The last topic in the title, forecast correction, is not as deep investigated as I would have. But in writing I realised that I had to speak to High School Students.
The presentation is in Italian, but I can translate it in English if someone is interested. In the case, I should do a further investment in making some parts more technical and add some examples.
The presentation can be found, as usual, on slideshare. A companion of the presentation, also in Italian, of this presentation can be this paper that I wrote more than twenty years ago about modelling, entitled: Introduction to the Mathematical Models of Environment. I dedicated this small contribution to Sandro Marani with whom I discussed a lot the topic.