In computer science, computational complexity is a description of the computing time or memory usage required to solve a problem using computers. The time required is expressed as a function of the input data set size using big "o" notation.
From a computational point of view, you should consider whether or not it is possible to accurately predict the weather or the climate. Those who say that the planet is suffering from "global warming" use computer models to assert and back up their claims. We already know that untold billions have been spent on computer models to try to accurately predict the weather tomorrow or next week, and that the models are frequently wrong. In fact, if a computer model could be built that accurately and always predicted the weather just 30 minutes into the future, the builders would be billionaires themselves.
Climate is the sum total of weather over an extended period of time and area. Global climate is climate over the entire planet. On first look, it seems utterly ridiculous that someone could accurately forecast the climate in 1 year's time, much less 50 or 100 years.
Well, it is ridiculous from a computational perspective. I doubt that all of the computing power put together for all time would be enough to accurately or reliably describe a single moment in the global climate, much less predict it for any point in the future. Take a look at what is known about the input data size, and consider that there is most likely as many unknowns as there are knowns at the present.
The best computer algorithms execute in constant time and use a constant amount of memory. Very nice ones execute in linear time relative to the input size. Fairly nice ones execute according to some fixed low order polynomial function when the input size is small. Even if an accurate computer model of climate change (highly unlikely) implemented an algorithm that required only constant time and memory (highly unlikely), I suspect the constant time (using all the worlds computers) required to compute climate change from one moment to the next would be far more than the lifetime of any one of the modelers.
Don't forget about all that computational time spent debugging the computer models.
The best still not good enough:
UK's most powerful.