Atrium walls are exterior walls, the same as...well...your other exterior walls. Thus, all exterior walls, including those for the atrium, well have continuous reinforced footings which go below the freeze depth, according to your local building code. Depending on conditions and local building customs, the footings may either be poured first, before the slab work, or continuous with the slab work. With a garden, rain and watering, you will want to provide drains to the exterior of the house, beyond your perimeter footings. Otherwise the garden may some day become your swimming pool...

Planting trees or any large plant material with strong, spreading invasive roots in an atrium is a suicidal decision. Plant materials for such locations should be very carefully selected by someone knowledgeable about landscape materials. All plant materials will need a certain depth of good top soil, access to light and water, and there will need to be good, consistent drainage for water, whether from regular watering of plant materials or from rain. A drip irrigation system on a timer is probably a good idea.

Building a concrete "swimming pool" with perimeter concrete footings and a continuous, reinforced concrete bottom is probably not a good solution, unless you will be limiting plant materials to potted plantings sitting on gravel. Even then, rain water has to have several places to drain to the exterior.

Termite and bug maintenance would be the same in the atrium as along the exterior perimeter. Many species can fly you know!

"We want a Rocky Mountain type native garden with a small Aspen, meadow grass, wildlfowers, etc"

In Tucson? Not going to happen, because aspen doesn't grow there. Actually, not going to happen even in aspen's native territory because the stress of living inside an atrium away from its colony of other aspens would kill it. Not enough light, wrong soil microbes, indoor air pollutants, etc. The grass and wildflowers need full sun, not atriums.

I can think of plant materials to make it kinda-sorta look like your idea.

And I'm not even going to get into the construction and drainage for an atrium with trees.

Slightly off topic but don't forget that walls have a thickness which can significantly add up. For example over the depth of the house, on the right side you're looking at about 2'4" of walls.

Im not following. Are you saying you want an atrium with plants that are not native to your area?

Yes, sorry for the confusion. I appreciate all the advice so far. Maybe "atrium" is not the right word for it. It's going to have a roof on it with a ventable skylight as well; it will not be open to the outside air. The exterior wall will have a glass patio door and celerestory windows for light.

And yes, we wanted if possible, to have an atrium with plants that are not native to our area. It will be totally enclosed indoors. Since Aspen's have shallow root systems I thought that would work potentially.

The atrium will have a roof over it with a skylight and not open to outside air? Which direction will the exterior wall with glass patio door face?

Sounds to me you are building a greenhouse, depending on the direction of the glass wall and the type/amount of sunlight it will provide.

This is a rather special growing environment, suitable for some plant materials and not others, particularly those which grow over about 8'-10' which will be near the enclosing roof. The roof presents some issues of moisture collection in the space (and all that goes with that), and the enclosed space with a large glass wall presents some heat gain issues.

I'm wondering if leaving the roof off the area, and making it a true atrium isn't a better idea?

Are you a landscape architect or botanist?

Aspens may have shallow roots, but they have requirements for climate, soil, microbes in the soil and sunlight that you won't be able to give them.

They also send out sprouting roots many feet, which is how you get a grove of clones.

https://www.srs.fs.usda.gov/pubs/ja/1962/ja_1962_farmer_002.pdf 

Virgil, thanks for the feedback. Yes, we were planning to have a ventable skylight and have the atrium enclosed on the roof. The patio door will face north, we positioned it that way to reduce heat gain. We are planning to use electrochromatic SmartGlass for the skylight and are open to using it for the patio door as well to reduce the heat gain.

The house is going to be super energy efficient and if possible we would like to leave the roof over the atrium for simplicity of roof design, as well as keeping the comfort of the house priority. If we were to open the atrium up to outside air we would be cutting huge hole, effectively, in the thermal envelope of our home.

We are not landscape architects or botanists, but I have advanced degree in biology and my husband in plant physiology, so we understand basics at least. I realize this is not a replacement for a landscape architect and fully plan to bring one onto the project to design both the outside and indoor vegetation and irrigation. I was just looking for a basic idea for the foundation that might work for now, so we can get a bid from our builder for the basic design. The plants within are not as critical, and we are open to lower moisture plants if needed.

An architect could design the space as an open atrium where you could do a native garden.

Cpartist, thank you for the suggestion, but we really want it to be enclosed for energy efficiency of the home. That much glass open to the exterior temperatures would be a heating and cooling nightmare for us

It may be a moisture nightmare they way you are describing it now.

Agree with everyone above. If you enclose it, it's more greenhouse than atrium and attached greenhouses are generally a poor fit with efficient homes. Are there privacy concerns with the site pushing you this direction? Good designers can probably do better without compromising the efficiency of your mechanical systems and building envelope. A north facing courtyard of that size will see little winter sunlight, even in Tuscon.