The problem starts with the old story about a butterfly’s wings fluttering in the Amazon can affect the weather a continent away which is of course an exaggeration but to a degree that is what happens.
Mathematicians are constantly working with weather forecasters to develop computer models which take what is known about atmospherics and applies it to a detailed weather map complete with atmosphere pressure gradients and fronts. In its simplest form this would give a forecast for two or three days ahead but farmers, fishermen and many other industries and people are looking for longer periods.
If the old forecast used detailed information in squares of the earth surface which are 100 kilometres on each side, then to achieve a longer range forecast more information is needed and by the use of satellites, weather buoys, aircraft, ships and automatic weather stations forecasters are able to get squares down to one kilometre on each side. This is 10,000 times as much information and with all the information and calculations it requires some of the biggest computers on the planet.
Even this is not sufficient because there are slightly different ways of calculating weather which might give different emphasis to pressure, or clouds or wind strength or the upper atmosphere and so the forecasters might run fifty or a hundred different models to see what the differences are. If thirty say a different outcome is expected then that can be taken into account and a warning given.
If more information is available, say down to 250 meters on each side of the square, as it might over land where there are a lot of stations, then fuzzy logic can be applied. This is when the extra information taken into consideration in the main program but it becomes so vast that this entails leaving some of the information out so that fuzzy logic fills in the gaps.
Weather forecasts are not the same as climate change predictions but it does entail vast amounts of information being applied to known laws of physics and chemistry and what has happened in the past and then run foreword into the future and this gives us a fairly good idea of the future.
What the Porto scientists did was used was used phase transitions which is where a material, such as water behaves in a certain way when as a liquid but behaves differently when it becomes a gas after evaporation.
When this is applied to climate change the world is predictable to a certain point, like an increase of 3C, but then it swings violently and chaotically into severe storms or drought, and then returns to near normal for a while.
These swings are triggered by tipping points and when they are exceeded nothing is predictable again and the climate performs in a chaotic pattern which is outside our forecasting and comprehension.