IN North America, a winter weather change that might be associated with large amplitude Rossby waves is

A jet stream that alternates between hot and cool periods.

Explanation:

Winds typically travel at the very same latitudes, but Rossby waves occur when winds shift it into hurricane pattern. The Rossby waves go in a north-south direction and then return again. Whenever the Rossby waves' breezes swing up, they transport warm air first from tropical to the northern, while when they swing down, they transport cold air from either the Arctic to the south, resulting in alternating warm and cold spells.