It could be the opposite. Numerical models could be giving us a false sense of security, a belief that we have plenty of time to fix pollution issues.
Writing in Nature Geoscience, Paul Valdes from the University of Bristol School of Geographical Sciences, discusses four examples of abrupt climate change 'tipping points' over the last 55.8 million years that have been reconstructed from palaeoclimate data and states that the level of inaccuracy could be too comforting.
Two complex climate models used in the assessments of future climate change did not adequately simulate the climate configuration conditions before the onset of change while two other models needed an unrealistically strong push (10X) to produce a change similar to that observed in records of past climate, meaning the models were overestimating the real-world conditions needed to make the historical effects appear - it could actually be much easier.
The Palaeocene–Eocene Thermal Maximum nearly 56 million years ago is an example of a rapid warming event that corresponded to a change in the carbon cycle - carbon levels spiked due to methane from submarine hydrates to what some project will be carbon levels later this century. Fair enough, but geological data shows that the background climate state and the gradient between the equator and the poles isn't adequately modeled in the types of simulations used by the IPCC; without a way to model a realistic global temperature you can't really be sure you are modeling further warming.
56 million years ago is a long time but more recent events, such as the desertification of the Sahara 5,000 years ago, also aren't rigorously modeled using the methods he examined - but we know they happened, which is why current models may not be the hysterical projections skeptics want to believe, they could be too conservative.
What is the solution? It takes a lot of processing horsepower to do huge simulations, so often we have to rely on boundary conditions and, as he puts it, " we need to challenge the palaeodata and continue to improve our knowledge of past forcing factors and the ensuing climate response.
"If the models are to be used for the prediction of potential future events of abrupt change, their ability to simulate such events needs to be firmly established — science is about evidence, not belief systems," writes Valdes.
Climate change skeptics will agree with that last part, but how many will agree that a lack of accuracy could mean we have less time to implement solutions?