Is the altitude of the surface of the ice at the south pole determined by barometric pressure? In one section of his auto-biography, Alvarez: Adventures of a Physicist, Luis Alvarez describes a tour of Antarctica.  This comment about a flight over the south pole caught my attention:

The South Pole is located on level ice nine thousand feet above sea level, so one goes up to the pole.  After passing the pole, we flew for hours at constant barometric altitude and at a constant radar altitude of three hundred feet above the surface.  It was hard for me to believe that ice, like water, seeks its own level to that accuracy.

He's saying that the surface of the ice is a surface of constant air pressure.  Is this true?
I can imagine that the thick sheet of ice is sufficiently compliant that it would respond to changes in pressure from above.  But how quickly, and over what length scales?  And is he really implying that the air pressure at the south pole is the same as the air pressure several hours' flight away?
 A: The answer is in your question: "It was hard for me to believe that ice, like water, seeks its own level to that accuracy." - Not intuitive perhaps, but over time, ice will indeed creep and flow in response to stress. 
Because the density of ice is larger than air, the weight of the ice makes a larger contribution to the hydrostatic pressure in the Antarctic ice cap (glacier) than does the air pressure at the surface.  The layer of ice covering Antarctica is very thick, and the ice is a solid near its melting temperature. The ice creeps (flows) and the thick ice layer moves so as to become closer to an isostatic equilibrium state (lower energy.) Of course Alvarez would have been aware of this explanation.
The glaciers of Antartica also flow from the interior to the edge of the continent. The edges of the glaciers are wasted into the sea and snow falling in the interior provides a source of ice to the glaciers.
Thanks for mentioning this book. I think it's an interesting quote, because I expect it was made at a time (1960's?) when the high-temperature creep of geological materials (rocks and minerals) were an active area of experimental research at the University of California. It would be interesting to know what prompted the comment, and what discussion on this subject he may have had with David T. Griggs and his students at UCLA. 
I believe he accepted the explanation as the correct one, but I would like to know whether he withheld that until there was laboratory evidence of ice creep.  
A: Over water, low pressure pulls water up, as under a hurricane.
High pressure pushes it down.
If you are in an airplane, flying at a constant barometric pressure, if you encounter a region of low atmospheric pressure, the levels of constant barometric pressure bend downward.
Similarly, high atmospheric pressure make the airplane rise, if it is tracking an isobar.
(This is why aircraft altimeters must be adjusted for the current meteorological air pressure. You don't want to descend to 200', expecting to pop out of the clouds, and find yourself below ground.)
So, I could imagine if the atmospheric pressure is very high over the pole (like 9 inches of mercury) it would cause the plane to climb about 9000 feet.
What I can't imagine is that that would cause the ice to be 9000 feet high.
It should have the opposite effect, if it has any effect.
