Question

What does this paragraph mean? Why is the air sinking over the desert and how does it rise with rain systems thousands of kilometers away?

In fact, it has been calculated that the Sahara Desert actually loses more infrared radiation than it gains solar radiation from the sun. This net loss of radiant energy is balanced by the sinking air over the desert, which warms as it is compressed. The air over the desert is, in turn, being forced to sink by rising within rain systems hundreds or thousands of miles away. Thus, in some sense, rain can be considered the cause of deserts(!).