Optimists estimate the Paris Accord will reduce from business as usual ~6C warming to 'well below 2 with measures taken towards achieving 1.5' (the target in the accord, paraphrased from memory). Lowball estimates (eg Bjorn Lomborg's) are that it will have an effect of 0.05C. The truth will no doubt lie somewhere between these two, and no doubt does not depend on the accord alone, but if/how it is followed up in practice. Note that even the denialist estimates 0.05C, so yes, it will have an effect. The chance of keeping the world below 2C warming is, however, in my opinion, almost nil, we will fail to hit that target the same way we will fail to achieve any of the 'sustainable development goals' - these are really mostly unachievable aspirational targets that seek to catalyze progress in the right direction. The mood is very positive, and such positivity can be a good catalyst. Indeed, the biggest win was one of politics. The UN works. Countries are unified. This political capital could be squandered (as GW Bush famously did in his second term) or could, everyone hopes, deliver substantial progress towards the goals of 2C on mitigation, and building resilience on the adaptation side.
So, now, I am updating with my take on Trump's unilateral withdrawal. As far as atmospheric greenhouse gas levels are concerned the direct impact is unlikely to be distinguishable from zero. Paris after all was a voluntary mechanism - it mandated no action by countries. So the bits of the US that were going to reduce their emissions under Paris (various states, cities, industries) can (and indeed have already stated they will) still do so. In terms of the global degree C measuring stick the parties to the conference are so fond of, I would estimate the direct impact of this decision to be 0°C with a fairly small range of uncertainty around that number. In terms of finance for climate change mitigation and adaptation in the developing world, there is also no clear effect arising from this decision. The decision to stop US funding the green climate fund was already taken long before this one, and despite lack of similar outcry at the time was far more damaging in my opinion.
The more likely consequences of Trump's political decision are also political. These are of course far harder to predict than climate change. Some say that China will take up the global 'leadership' vacuum. I find this highly unlikely. China's corrupt, totalitarian and environmentally disastrous regime is an extremely unlikely government to inspire leadership in anyone other than the most naive end of the spectrum. A more plausible scenario may be that Trump's successor - POTUS 46 - will score enormous international goodwill, perhaps even a nobel peace prize, when she asserts new, bold American leadership and announces the US is rejoining the accord.
