I was researching solar insolation and found that solar insolation at the poles over summer is roughly equivalent to several places on earth that have relatively warm summers. Below is a Matlab graph showing the average insolation received by Fairbanks, Chicago, and the North Pole between June 1st - August 31. The only contradictory thing I can think of is that I calculated Solar Insolation, and not Direct insolation. Direct Insolation accounts for the length in the atmosphere that radiation has to travel through before reaching the surface, but attempting to graph it using the equation 
from Wikipedia resulted in the graph labeled "Direct Insolation Example", which appears to be incorrect. In any case, that effect seems to be relatively minor. The only major difference that I can think of between the summer climate characteristics of the cities and the north pole is that the north pole is oceanic, and thus has to deal with the very high thermal inertia of the very cold water surrounding it, making it unable to have warm summers despite similar solar insolation. In addition, I understand ice has a higher Albedo than land, and thus the actual amount of energy received is lessened. However, how is that fundamentally different than locations with thick snowpack that eventually melts over the summer?
Chicago Avg Summer Temp - 73.3
Fairbanks Avg Summer Temp - 60.3
North Pole Avg Summer Temp - 32
Also a few related relevant questions.
- Why does the North Pole have slightly warmer winters than extremely continental climates like Yakutsk? The difference isn't huge, but it's still odd considering that the poles should be surrounded by ice (Which should act like ground in terms of continentality) in the winter.
