Abstract
The numerical aspects of physical parametrization are discussed mainly in the context of the ECMWF Integrated Forecasting System. Two time integration techniques are discussed. With parallel splitting the tendencies of all the parametrized processes are computed independently of each other. With sequential splitting, tendencies of the explicit processes are computed first and are used as input to the subsequent implicit fast process. It is argued that sequential splitting is better than parallel splitting for problems with multiple time scales, because a balance between processes is obtained during the time integration. It is shown that sequential splitting applied to boundary layer diffusion in the ECMWF model leads to much smaller time truncation errors than does parallel splitting. The so called Semi-Lagrangian Averaging of Physical Parametrizations (SLAVEPP), as implemented in the ECMWF model, is explained. The scheme reduces time truncation errors compared to standard first order methods, although a few implementation questions remain. In the scheme fast and slow processes are handled differently and it remains a research topic to find the optimal way of handling convection and clouds. Process specific numerical issues are discussed in the context of the ECMWF parametrization package. Examples are the non-linear stability problems in the vertical diffusion scheme, the stability related mass flux limit in the convection scheme and the fast processes in the cloud microphysics. Vertical resolution in the land surface scheme is inspired by the requirement to represent diurnal to annual time scales. Finally, a new coupling strategy between atmospheric models and land surface schemes is discussed. It allows for fully implicit coupling also for tiled land surface schemes.
Highlights
Sub-grid processes play an important role in numerical weather prediction and climate models and parametrization development has been a major research activity for many years
Three different schemes are used for the vertical diffusion scheme: (i) parallel splitting, (ii) sequential splitting in which the dynamics tendency is used as source term during the implicit integration of turbulent diffusion, and (iii) sequential splitting as in (ii) but the diffusion coefficients are not computed from time level n, but after the profiles have been incremented with the dynamics
A revised coupler has been introduced as proposed by Best et al (2004). It has the advantage of being fully implicit on all tiles and it allows for a “universal” way of coupling land surface schemes with atmospheric models
Summary
Sub-grid processes play an important role in numerical weather prediction and climate models and parametrization development has been a major research activity for many years (see e.g., ECMWF, 2008, 2015). From the model development point of view, a more attractive approach is to have a numerical scheme that solves the parametrized equations with an accuracy that is better than the uncertainty of the parametrization. In this way, parametrization questions can be separated from numerical issues. Parametrization packages have separate modules for different processes Such modularity is desirable from the model development and code maintenance point of view, but may be in conflict with numerical issues. The accuracy of the numerical approximation of the parametrized equations is often ignored and parametrizations are sometimes optimized for a given resolution and time step This is obviously undesirable for the IFS, because it is operationally used at different resolutions and time steps. It is argued that it is important to understand the nature of the physical process in order to make a proper numerical approximation
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