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The general problem of
parametrization
March 1984
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1 . Introduction
Numerical weather prediction is generally performed by numerical integration of the hydrodynamic equations governing atmospheric motions. Therefore, the differential equations taking a grid-point model, for example, are approximated by finite difference equations applied to a grid of finite volumes. In contrast to the original differential equations which describe the whole spectrum of atmospheric motions, the finite difference equations of a grid-point model describe only those scales which are larger than twice the grid length. For practical reasons the grid length in numerical forecast models cannot be reduced very much below 100 km and, therefore, atmospheric processes on scales smaller than 100 km are excluded from those models. However, small-scale flow affects the mean flow as, for instance, considerable amount of water vapour, sensible heat and momentum are transported by turbulent and convective motions. The effects of the subgrid-scale flow on the mean flow may be ignored for short forecast periods of up to 1 to 2 days, but they become increasingly important for longer periods and must be considered in models for medium-range forecasts and in general-circulation models. Since subgrid-scale processes are not included in models, only their statistical effects on the mean flow can be taken into account. The statistical contributions by the different processes must, therefore, be expressed in terms of the large-scale parameters themselves. The mathematical procedure involved is generally called parametrization.
In the following section the problem of parameterization is discussed from a general point of view, i.e. in relation to the scales of atmospheric motions.
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12.06.2002 |
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