The Current State of Meteorological Modelling

Abstract

Numerical weather prediction involves the solution of large systems of coupled partial differential equations which describe atmospheric motions. A brief description of the physical and mathematical basis of numerical models of the atmosphere is given in the paper by Bengtsson in this volume. For our purposes the governing equations may be written formally as

$$ \frac{{\partial x}}{{\partial t}} = \underline D (x) + \underline P (x) $$

(1)

where X is any model variable .... wind, temperature, humidity etc.... The problem is 3-dimensional, with the dependent variable X being a function of spatial co-ordinates x, y and z and a function of time t. The term D represents the “dynamics” — advection, pressure forces etc — and the term P, normally referred to as the “physics”, is a source/sink term which for large-scale models of the atmosphere describes physical processes such as the evaporation and condensation of water, solar heating, infra-red cooling, and frictional drag at the earth’s surface. For fine-scale models of thunderstorms a description of cloud physics processes is required; this adds new variables to the problem — cloud water drop-size spectra and for each drop-size an electrical charge spectrum. With present computing power, severe compromises must still be made for such models. In contrast to the “dynamics” embodied in the term D, the “physical” processes, P, are intermittent and are often represented by on/off processes. The programming or implementation for these processes largely effects the efficiency of vectorization on computers such as the CRAY-1 and the CYBER-205, with different strategies being required for different computers. For large-scale models such problems have been overcome by carrying out redundant calculations. The effect on parallel processing is discussed in the paper by Dent in this volume.