I used to be involved on the periphery of research into this.
Radiation increases with altitude though above some 40,000ft the rate of increase reduces (at least for levels where civillian aircraft fly). At a constant altitude it increases from the equator towards the magnetic poles because a) the particles are attracted to the poles and are therefore more concentrated in that region and b) radiation is attenuated by the atmosphere; the atmosphere being deeper at the equator, you have more atmosphere above you and you are therefore more protected.
A trace of the measured radiation on a flight from the UK to Singapore showed a steep increase as the aircraft climbed to its initial cruising level and then a steady reduction as the aircraft progressed south, punctuated by two distinct upticks as higher cruising levels were attained. The level of radiation at TOD Singapore was very significantly lower that at TOC UK even though the aircraft was 8,000ft higher.
It's not much but I hope it helps...
MT
Last edited by Mach Tuck; 10th November 2011 at 13:28.
Reason: Spelling