Solar Cosmic Rays
Solar Cosmic Rays (Solar CR) are high energy particles released by massive explosions on the sun called Coronal Mass Ejections (CME).[1] They are not the normal solar wind which is easy to shield against, but much higher energy particles with far more penetrating power.
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Frequency and Energies of Solar Storms
Coronal Mass Ejections (CME) are usually small and common. They can happen about once a week when the sun is least active, to a couple times a day when the sun is at the peak of its sunspot cycle. Not all CME are aimed at Earth or Mars. If the explosion is on the far side of the sun facing way from us, it will have no effect on colonists. [2]
The energy of solar cosmic rays varies widely, the lowest energy ones are from 10,000 electron volts to a couple hundred mega electron volts (~200,000,000). However, in the most powerful CME, about 1% of the time particles in the giga-electron volt range are detected.
This is a huge range, the weakest particles are 100 million times less energetic than the most powerful ones. (Fortunately the very powerful ones are quite rare.)
The thin Martian atmosphere provides significant protection against the weakest solar cosmic rays. However, space suits and Mars rovers should have radiation protection. Against the common Solar CR, this is just part of the day to day higher radiation to be found on Mars. However, on the rare cases when a powerful solar storm will hit Mars, mitigation strategies must be taken.
Mitigation Strategies
We can optically detect the solar flares associated with Coronal Mass Ejections (CME), and can have several days of warning (for lower energy ones) to only hours of warning for the most powerful ones. Thus colonists on Mars' surface are likely to have time to get into radiation shelters, if a CME is detected.
Habitats on Mars will likely have normal radiation protection (say 2 meters of water or dirt above living quarters). But it would be wise to have a smaller volume with very high radiation protection as a Storm shelter, which people can go into for the couple hour solar storm. People might crowd together and watch a movie or two during the solar storm.
Note that if a CME happens at night, the colonists will be protected from the sun by the mass of the planet under them.
A colonist in a rover far from a base, which is caught in the open at noon by a rare, very powerful CME is in trouble. They might stop, cover the top of the rover with sand bags (maybe not enough protection), then wait a couple hours UNDER the rover to maximize protection. Rovers might have a tiny storm shelter which people can lie in for a 2 or 3 hour solar storm. However, volume inside a rover is small, and there might not be room for such a storm shelter. A huge solar storm when a colonist is far from shelter is a real concern.
Effects of Terraforming
If Mars was to be given an artificial magnetic field (say by running a super conducting loop around the equator and pushing a current thru it) then Solar Cosmic Rays are weak enough that some of them will be directed to the poles reducing the radiation count in the low and mid latitudes.
As Mars atmosphere gets thicker, proportionally more low energy Cosmic Rays will be stopped.
Note that while terraforming will help protect against solar cosmic rays, it will have little effect against more powerful forms of cosmic rays.