There are two posts that point out the basic problem.
I will illustrate the problem. Let’s say you have four-digit precision, with scientific notation (sixteen-digit precision is routine, and thirty-two digit precision or higher may be necessary for special applications).
The scientific notation part keeps track of the order of magnitude of the number, e.g., ones, billions, billionths, etc.
OK. Now add 1 to X and repeat. With four digit precision you go up to 9999, and then to 10,000 or 10,00E+1. Add 1 to 10,00E+1 and you get 10,00E+1. Do this 5 million more times, and you still get 10,00E+1.
This reveals one of the problems with “Big Data,” lots and lots of data, each datum of which is small relative to the order of magnitude of their total. There are strategies to deal with this, but there is a certain culture among the climatologists that because they have lots of data (e.g., hourly readings at thousands of thermometers over thirty years), they are gods. We have a similar problem with exchange rates, stock prices and so forth, in financial markets. But, just because you have high frequency data doesn’t mean you have that much more information.
The next problem in climatology is the kind of calculations they perform. They use power functions. These make big numbers in to very, very big numbers, which are challenges to handle inside the computer, with floating point numbers. We economists have our own sin, which is to invert large matrices.
Yes, because of computational uncertainty, it is sometimes important to perform calculations using different platforms, operating systems and application software. And, if you get significantly different results, to think about what you’re doing that the computers find offensive.
I also find that, if your model fails to match reality, your model is wrong - not your reality.