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The New Dynamics dynamical core for the Unified Model

The fully compressible, nonhydrostatic, deep-atmosphere equations in spherical geometry. In the shallow-atmosphere approximation the terms in yellow boxes are dropped and in the hydrostatic approximation the term coloured red is dropped.

The dynamical core referred to as New Dynamics is based on a semi-implicit semi-Lagrangian discretization of the fully compressible, nonhydrostatic Euler equations.

The New Dynamics dynamical core is based on the fully compressible, nonhydrostatic Euler equations which enables it to be used over a wide range of scales - from very high resolution convection permitting scales (of order 1 km) to hundreds of kilometres in climate models run for centuries.

Note: The dynamical core, used operationally within the Unified Model, was changed from New Dynamics (as described on this page) to Even Newer Dynamics for General atmospheric modelling of the environment (ENDGame) in 2014.

New Dynamics

The system of equations in New Dynamics is solved using a predictor-corrector technique employing semi-Lagrangian advection and semi-implicit time stepping. The continuity equation is used in Eulerian flux form to conserve mass since such conservation is considered vital for long climate simulations. The correction step uses a linearized form of the equation of state to obtain a three-dimensional, second-order PDE for the pressure increment. This PDE has variable coefficients and is solved using an iterative GCR method.

A latitude-longitude grid is used in the horizontal. The grid spacing can be regular or can be stretched in each horizontal direction. The grid can also be rotated so that LAMs can use a grid that is almost isotropic over the region of interest. The grid spacing in the East-West direction reduces towards the poles.

In contrast to Eulerian grid-point models, SISL schemes do not require filtering to remain stable. However, in the New Dynamics dynamical core the converging meridians result in very small scale variability near the poles and unless some filtering is applied to the smallest scales the iteration count in the solver increases significantly.

Variables are staggered in both the horizontal (Arakawa C-grid) and vertical (Charney-Phillips) to optimize the natural oscillations and to avoid producing computational modes.

The New Dynamics can handle a large number of tracer variables, e.g. various phases of moisture (vapour, cloud water/ice, snow, graupel), aerosols and chemical species. The computational overhead for each tracer is modest since they share the same calculations except for the interpolations to obtain values at departure points. In a typical climate model there are over 25 individual tracers.

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