The dynamical core for the Met Office's Unified Model

The current dynamical core for the Met Office's Unified Model 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.

The same model is used for NWP and climate, in both global and LAM configurations. The LAMs, therefore, use lateral boundary conditions generated from a model using the same science.
 
The system of equations 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 linearised 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, 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 optimise 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.
 
The new dynamics uses two-dimensional domain decomposition to divide the computations over a number of parallel processors. For current production configurations this is fast and efficient but when tens of thousands of processors become available (and affordable) additional optimization will be required.

Key aim

To provide a fast and  efficient dynamical core for the UM to be used for all NWP and climate modelling.

Last updated: 26 March 2010