What is climate?

What does climate mean anyway?

We could use imprecise and impressionistic definitions, but it's best here to just use the physics of the atmosphere and isolate the variables. They're related in a straightforward way to more popular terminology, so there's nothing hard.

At any point in space and time, the state of the static dry atmosphere is given by this list:

• Temperature T (absolute zero: T = 0)
• Density rho (mass/volume)
• Pressure P (force/area)
• Chemical weight µ (80% N2 and 20% O2)

Not all these variables are independent. The mass density of air is nearly constant at a fixed altitude, so it doesn't need much discussion. The four variables are also related by a constraint, the ideal gas law: P = universal constant*rho*T/µ. So only two variables are independent. In technical meteorology, these are usually taken to be T and P.

Now add water to the mix. To specify the state of the atmosphere now requires knowing the water state (vapor, liquid-precipitation, or condensed-suspended = cloud/fog). Water vapor is roughly a percent of the real atmopshere (that can vary obviously), so it modifies the chemical weight µ slightly. This percentage is equivalent to knowing the humidity.*

Finally, put the atmosphere in motion. The dynamical laws of the atmosphere relate the accelerations (second time derivatives) to forces and heat dissipation (first time derivatives) to heat flows. The important independent motion for climate and weather is the wind velocity, which is a vector field. Imagine it as a bunch of arrows, with direction and magnitude; each point in the atmosphere has one of these arrows attached. The arrows (their length and direction) can vary in time.

In technical meteorology, all five are used: T, P, water state, humidity, and wind field. If you know the humidity and T, then you know P (by the ideal gas law), so only four are independent. Those are the four familiar from regular weather forecasts:

• Temperature (how hot is it?)
  
• Humidity (how muggy is it?)
  
• Water state (are there clouds? is it raining/snowing/sleeting?)
• Wind direction/speed (how fast is it blowing and in what direction?)
  

This set of four is defined for each point in space and each instant in time. Weather forecasts are fuzzy averages of these over a few hours and over several hundred square miles.
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* Actually, something called relative humidity, which is relative to the saturation point of air - the point at which the air can absorb no more water vapor. The technicalities are explained later but are unimportant here.