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Just as many features in the atmosphere cannot be properly observed by widely-separated instruments, they also cannot be simulated by a model which contains widely-separated grid points. The basic rule of thumb is that models can only simulate phenomena whose size is at least four times the distance between grid points.
Consider again the case of moist convection. The figure below shows the airflow that might exist within and around an ensemble of cumulus clouds, with updrafts inside the clouds and downdrafts outside.
A numerical model only forecasts the state of the atmosphere at grid points separated by (usually) tens of kilometers. So the computer cannot directly simulate the airflow within an ensemble of cumulus clouds. Instead, the best it can do is simulate the larger-scale temperature and airflow on the same scale as the grid points.
Another example, using wind, is the turbulence contained within the lowest levels of the atmosphere. We experience this turbulence as "gustiness", winds at the surface which periodically increase and decrease in intensity.
In a cross-section view, the air is seen to be slowed down and disturbed by the Earth's surface, causing overturning, irregular air motion.
Again, a numerical model cannot simulate motions taking place entirely between grid points. The model can only directly simulate the "average" wind, which is nearly horizontal and weakest near the ground.
How does a model deal with these processes? It can't ignore them completely, because they affect the larger-scale weather. Without the turbulence, for example, the winds near the ground would be just as strong as those aloft. The solution is called "parameterization". To parameterize something means to devise an equation or set of equations which allow the model to deduce the effect of what is probably going on between grid points, given only the large-scale directly-simulated weather.
In the case of surface turbulence, the parameterization might represent turbulence as a retarding force on the lowest levels of the atmosphere, given the wind strength, the stratification, and the roughness of the land surface. Similarly, a parameterization of convection might produce an estimate of large-scale changes in temperature, moisture, and rainfall caused by convection, based only on the changing large-scale convective instability in the atmosphere.
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