Question

Part I

In the first part of this homework, you are going to derive a relationship between pressure, temperature and height in the atmosphere. The equation that you will derive is called the Hypsometric Equation (or sometimes the Thickness Equation) and it has practical uses as well as being helpful for understanding why the general air flow in the midlatitudes is from the west so once you have derived the equation, you will apply it to a real-life example.

Begin with a hydrostatic atmosphere that follows the following relationship:

Where p = atmospheric pressure, rho = atmospheric density and g = 9.8 m/s^2 (gravitational constant)

Assume the atmosphere behave as an ideal gas (assuming a dry atmosphere) which gives you the additional relationship:

Where R = 287 J/kg K

Ok, what I want you to do is to show that difference in altitude between two arbitrary pressure levels is proportional to the average temperature in the layer between them. Please show your work.

Part II

In meteorology, we often calculate the thickness between several different pressure levels and use then in operational meteorology. In particular, we define a couple of critical values that are particularly useful. One such critical thickness when the 1000 mb – 500 mb thickness equals 5,400 m. For Part II, using the relationship you derived in Part 1, solve for the average temperature in a slab of atmosphere with a thickness between the 1000 mb and 500 mb pressure surfaces equal to this critical value then explain why it is useful in operational meteorology.

Answer 1