Besides the scales imposed by the planet itself and its motions in the solar system, the atmosphere and ocean can generate their own scales. A characteristic of fluids is that their motions can, at least in principle, have any scale that their total dimensions allow. In any turbulent fluid motion – for example, a smoke plume billowing from a smokestack - there are whirls or “eddies” of many different sizes, from the total size taken up by the fluid (say, the total width of the smokestack plume) down to something much smaller. This multiplicity of scales is almost a working definition of turbulence, in fact, and the atmosphere and ocean are turbulent in this sense.
In a turbulent fluid, like in other physical systems (e.g., atomic gases) we can compute a “spectrum”, in either space or time. If we have enough measurements of the fluid motion, we can compute a spatial spectrum which tells us how much energy is in eddies of each size, or a temporal spectrum which tells us how much energy is in fluctuations of each frequency. The idea and the math involved are exactly the same as for the wavelength and frequency spectra of atomic gases, but the results are completely different. In a fluid undergoing pure turbulent motion, there are no distinct frequencies or wavelengths which have either much more or less energy than those nearby – no spectral lines. Rather, the spectrum is smooth, but "red". This has nothing to do with the color red now, but just means there is more energy in large scales than small. The bigger and slower the eddy, the more energy it has, but no specific size or speed is favored - there are no particular natural scales that emerge from the dynamics.
The atmosphere and ocean are turbulent, but they are not pure turbulence. On top of the overall continuous red spectrum, there are a few “peaks” – not precise frequencies as in atomic gases, but distinct frequency ranges (just like the range of heights in a group of human beings, different but all not too far from a typical value) – with which the fluids oscillate preferentially. These correspond to particular weather or climate phenomena, and the task of atmosphere and ocean science is to explain these phenomena. Just as in other sciences, any successful explanation must explain the scales.
One example is the “synoptic” low and high pressure systems that produce most of the weather in the middle and high latitudes. These have time scales of a few days – most of the time, we know that’s about how long the weather we’re experiencing at the moment is likely to last – and spatial scales of a few thousand km (say, the size of the United States, or some good fraction of it; look at the weather map today, and see how big the region is that is under roughly the same weather pattern as where you live). The space and time scales are related by a speed; if you know how far away the next weather change is, and you know how fast it is moving, you can figure out how soon it will arrive. That speed is also an important scale of the system, a velocity scale. For the midlatitude weather, it’s a few meters per second; this happens to be (not entirely by accident) similar to the scale of the actual wind velocity near the surface of the earth.
The scales of midlatitude synoptic weather systems were successfully explained by the theory of baroclinic instability developed by Jule Charney and Eric Eady in the 1940s, building on earlier work of Carl-Gustav Rossby and others. The enterprise of modern numerical weather prediction – the practice of using computers to solve equations derived from physics in order to produce the weather forecasts that we all rely on – grew out of that theory. The scales are ultimately related to the natural scales of the system – the size and rotation rate of the earth, etc. – but not in a simple way. The inherent dynamics of the fluid system plays an essential role in setting the scales of the weather systems we observe.