Why can't we use bad ozone from pollution to replenish the thinning ozone layer?
How come all the bad ozone that shows up during pollution alerts doesn't float up to replenish the good ozone that's disappearing from the ozone layer? Where does the bad ozone go? If we sawed off LA and floated it down to the Antarctic would we solve all our problems? Conversely, during the next ozone alert, could we break into a warehouse full of old chlorofluorocarbon-laden hairspray and clear the air?
Further proof, boys, that the difference between a Nobel prize winner and a lunatic is a fine line indeed. Your ideas as proposed are a bit over the edge, but something not too far removed from them has been seriously proposed. More on that later. First, however, let's get one thing straight: you can't literally use bad ozone to replenish the good ozone.
The problem with ozone is that it's unstable — it breaks down in a few minutes, long before it can float much of anywhere. Ozone is created and destroyed continuously as a result of the sun acting on oxygen in the presence of pollution (in the lower atmosphere) or on oxygen alone (in the upper atmosphere). Lower-atmosphere ozone, hereinafter called local ozone, decomposes once it gets beyond the cities that spawn it and never reaches the upper atmosphere.
But supposing somebody cooked up a tough, long-lasting ozone. And supposing we were able to transport a couple cities' worth of it to the Antarctic, where there's a "hole" (actually a thin spot) in the ozone layer. Our troubles still wouldn't be over. The amount of ozone generated by urban pollution, while it seems like a lot to us, is trivial compared to the ozone hole, which extends over roughly all of Antarctica. Another problem is that vertical mixing between the troposphere (where we and our ozone-laden cities are) and the stratosphere (where the ozone layer is) is poor.
But here's a twist. Some scientists say it doesn't matter if the local ozone never gets to the upper atmosphere; it might still do us some good just hanging around near the ground. The importance of ozone is that it blocks ultraviolet radiation that causes skin cancer. It's more convenient if the ozone is in the upper atmosphere, but the process will still work if the ozone is near the ground. It's just that the stuff then also irritates your throat. In addition, local ozone is quite variable, so the UV protection it provides isn't as reliable as what you get from the upper-atmosphere variety. But hey, these days you take what you get.
Now for your last question. Suppose we decided to take our chances with UV and get rid of excess local ozone instead. Could we do it by spraying the air with chlorofluorocarbons (CFCs), the leading cause of ozone depletion in the upper atmosphere? Nice try, but no. CFCs as such don't destroy ozone; the dirty work is done by chlorine, a CFC breakdown product. CFCs don't break down until they reach the stratosphere (unlike ozone, they're quite durable), where ultraviolet radiation causes them to release the fatal gas.
There's more to it than that, though. Free chlorine is unstable. In most of the world it recombines quickly into relatively harmless compounds like hydrochloric acid and chlorine nitrate. The exception is the Antarctic. There the bitter cold (even colder than the Arctic) causes ice clouds to form in the stratosphere, something that rarely happens elsewhere around the globe. These clouds enable the free chlorine to survive long enough to do a number on the ozone, which is why the ozone hole is over the South Pole and not North America. What makes the problem so bad is that when chlorine destroys ozone, it's not itself destroyed — it remains free to kill again. A little chlorine can thus do major damage. But releasing CFCs wouldn't disperse local buildups of ozone because the stuff doesn't break down this low.
Still, your plan isn't totally off the wall. At least one scientist has proposed an idea that isn't all that far from what you're suggesting. Ralph Cicerone, a professor of geosciences at the University of California at Irvine, has suggested spraying 50,000 tons of propane or ethane over the South Pole early each winter. The resultant chemical reaction, he wrote in a 1991 article in Science magazine, would temporarily neutralize the ozone hole. It would also cost a zillion bucks. But if things keep up like they have, we may yet have to do it.