Pre-processing
In the pre-processing weather observations received via the Global Telecommunication System (GTS) run through a quality check. The accepted observations are converted to a format required by the analysis scheme. Limited Area Models (LAM) also require boundary values to determine the evolution of the atmospheric state at the lateral boundaries of the LAM domain. The processing of lateral boundary values is a part of the pre-processing.
Climate files
Certain fields, e.g. orography, surface roughness length over land, albedo and vegetation type, are kept constant in a forecast run. The climate file generation makes these fields available for analyses and forecasts.
Analysis
The most common analysis methods are optimum interpolation (OI) and variational data assimilation (VDA). The analysis scheme at DMI apply at present OI. This is a statistical procedure, making corrections to a first guess forecast (typically a 6 hours forecast from the precious analysis time 6 hours earlier) in such a way that the differences between the corrected first guess and the accepted observations at the analysis time are minimized. The corrections to the first guess are made such that certain large scale force balance constraints are retained.
In the VDA approach, the data assimilation problem is redefined as an iterative process in which the gap between observations and initial model state is minimized. Usually an adjoint model, which is derived from the forecast model, is used in the iterative minimization The adjoint model performs calculations of model states backward in time. Development of a VDA analysis system at DMI is in progress.
Initialization
Analyses based on OI are not in a completely balanced state. Consequently, if forecasts are run directly from the analyses, adjustments of the mass and wind field usually generate unwanted large amplitude gravity wave oscillations in the first few hours of the forecast. The initialization removes these oscillations without destroying the meteorologically significant structures. Different techniques can be used in the initialization, i.e. digital filtering or normal mode initialization. The operational DMI-model applies at present an implicit normal mode initialization.
Dynamics
The forecast model apply numerical approximations to the governing equations of the atmosphere. The latter are derived from momentum, energy and mass conservation. The ideal gas law, relating density to pressure and temperature, is applied in the atmosphere. The influence of the variable amount of water vapor an cloud substance (cloud water/ice) is taken into account in the ideal gas law for a dry atmosphere by replacing temperature by virtual temperature.
In models with a horizontal resolution coarser than 5 to10 km the hydrostatic approximation is normally used in combination with a hybrid vertical coordinate defined such that model levels become sigma surfaces (s = p/ps) and pressure surfaces at the bottom and top of the atmosphere, respectively. The various meteorological fields on the model surfaces are usually represented as discrete values at grid points (grid point models) or as continuous functions obtained by summation of spherical harmonics in wave number space (spectral models). A centered in time difference scheme (the leapfrog scheme), which is second order accurate, is commonly used in the time stepping. In the dynamics semi-implicit adjustments are normally added to the explicit tendencies. This makes the main terms responsible for gravity waves unconditionally stable. Either Eulerian or semi-Lagrangian advection is applied.
In grid point models spatial gradients are usually approximated by central differences, which are second order accurate.
At present the operational DMI-model is semi-implicit, with Eulerian advection and leapfrog time stepping. Semi-Lagrangian advection is optional.
Physical parameterization
Physical processes play an important role in the atmosphere. These processes occur both on horizontal and vertical scales which are resolved and unresolved by the numerical model. Even in very high resolution models physics on unresolved scales have important impacts on the evolution of the state of the atmosphere. Physics such as short and long wave radiation, turbulence (including gravity wave drag), deep and shallow convection, cloud and precipitation generation and air-sea/air-land interactions need to be parameterized . Parameterizations are formulas (empirical or derived from physical hypothesis) calculating the effect of sub-grid scale physics on the resolved scales by means of prognostic and diagnostic model variables. Parameterizations of all the physical processes listed above, except gravity wave drag, are included in the present operational DMI-model
Post-processing
The post-processing takes care of the output from the analyses and forecast runs, including archiving in a suitable format. Field verification and verification against observations (obs-verification) of selected meteorological fields are also parts of the post-processing
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