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Vertical has a much larger variation of pressure due to temperature variations as one moves farther and farther away from earth's terrestrial radiation.

For example: The distance from Key West, Florida to Fairbanks, Alaska is about 6500 km. The surface temperature of Key West is 27.2 degrees Celsius, while fairbanks has an average surface temp of .4 degrees Celsius. According to the ideal gas law, the temperature of a gas is directly proportional to it's pressure, so lets say the change in temp for a horizontal distance between these two places is 26.8 degrees Celsius.

Already stating the surface temp, the temperatures of Key West and Fairbanks at 6,500 km are -9.95 and -36.05 respectively. This makes the difference in vertical temperatures 37.15 and 36.45 degrees Celsius.

Because the change in temp at these two points is greater than the change of temp between them, according to the ideal gas law, the change in the vertical pressures at these two points is also greater

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