The sun beats down on lakes, rivers, and oceans, causing water to evaporate off the warm surfaces and into the air. Winds blow this moist air all around the world, and perhaps over your house. Nothing special happens, unless this air rises high in the sky and then cools. The water vapor in the air condenses into drops, and falls to earth as rain, which flows into lakes, rivers, and oceans, where the process starts again. This is called the hydrologic cycle, driven ultimately by the energy of the sun.
Why doesn't this happen in your livingroom? Place a large pan of water on a table, and slowly, very slowly, the water evaporates into the air, but it never rains. Accelerate the process by boiling water on the stove. The kitchen is full of steam, and you might even feel some condensation on the walls, but there are no cumulus clouds forming beneath your ceiling, and rain does not fall. Why not?
Put simply, your house is too small. The upper air is not 14 degrees colder than the lower air - if anything it is warmer - and air on one side of the room is not more or less humid than air on the other side. Water vapor distributes quickly and uniformly throughout the house. Is there, somewhere, a room large enough to support weather at some level? There is, although that was not the designer's intent.
In 1962, John F. Kennedy directed us to "Go to the moon", and do it by the end of the decade. Americans were in a scramble. Along with rockets and lunar landers, considerable infrastructure had to be developed, and quickly. In 1966, NASA built the Vertical Assembly Building, a structure large enough to house the Saturn V rocket, the workhorse of the Apollo program. The rocket could be assembled, stage by stage, inside the building, shielded from the elements. In particular, the VAB can withstand a hurricane, a weather phenomenon that is not uncommon at the Kennedy Space Center on the east coast of Florida. Setting severe storms aside, even a light rain can damage individual rocket components prior to their assembly. Space shuttle tiles are particularly vulnerable. Along with the equipment, inclement weather can put workers at risk, as they stand on platforms and ladders high above the ground where slippery surfaces and lightning present serious hazards. Clearly this is an indoor operation.
The VAB is 526 feet (160 m) tall, 716 feet (218 m) long, and 518 feet (157 m) wide. Except for bays, overhead cranes, and machinery, the building encloses empty space, and lots of it, nearly 130 million cubic feet, or 3.6 million cubic meters. This is sufficient to construct a complete Saturn V rocket with capsule, or a space shuttle mated to its external tank and solid rocket boosters, or the up-and-coming Space Launch System. Since the same building services many different vehicles over time, it has been renamed the Vehicle Assembly Building. Fortunately we can retain the acronym VAB.
Pretend you are a NASA technician, working in the VAB. A rocket engine stands before you with its panels open. You have an arm full of diagnostic tools, and behind you, a table holds an assortment of computers and tablets, a notebook with pen and paper, and your cup of coffee. It's been hot in Florida, hot and humid for the past two weeks. As you study the engine, you think you feel a tiny drop of something land on your head. You look up the length of the rocket to see if something is leaking - there are plenty of toxic chemicals in this bird. You take a few steps back just to be safe. Everything looks in order, and then you feel another drop on your right shoulder, and another drop on your left arm. You look straight up and see clouds hanging just below the ceiling. These aren't puffy cumulus clouds, it's more like a mist spreading across the top of the building and releasing fine droplets on everything below. You wouldn't really call it rain, but you close your notebook and laptop just to be safe. Other workers are doing the same.
This is a weather phenomenon that is unique to the VAB, and it isn't particularly compatible with delicate electronics or worker morale. To ameliorate this situation, NASA has installed ten thousand tons of air conditioning and dehumidifying equipment. If need be, the air in the VAB can be replaced every hour. This keeps the overhead rain clouds at bay. Indoor weather is something we really don't want or need.
In his novel, Under the Dome, Stephen King places Chester's Mill, a small town in Maine, under a transparent, impenetrable dome, thus separating it from the outside world. With no state or federal oversight, small town politics runs rampant, but I am more interested in the science. Let's assume the dome is indeed invisible and indestructible. Does the town still have weather? It depends on the dimensions of the dome, its height in particular, which is not specified, but it is high enough to trap planes in flight. I will assume the dome extends 10 miles above the earth, and 20 miles below, precluding the possibility of digging a tunnel underneath, and a mile in diameter, as per the size of this fictional small town. When you consider our VAB experiment, that's plenty of room for weather. A new hydrologic cycle develops, wherein water pools at the low points of the town, which are, perhaps, at the edges of the dome where creeks and rivers use to run down to the sea. Those outlets are blocked by the dome, forming a small lake. On warm days the sun evaporates the water, which rises into the air, and eventually falls back as rain. In the winter we can expect snow, or perhaps a serious water shortage if the lake freezes over.
The population is somewhere around 2,000, approximately one person per acre. Are they going to run out of oxygen or accumulate too much carbon dioxide? Not any time soon with so much air above them, but I fear they might eventually. We ran this experiment in 1991. Biosphere 2 isolated 3.14 acres of land in Oracle, Arizona, under a dome of sorts, to create a closed ecological system. Eight people volunteered to remain inside the enclosure for two years. This is the population density of a small town, comparable to Chester's Mill. They grew bananas, papayas, sweet potatoes, beets, peanuts, rice, and wheat. Crop yields were inadequate during the first year, and they were chronically hungry, losing 16% of their body weight. By the second year they had become better farmers, growing a ton more food than the first year, and their weight stabilized. Most of the livestock and all of the pollinating insects died, leaving an assortment of pests such as ants and cockroaches. Oxygen began at 20.9%, consistent with ambient levels, but dropped steadily, reaching 14.5% after 16 months. This is comparable to an elevation of 4,080 meters, or 13,400 feet. This was considered unsafe, so additional oxygen was pumped into the structure. Biosphere 2 was not in balance! A dome 10 miles high would postpone this problem for decades, perhaps centuries, but I suspect Chester's Mill would eventually run into the same problem, assuming its population found a way to feed themselves and maintain a social structure for the duration, which they did not in the book.
Earth is about 200 million square miles in area, or about 128 billion acres. This is about 0.06 people per acre, far less than a rural town or Biosphere 2. The oceans, with their large swaths of algae, contribute mightily to the O2 CO2 balance. An enclosed town, or even an entire state, might experience an oxygen shortfall if the dome remained for several centuries.
A more immediate problem is power. Biosphere 2 was supplied with electrical power, but this is not the case in our science fiction thought experiment. All lines are cut, and even if a large city contains a power plant, it will soon run out of coal. A hydroelectric plant will also stop, because the dome will interrupt the flow of the river. It is theoretically possible to import power from the outside, if the enclosed area is large, and contains natural resources, manufacturing facilities, and skilled engineers. The dome is transparent to all electromagnetic radiation, including the induction currents that allow devices such as your electric toothbrush or your Macbook to charge without physical contact. If the dome is a meter thick, this isn't going to work, but if it is sufficiently thin we are on our way. Place induction coils against each other on opposite sides of the wall, and power from the outside can be transmitted to the coils on the inside. This power is then distributed to the residents through a modified grid, and some semblance of civilization returns. A mid sized city might not have the technology needed to pull this off; you probably need a metropolitan area with copper and iron deposits and factories to build the specialized equipment. Of course on-site generators will have to run the factories in the interim, until the power coupling is complete.
How large must a dome be to support ongoing technology? If the dome circled the entire earth, technology would continue, although communication satellites would eventually fail. We'd all be lost (literally) without GPS, but perhaps we would come up with an alternate, terrestrial implementation. If you shrink the dome down to a small country, or a mid-sized state, I think we're in trouble. Power is a major concern, as described above, but computers are the greatest challenge in the long run. Everything runs on integrated circuits, which fail after a while, and must be replaced. Semiconductor factories are few and far between, and most countries, if isolated, would not be able to replicate one of these billion dollar facilities. Remember, it takes advanced computers and specialized clean rooms to fabricate integrated circuits. If I had to put a dome around a state, I would probably choose Texas, because it is large, sparsely populated (0.16 people per acre), and home to the semiconductor industry. Also, its oil could supply internal energy for a time, although burning fossil fuel in a confined space could turn the entire state into a runaway greenhouse, a colossal nightmare in the making. Those semiconductor factories better start cranking out solar panels in a hurry. Texas is part of the North American breadbasket, so food should not be a problem, assuming they grow more vegetables and raise less cattle. Their biggest problem might be a shortage of metals, copper and iron in particular, which are required for ongoing technology. You can't create an element that isn't there. In conclusion, the dome would spell the end of technology, and perhaps the end of social cohesion, for almost every state or country, and certainly for every city. We really are a global community.
The Vehicle Assembly Building with its own internal weather
Space Shuttle tiles and rain
Under the Dome by Stephen King
Semiconductor fabrication plants in Texas