More on climate basics.. Why is the lower atmosphere – the troposphere – like it is?
The pressure vs altitude relationship is the first point to understand. Notice that (in the graphic above) the left vertical axis – height – is linear, while the right hand corresponding vertical axis – pressure – is logarithmic. Here is one sample atmospheric profile:
As a “conceptual idea” to help understand this, the pressure at any level is dependent on the total weight of atmosphere above. As you go up higher in the atmosphere the weight above decreases. As the weight above decreases, the atmosphere below is less “compressed” due to the pressure and so the pressure change is not linear with altitude. There is some maths at the end for people interested.
The temperature decreases with altitude through the troposphere. What explains this?
Firstly, the atmosphere is mostly transparent to solar radiation so the solar radiation passes straight through the atmosphere and is absorbed by the surface – whether land or sea.
Secondly, the surface heats up because of this radiation and consequently warms the lower atmosphere. What we need to understand is the dominant mechanism by which it heats the lower atmosphere.
If we calculate the movement of heat upward through the atmosphere only by radiation (the atmosphere absorbs and emits longwave radiation) we find a vertical temperature profile which doesn’t match what we observe. When the atmosphere is “optically thick”, radiation doesn’t provide a good “re-distribution” of heat. In the troposphere, if radiation was the only mechanism for moving heat, the “lapse rate” – or change of temperature with height – would be more than 10K/km.
As we go up through the troposphere the temperature decreases with altitude. This introduces terminology problems with “more than” and “less than” (especially if we are trying to avoid maths). More rigorously I could say that the temperature change would be less than -10K/km. E.g. -12K/km.
And yet, the actual environmental lapse rate is around -6.5K/km. The “environmental lapse rate” is what we observe in practice.
Now radiation is only one mechanism for moving heat – the others are conduction and convection.
Convection is a very effective mechanism for redistributing heat. The sun heats the earth’s surface (through the almost transparent atmosphere) – the earth’s surface heats the lowest levels of the atmosphere via conduction and convection. What happens to air that is heated? If air heats it expands, and if it expands then its density becomes lower and so it will rise. The first law of thermodynamics – conservation of energy – says that if there is no change in energy then work done by a parcel of air in expanding must equal the change in heat.
This means that for dry air we can easily calculate the temperature change as air rises. The adiabatic lapse rate of dry air is -9.8K/km (=-9.8°C/km).
Calculating the value for moist air is not so simple (but is still basic physics) and depends on the humidity.
First, let’s use the dry lapse rate to consider what might happen in the atmosphere. Suppose the temperature profile has been determined by radiative equilibrium, and is therefore more than 10K/km.
So if the surface is 15°C, then 1km up the temperature will be less than 5°C, and 2km up the temperature will be less than -5°C.
If a parcel of dry air at the surface moves upward 1km then as a result of the change in energy in expanding it will reach a temperature of just over 5°C. It will be warmer than the equilibrium profile that has been established by radiation. This means it will be less dense than the surrounding air and so it will keep on rising.
Therefore, in practice, any dry air which is slightly perturbed vertically will find itself warmer than the surrounding air and will keep on rising.
So convection dominates the temperature profile of the lower atmosphere. If radiative equilibrium dominated, convection would quickly take over – because it is more effective at moving heat in the troposphere (a different story in the stratosphere).
Now let’s consider humid air. As air cools it can hold less water vapor. So water vapor will condense, thereby releasing heat. Therefore, the more humid the air, the warmer it will be at higher altitudes (because of release of latent heat). And so, humid air has a lapse rate which is “less negative” than dry air. This value can be as “low” as -4K/km in the tropics.
And on average the “environmental” lapse rate is -6.5K/km.
Convection determines the temperature profile in the troposphere. But radiation is the only mechanism for moving heat into and out of the earth’s climate system.
Radiation is also still very important in moving heat from the surface as can be seen in Sensible Heat, Latent Heat and Radiation.
It’s common to see “criticisms” on blogs that somehow “climate science has ignored convection and latent heat”. Atmospheric physics 101 always works through these basics to explain the temperature profile of the troposphere.
Convection, latent heat and radiation are all important movers of heat from the surface into the atmosphere. And in the case of radiation, it is also an important mover of heat back to the surface from the atmosphere.
But convection is what determines the actual temperature profile of the lower atmosphere – the troposphere.
Maths of Pressure Changes
dp = -ρg.dz
The ideal gas equation says:
PV = nRT
ρ = M/V
dp/p = -dz/H, where H is the scale height, or H=RT/mg
H is dependent on temperature and therefore on the altitude, but as a very rough and ready approximation H doesn’t change too much. At the surface H = 8.5km and at the top of the mesosphere, H= 5.8km. The value of H tells us the change in altitude needed to reduce p (pressure) to 1/e (36%) of its original value.