80 Modelling theclimate
Setting up a numerical atmospheric model
A numerical model of the atmosphere contains descriptions, in appro-
priate computer form and with necessary approximations, of the basic
dynamics and physics of the different components of the atmosphere and
their interactions.^3 When a physical process is described in terms of an
algorithm (a process of step-by-step calculation) and simple parameters
(the quantities that are included in a mathematical equation), the process
is said to have been parameterised.
The dynamical equations are:
The horizontal momentum equations (Newton’s Second Law of
Motion). In these, the horizontal acceleration of a volume of air
is balanced by the horizontal pressure gradient and the friction.
Because the Earth is rotating, this acceleration includes the Cori-
olis acceleration. The ‘friction’ in the model mainly arises from
motions smallerthan the grid spacing, whichhave to be parame-
terised.
The hydrostatic equation. The pressure at a point is given by the
mass of the atmosphere above that point. Vertical accelerations are
neglected.
The continuity equation. This ensures conservation of mass.The model’s physics consists of:
The equation of state. This connects the quantities of pressure,
volume and temperature for the atmosphere.
The thermodynamic equation (the law of conservation of energy).
Parameterisation of moist processes (such as evaporation, conden-
sation, formation and dispersal of clouds).
Parameterisation of absorption, emission and reflection of solar
radiation and of thermal radiation.
Parameterisation of convective processes.
Parameterisation of exchange of momentum (in other words, fric-
tion), heat and water vapour at the surface.
Most of the equations in the model are differential equations, which
means they describe the way in which quantities such as pressure and
wind velocity change with time and with location. If the rateof change of
a quantity such as wind velocity and its value at a given time are known,
then its value at a later time can be calculated. Constant repetition of
this procedure is called integration. Integration of the equations is the
process whereby new values of all necessary quantities are calculated at
later times, providing the model’s predictive powers.