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How does the radius of curvature of a planetary wave vary with latitude, everything else being equal?

Suppose you are given 1 kg of ice at 0 (degrees C). If the ice is placed in 1 kg of liquid water initially at 20 (degrees C), what will be the final temperature after all the ice melts?

How does the radius of curvature of a planetary wave vary with latitude, everything else being equal?

Is there an upper limit on the number of warm fronts and cold fronts that can extend from a low-pressure center? Why?