Which process produces rising air due to unequal heating of earth’s surface?
when a layer of air with temperatures above freezing sits above a layer of subfreezing air near the ground, which type of precipitation is likely to form?

The answer for the first question is localized convective lifting. Air in the atmosphere rises when there is unequal heating of the Earth's surface. This is due to its buoyancy. Colder air then sinks, as the hotter air replaces it. 

The answer for the second question is freezing rain. Freezing rain is formed when snow passes through above freezing air atop a layer of below freezing air near the surface of the Earth.

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