Note: The context of Terraforming in my question does not involve changing the atmosphere in any way. It involves creating water sources, changing soil type, rapidly accelerating foreign plant growth and making landforms.
Over tens of thousands of years, humankind has been doing exactly what you suggest -- transforming local patches fo the Earth to better suit the local human needs and ambitions. The planet has been vast. Experiments sometimes destructive. Change abounds. And if something locally goes wrong, there is greenfield territory to move to, repeat, and repeat.
The human endeavor has been successful at promoting the interests of humanity on such a scale that the earth is running out. The local terraforming experiments have merged together into a planet-wide transformation.
This seems to be happening with unnatural suddenness because we have caused a state change.
It is as if many small forest fires are burning, but there is little large scale danger, but then the fires start merging, the convection currents join together to create unstoppable winds driven by the fire itself.
It is as if every population feeling environmental stress in their home looks to ever more distant patches of green, thinking they can escape there, but gradually the patches of remaining green are further away, and other humans are preparing to defend them.
It is a consequence of exponential growth crashing into a limited resource. At every point on the curve, nothing seems to be changing. It is forever growth as usual. Until it hits the ceiling.
Our experience with local transformations has been wonderful. We proceeded for years gaining human wealth, increasing health, lifespan, and happiness. We have recognized that there is less space for animals and plants, and less room to isolate ourselves from extreme pathogens. Suddenly everything changes. Exponential growth is an unforgiving master.
To answer your question, terraforming unhospitable regions of the earth would work as it has always worked. We go in, build structures, modify the geology, capture or divert hydrological resources, apply chemicals, fertilizers, and pathogens to kill what we don't want and nurture what we do.
Our problem today is that the future of these inhospitable regions is linked with the fate of the Earth and the currently hospitable regions. The tradeoffs are more complex and nuanced.
The tradeoffs are much too complicated for these examples to be the true balancing points, but they should serve to demonstrate the interactions.
Do we make New England warmer while making Old England dryer? Do we bring more rain to the US mid-west at the cost of drying Brazil? Do we raise the temperature of Iowa at the expense of an invasion of biting flies that lower pork productivity? Do we open trans-Arctic shipping at the expense of crashing the Atlantic cod population?
There are things we will inevitably change. Our challenge is to move carefully, but move none-the-less. We must take actions, and measure the results carefully to identify what helps and what hurts. We have moved out of your proposed regimen of local decisions causing local changes and into the regimen where local changes have important global effects.
So, we can do these local terraforming projects on the Earth to increase the habitability of local regions, but we are past the point where they are isolated. Your question is important, but may be 100 years too late.
Early landsat images showed an oddity: A green pentagon on the edge of the sahara.
Someone went to look. Ranch was raising cattle on a 5 year rotation. Graze each segment of the pentagon for 1 year, then give it 5 years to recover. Well at the centre of the pentagon for drinking water for the cattle.
There are a bunch of different terms for different kinds of local modifications. Most in essence are to make farming possible, or to extend the range of crops grown.
Shelterbelts during the Dirty Thirties. This was an effort to keep dirt in the same state. Now this is done with zero till agriculture.
Rice terraces throughout far east.
Corn and potato terraces in the Andes mountains -- still being used by local Quechua farmers.
Terra Preta -- high carbon charcoal soils in the Amazaon. Carbon acts to stabilize nutrients and prevent leaching.
Adding Lime or Sulphur to soil to raise/lower the pH of the soil
Making microclimates on Rapa Nui with stone walls to extend the growing season.
Use of stone wall gardens in France to grow peaches -- in effect concentrating the heat.
Hugelkulture -- putting whole logs in gardens, creating soil mounds. The wood acts as both nutrient source, and water storage, enabling crops all summer without irrigation.
Afforestation -- planting land to forest that hasn't been forest for a long time.
Agroforestry -- schemes to mix tree crops/wood production with more conventional agriculture.
Wildcrafting -- carefully extracting multiple products from wild lands in an at least short term sustainable manner. Trapping, some forms of fishing, balsam poplar buds, ginseng, some kinds of mushrooms,
Terra has multiple meanings:
- earth, dirt, soil
- Land -- Terra incognito = unknown lands
Terraforming usually refers to working on a planetary scale, and is using the third meaning = world shaping.
You are asking about the first meaning -- shaping a more local scale. I see this as an acceptable stretch of the term.
I think it would be worth running manned expeditions to some of these places using the time scales of Mars missions. E.g. A mission to Cornwallis Island in the Canadian archipelago. The object is to be as close to self sustaining as possible. Lot cheaper than Mars, and we would pick up some essential skills about how to plan missions like this. (Yes, I'm aware that the Inuit have traditionally lived in the far north. And some of their techniques are useful. But how many died learning those techniques. I see this notion as a means of learning how to pre-plan living in difficult places.
The empty quarter in Arabia would be another challenge, as would Savage's Aquarius Project. Or 30 feet underwater on the continental shelf.
How do you plan a venture when the nearest hardware store is a year away?
How do you best make a greenhouse with enough redundancy that you don't lose your entire crop when some circuit board fails?
How do you keep people sane?
What new communication protocols are needed with it's a 40 minute round trip.