I am, however, talking about the European response.
While your counter-missiles and missiles may not be targeting Europe directly, most of the missiles you detonate in mid-air to avoid them reaching the United States will be hit over the Atlantic or somewhere in the East Baltics and Western Russia.
Anti-Ballistic Missiles have existed for some time. Systems like the Nike Zeus were developed for two purposes - to swat down entire Soviet bomber formations, and to vaporize re-entry vehicles. Those solutions, however, were nuclear - and the prospect of fallout was not at all a pleasant one.
What many people don't understand is that missiles rarely actually strike their target. The equipment necessary to guide a missile into a maneuvering target like an aircraft is just not cost effective. Instead, missiles are equipped with area-effect warheads - 'claymore mines' - if you will. The objective of the missile is then merely to make sure that the target flies into the kill-zone before it detonates - sending shrapnel and other nasty things into it.
Amping it up to a nuclear warhead was just because you were trying to hit a target that was just that much harder to hit... or you had targets across a much larger area (the Aim-54 Phoenix Missile could be equipped with a nuclear warhead for carrier defense operations... the idea being that a single missile could eliminate entire flights of aircraft... it was the counter to soviet zerg-rush tactics).
But what is unique about the modern ABM shield is that it actually strikes the target. Let me back up a bit and explain why this is necessary.
A normal missile -can- destroy an incoming re-entry vehicle. RIM-66/RIM-156 SM2 surface-to-air missiles can be given firmware updates that allow them to intercept re-entry vehicles. It has a low probability of success... but it's better than nothing. The low probability of success is due to the speeds involved, and also due to the nature of the warheads - which are designed to damage critical systems all across an aircraft - not bust up a vehicle designed to carry a nuclear warhead through re-entry. Damaging the re-entry vehicle and sending it off-course is the most likely result... but that doesn't do much to guarantee that Marvin Martian is asking where the Kaboom is supposed to be.
Which is the objective.
So, we have to hit the re-entry vehicle with something solid enough to destroy it and separate the components of the bomb so that there is no chance of detonation. This requires powerful radar systems from land, sea, or air assets as well as sophisticated and fast processing on behalf of the missile. Since we are, basically, trying to throw a telephone pole into an object the size of a basketball traveling at 24 times the speed of sound and 'jiggling' through various layers of atmosphere. From 100 miles away.
In both instances, the Atlantic current in the west and the winds in the East will lead to nuclear winters in Europe.
Nuclear winter - the idea that enough fallout can block out enough sunlight to trigger dramatic climate shift - was an idea popularized by the media and has been reinforced as fact via dogmatic principle, alone. None of the research done suggests that nuclear winter is at all a realistic proposition.
But it's moot - since there will be no detonation of the intercepted missiles.
I'm not talking about a particularly cold night in Oslo, I'm talking about the radioactive fallout that follows a mid-air detonation.
Radioactive fallout and nuclear winter are two different things.
Radioactive fallout is triggered by two things - first, it is unspent portions of the bomb - uranium, plutonium - whatever. Second is byproducts of the fission process - this usually includes things like cesium 141. Cesium 141 is of particular concern because it is chemically similar to potassium and will replace it in many organic processes (even though it is a radioactive isotope). This can cause crops grown in those areas to have substantially higher levels of radioactivity when compared to the background.
The threat of nuclear winter, as I said above, is mostly cultural mythology. The vast majority of the classic 'mushroom cloud' is precisely that - a cloud. It's super-heated water vapor. While there is temporary occlusion of the sun - even subterranean bursts do not throw enough solid material into the atmosphere to "blot out the sun" for any substantial length of time. No matter how many nuclear weapons you set off.
Your war with China would cripple Europe for generations to come, should it become reality.
If it should come to a full-scale attack by China and a full response by the United States, then you can bet your ass that both France, Germany and the United Kingdoms will fire their own weapons, not as an agressive force, but to detonate your missiles as far away from Europe as possible.
That's not how ICBMs work. They are only useful against strategic land targets. They are not even remotely capable of being used in the anti-ballistic-missile role.
I mean... I could come up with a few creative ways to -possibly- use them... but it would require Itachi-level foresight and it would have to come down to a few specific conditions. Even then - it would be kind of moot as you would be launching your own 5 megaton warhead to blow up another 5 megaton warhead.
You would be better off trying to use cruise missiles with tactical nuclear warheads... or just welding those warheads to the rockets we use to send satellites into orbit and try to take down some missiles during their orbital phase.
Not that it would matter. Most of our missiles would be going over the Pacific, not the Atlantic.
By the way; should it come to the point where China fires its missiles and the United States responds, then I'm pretty sure a nation like Israel will see their chance to settle some old debts.
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If they, somehow, had 400 nuclear warheads, they are almost all tactical yield and not strategic. The difference between tactical and strategic yield is two to three orders of magnitude. A tactical yield weapon may be 25 kilotons (takes out a few city blocks and scares the **** out of people). A strategic yield weapon is hundreds of kilotons to a few dozen megatons (thousands of kilotons) and crushes entire city districts (theoretically, at least).
If they do anything - it's wipe out pains in the ass like Iran. Israel can be manipulative and a little difficult to work with at times... but at least they can be worked with.
Really, an agressive nuclear attack from any nation in the world would have catastrophic consequences for the entire world.
The largest threat would be that people would believe it to be the end times and there would be mass rioting for no reason. That's really about it.
We have been raised on dogmatic lies that our nuclear weapons have the power to destroy the planet - that a single nuclear bomb can wipe out a city... all of these things are factually incorrect. Nuclear weapons are, simply, very very big explosions with some particularly nasty residues left behind.
The only reason any nuclear war (even a full exchange between every nation on the planet) -COULD- be the "end of the world" is if people act stupid about things. The damage that could be done is quite high - but many areas would survive and people could work around the destroyed areas to stitch things back together.
We've just been raised to fear the things so much that the fear they instill is actually greater than the actual damage they can do.