I want a short little aside here to talk about a little pet peeve of mine:
People talk as if Mars’ atmosphere does basically nothing to reduce the radiation dose as compared to free space. This is definitely not true, but the confusion comes from a few areas, but largely because people have not bothered to do some basic math and geometry.
1) People use the datum or even higher altitude sites to calculate the surface pressure. The pressure at the datum (the sort of average height on Mars, analogous to “sea level,” but not really) is 636 Pascals (6.36mbar http://nssdc.gsfc.nasa.gov/planetary/factsheet/marsfact.html ). But the scale height of Mars is 11.1km. Scale height is the constant used to determine pressure given a simple exponential model of the planetary atmosphere. The lower altitude, the higher pressure, determined by this equation:
Where P is the pressure at the altitude “z”, and P0 is the pressure at “zero” altitude, and H is the scale height.
So at Mars, P0 = 636Pa, H=11.1km, and the lowest point on Mars is in a corner of Hellas Basin at z=-8.2km (i.e. 8.2km below the datum), whereas pretty much all of Hellas Basin is 6km below the datum. https://www.psi.edu/epo/explorecraters/hellastour.htm
That gives us an estimate of over 1300Pa surface pressure at the deepest point ( https://www.google.com/webhp?#q=636Pa*e^(8.2/11.1) ) and at least 1090Pa anywhere inside Hellas basin ( https://www.google.com/webhp?#q=636Pa*e^(6/11.1) ).
2) People forget that Mars having a lower gravity means that the mass needed to get a certain pressure is higher than on Earth. So while 1kPa on Earth would mean just 10 grams per cm^2 of shielding, on Mars it is:
https://www.google.com/webhp?#q=636Pa*e^(8.2/11.1)/(3.71m/s^2) = 35.9g/cm^2.
https://www.google.com/webhp?#q=636Pa*e^(6/11.1)/(3.71m/s^2) = 29.4g/cm^2
3) That’s already decent shielding. However, there’s another significant point: That’s just the shielding at the zenith of the sky, which is the thinnest part! Everywhere else is thicker shielding, near the horizon is MUCH more shielding.
So as you can see, the vast majority of your sky shielding (at least 70%) is over 1.4 (i.e. sqrt(2) ) times your zenith shielding. So we can write that as:
So, anywhere in Hellas Basin has basically half the dose of free space (shielded by the planet itself) PLUS another at least 40 grams per square centimeter of shielding just from the atmosphere.
EDIT: to give an idea of how much 40 g/cm² of shielding can do here is this graph that shows roughly the attenuation capabilities of polyethylene and aluminum. Mars’ atmosphere’s shielding capabilities would be somewhere between those two. While this isn’t quite enough to be happy from a GCR dose long-term (you’d want shielding on your hab), it does make EVAs far less dangerous in case of a solar flare (especially any acute effects), and also makes EVAs in general represent a much lower risk of long-term exposure. But the main effect is that solar flares represent a risk less than a tenth than the case without shielding (ie just the spacesuit).
(Also, as a side note: much of the northern part of Mars is far below the datum as well. Not quite 40g/cm^2 of shielding, but a solid 30-35g/cm^2 in many places… But there are MANY reasons why you might want to build your settlement at low altitude anyway.)
EDIT AGAIN, 2015-09-08:
Here is a graph from Rapp et al 2006 which I’ve drawn roughly where the equivalent dose of 20 cm of water shielding would be for Hellas Basin’s >40g/cm^2 of CO2 shielding. I added the red horizontal line for 20cm of water, looks to be just under 30cSv/year (I believe this is in open space, not on Mars), the green line is for 40g/cm^2 of regolith, which is a worst case for CO2 (carbon has lower atomic mass than the typical silicon, calcium, and aluminum that make up the balance of regolith besides oxygen) at about 28cSv, and 50g/cm^2 CO2 (deepest spot on Mars) with 27cSv or so for GCR annual dose. But again, this is free space. Those are just rough numbers, so that’s a bit of false precision there, but it does show that Hellas Basin has about as much equivalent shielding as a foot of water.
(caption: “Figure 1. Point estimates of 5-cm depth dose for GCR at Solar Minimum as a function of areal density for various materials (figure1.jpg). (Simonsen et al. 1997)”)