form semi-Lagrangian transport scheme. Due to the finite-volume nature of the flux-form semi-lagrangian scheme and the application of the monotonicity constraint, which can be regarded as a subgrid-scale flux parametrization, essentially noise-free solutions are obtained without additional diffusion. Two selected shallow-water test cases proposed by Williamson et al. (1992) and a stratospheric vortex erosion simulation are presented. Discussions on the accuracy and computational efficiency are given based on the comparisons with a Eulerian spectral model and two advective-form semi-implicit semi-Lagrangian models.

An explicit flux-form semi-lagrangian shallow-water model on the sphere

An updated description is presented for the quasi-uniform Conformal-Cubic Atmospheric Model. The model achieves high efficiency as a result of using semi-Lagrangian, semi-implicit time differencing. A reversible staggering treatment for the wind components provides very good dispersion characteristics. An MPI methodology is employed that allows the model to run efficiently on multiple processors. The physical parameterizations for the model are briefly described, and results are shown for the Held-Suarez test, the Aqua-Planet Experiment and an AMIP simulation having 125 km resolution. Antarctic snow accumulation is also shown from a shorter simulation having 50 km resolution.

An Updated Description of the Conformal-Cubic Atmospheric Model

During the last 20 years data assimilation has gradually reached a mature center stage position at both Numerical Weather Prediction centers as well as being at the center of activities at many federal research institutes as well as at many universities.

/pdf/data-assimilation-for-numerical-weather-prediction-a-review-7zi7vp7cna.pdf

Data Assimilation for Numerical Weather Prediction: A Review

An adiabatic global multilevel primitive equation model using a two time-level, semi-Lagrangian semi-implicit finite-difference integration scheme is presented A Lorenz grid is used for vertical discretization and a C grid for the horizontal discretization The momentum equation is discretized in vector form, thus avoiding problems near the poles The 3D model equations are reduced by a linear transformation to a set of 2D elliptic equations, whose solution is found by means of an efficient direct solver The model (with minimal physics) is integrated for 10 days starting from an initialized state derived from real data A resolution of 16 levels in the vertical is used, with various horizontal resolutions The model is found to be stable and efficient, and to give realistic output fields Integrations with time steps of 10 min, 30 min, and 1 h are compared, and the differences are found to be acceptable

A Global Multilevel Atmospheric Model Using a Vector Semi-Lagrangian Finite-Difference Scheme. Part I: Adiabatic Formulation

Full physical parameterzations have been incorporated into the global model using a two-time-level, semi-Lagrangian, semi-implicit finite-difference integration scheme that was described in Part I of this work. Virtual temperature effects have also been incorporated into the adiabatic part of the model. The diurnal and seasonal cycles have been included, with prescribed seasonally varying climatological surface boundary conditions. The model has been integrated in both forecast and climate mode, at a resolution of 2° × 2.5° in latitude/longitude, 20 levels in the vertical, and a time step of 45 min for the dynamics. Medium-range forecasts using January and July initial conditions give highly encouraging anomaly correlation skill scores. Two parallel 17-month climate simulations, one without and one with mass restoration, show that the model successfully simulates many features of the observed climate. Mass restoration is shown to have no significant impact on the seasonally averaged climate stati...

A Global Multilevel Atmospheric Model Using a Vector Semi-Lagrangian Finite-Difference Scheme. Part II: Version with Physics

Four-dimensional variational data assimilation (VDA) experiments have been carded out using the adiabatic version of the NASA/Goddard Laboratory for Atmospheres semi-Lagrangian semi-implicit (SLSI) multilevel general circulation model. The limited-memory quasi-Newton minimization technique was used to find the minimum of the cost friction. With model-generated observations, different first-guess initial conditions were used to carry out the experiments. The experiments included randomly perturbed initial conditions, as well as different weight matrices in the cost function. The results show that 4D VDA works well with various initial conditions as control variables. Scaling the gradient of the cost function proves to be an effective method of improving the convergence rate of the VDA minimization process. The impacts of the length of the assimilation interval and the time density of the observations on the convergence rate of the minimization have also been investigated. An improved assimilation ...

Four-Dimensional Variational Data Assimilation Experiments with a Multilevel Semi-Lagrangian Semi-Implicit General Circulation Model

A vector semi-Lagrangian semi-implicit two-time-level finite-difference integration scheme for the shallow water equations on the sphere is presented. A C-grid is used for the spatial differencing. The trajectory-centered discretization of the momentum equation in vector form eliminates pole problems and, at comparable cost, gives greater accuracy than a previous semi-Lagrangian finite-difference scheme which used a rotated spherical coordinate system. In terms of the insensitivity of the results to increasing timestep, the new scheme is as successful as recent spectral semi-Lagrangian schemes. In addition, the use of a multigrid method for solving the elliptic equation for the geopotential allows efficient integration with an operation count which, at high resolution, is of lower order than in the case of the spectral models. The properties of the new scheme should allow finite-difference models to compete with spectral models more effectively than has previously been possible.

Integration of the shallow water equations on the sphere using a vector semi-Lagrangian scheme with a multigrid solver

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Papers

A Global Multilevel Atmospheric Model Using a Vector Semi-Lagrangian Finite-Difference Scheme. Part I: Adiabatic Formulation

A Global Multilevel Atmospheric Model Using a Vector Semi-Lagrangian Finite-Difference Scheme. Part II: Version with Physics

Four-Dimensional Variational Data Assimilation Experiments with a Multilevel Semi-Lagrangian Semi-Implicit General Circulation Model

Integration of the shallow water equations on the sphere using a vector semi-Lagrangian scheme with a multigrid solver