Blimey. I've got two assumptions as to what's happened to that:
1. It could be oxidisation. Caused by the elements. Which one? My guess would be H2O. Where's it been? Looks like it's been kept somewhere damp for an extended period of its life.
2. Failing that, someone has 'had a go' at either refinishing it or cleaning it with a harsh thinner and made a real mess of the cellulose finish. This is the most likely reason.
The thing with cellulose finishes is not to be too scared of them. Yes, they wear rapidly, unlike polyurethane, but that's a good thing when incidents such as this occur. It means it can and will polish out. As long as you don't use any harsh chemicals near cellulose its perfectly safe to work with.
You need to use a 'cutting compound' to polish it, effectively removing layers of the cellulose finish to reveal the fresh stuff underneath, leaving it shiny (hopefully!) The thing to remember is the composition of the cellulose lacquer that's been applied. It has been applied in many stages. Layer after layer. Its a single based material, thin and weak in its make up, unlike polyurethane that is only applied in two to three coats because its a two pack material, incorporating a chemical hardner. That's what gives poly its strength.
This polishing is all done with good old elbow grease. Buy some 'T cut' or 'Meguiars paint cleaner' as one knowledgable poster highlighted and use a clean, damp cloth with a liberable amount of compound each time using a circular motion to polish. Buff every so often to remove the resultant haze and see where you're at. If it still looks bad, you haven't done enough polishing. More elbow grease is in order.
If you appear to be breaking through to the woodstain that created the burst and it still looks bad, a refinish is in order.
If you're happy, apply a good quality car wax (I use autoglym) and you're done.
I wish you were near me as I'd like nothing more than to get that off you and make it look good as new.
Keep us informed and good luck :wink: