Interesting question here (about what evidence it might take to convince a climate change sceptic of the reality of human-generated climate change).
The simple answer – and one worth bearing in mind the next time you try to persuade someone by argument – is this: nothing.
Not because people are stupid (dumb), wilful or ignorant but simply because much of the time the opinions we hold are not based on rational thinking and the impartial sorting of evidence.
People rarely persuade each other to change their points of view by disputation (which is not to say that we don't enjoy a good rhetorical tumble) but this kind of "show me the facts" thinking doesn't shape much of our view of the world. We are highly selective – we only see what we expect to see, distrust and discount the witnesses who present what we don't want and devalue their evidence if they turn out to be from the other side.
Most of our opinions are received opinions – as Oscar Wilde put it disdainfully,
"Most people are other people. Their thoughts are someone else's opinions, their lives a mimicry, their passions a quotation"
They're not based on facts and evidence but on other people's (already second hand) opinions. Very often, the trickiest opinions to shift (like articles of faith) are stubbornly resistent because they are badges of membership to some group or other – a necessary cost of membership.
Add to this the fact that often times, they are also post-rationalisations of what you've already done or chosen (as Andrew Ehrenberg famously observed, I have to think my girlfriend is attractive because she is…after all…my girlfriend) and you can begin see the difficulty in lifting distinguished opponents out of their denial mode.
So next time don't try to win the argument – don't worry about the theology of the piece.
Get your opponents to do something – ideally together – and help them change their own minds after the fact.