Among the key words one hears often in the scientific discussion of climate change are "climate models" and "General Circulation Models (GCM)."  These refer to huge, complex mathematical models that require powerful computers to trace the circulation of the atmosphere and oceans, including realistic estimates of complicating factors such as the solar heat input, the changing composition of the atmosphere, the effects of the land surface, etc.  We know that many elements of the atmosphere-ocean system are nonlinear; but computational modelling on digital computers must be performed using linear mathematical methods.  The process of modifying the bits in a binary number inside a computer is inherently a linear action.  Therefore the people who develop these computer models must be very ingenious.  To circumvent the nonlinearities they must make the models run in as many tiny steps as possible.  Then they engage in a process of testing the models, to ensure that they can reproduce the climates of the past.
The great danger of computer modeling is instability.  A model must not take a few steps and then "blow up," producing ever more erratic and extreme results.  So the developers have developed many tricks to ensure stability.  This sometimes means inserting elements that damp out nonlinearities and numerical instabilities.
So the present crop of GCM models are very good at calculating gradual changes over tens to hundreds of years.  They cannot, in general, predict sudden changes in the circulation state.  Therefore a state "flip" or "tipping" might not show up in the models because such events may have been deliberately damped out.  Researchers have had to make great efforts to demonstrate that the results of the models are believable, and that they show an inexorable trend toward warmer climates.  They haven't always been prepared for surprises, such as a suddenly accelerated warming, as now seems to be happening in the polar regions.
This is not meant as a criticism of the climate modelers, but rather
to point out that they are working at the extreme limits of their craft,
and that they usually need detailed observational evidence of anomalies
before they can incorporate the anomalous behavior in the models.
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