You have several kinds of radiation to deal with:
Sunlight. Sunlight has a fair amount of UV. On Earth most of this is blocked by the ozone layer. Only a fairly small percentage gets through. Hence all the fuss and feathers about chloro-fluoro carbons (freon and friends) breaking down the ozone layer. On Mars you don't have enough free oxygen to form an effective ozone layer. Even with the dimmer sunlight, going outside without UV protection will be hazardous. UV also degrades many plastics quickly, leading to maintenance issues.
Solar wind. The sun emits a continuous stream of ionized gas -- mostly electrons and protons. On Earth these are intercepted by the earth's magnetic field. When the solar wind is more brisk, the particles rattling around the magnetic field can hit the atmosphere at the poles causing the aurora. During a pole reversal the earth is without an effective magnetic field for some unknown period of time. Recent evidence from New Zealand suggests significant ecological issues (die offs)
Solar wind ultimately causes the aurora, when energetic protons and electrons hit the atmosphere. On earth aurora effects range from 80 to 600 km above the surface. Very roughly the earth's atmosphee halves in density every 18,000 feet. So 80 km = 240,000 feet. About 1/8000 of earth surface pressure. So about 80 times the pressure on Mars.
My first guess then, would be that while solar wind is making off with Mars's atmosphere, there isn't much effect at the surface.
- Cosmic rays. Most of these come slamming into the upper atmosphere, each one producing a cascade of other particles. These are actually more dangerous with an atmospheric shield if the shield is thin enough that the tertiary cascade particles reach the surface. Cosmic rays are relatively rare.
The solar wind is the big problem, especially when the sun flares. A permanent terraformed Mars ideally would have a superconductor cable running around the equator with about 40 million A flowing through it. This would create a magnetic field similar to Earths. (Check the 40 MA figure. I did it once before and was surprised by how modest it was.)