No, we have to say season ticket. We cannot say seasonal ticket.

I'm afraid that it's largely a matter of learning which is the right collocation. The only advice I can give is the following:

noun + noun

The noun + noun structure, in which the first noun modifies or describes the second noun, is commonly used for expressions which specify certain kinds of thing.

They describe things that belong to well-known classes. Thus we have, e.g. a return ticket, a season ticket, a history/geography/maths book, science fiction, a gold/silver/bronze medal, theatre tickets, milk chocolate.

Substituting the adjectival form of the noun as a modifier would normally indicate particular instances of something. Compare the following:

• If you buy a season ticket you don't have to bother buying a return ticket every day.
• I still can't get used to the unseasonal weather which we get in Britain all the time now.
  

• The geography books that we used to have in school look very dull now.
• The geographical features of the mountain range were really quite stunning.

• Science fiction books are not as popular with the public as adventure stories.
• The scientific instruments that we used for the experiment were all made in Germany.

• In the 400 m race I was hoping for a gold medal but I had to make do with a bronze.
• She was wearing a tiny golden cross around her neck.
  

• Theatre tickets can be bought from the half-price ticket booth in Leicester Square.
• Such theatrical behaviour was not welcomed in a university department.

• My chocoholic friend always has her cupboards full of Belgian and Swiss milk chocolate.
• As I had missed my supper, she made me a milky drink before I went to bed.

adjective + noun

However, there are a number of exceptions where adjective + noun rather than noun + noun is used to describe well-known classifications. Here are a few of the most common:

• A monthly ticket is always much cheaper to buy than four weekly tickets.
• Musical instruments and personal computers were what my children want for Xmas.
• It is general knowledge among the general public that rail travel is unreliable.
• If we had a good regional network, this might lead to a national network for the trains.
• To achieve that objective, industrial relations will need to improve.
• The central heating had to be switched off in the natural history museum.
• Higher education is possible for Jo - if not higher education, then further education.

Note that there are three main ways of expressing compound nouns:

Usually only one way is possible. We would not say for instance: a film of feature or a feature's film. We would not say: goat milk or milk of a goat. We would not say: the hill's bottom or the hill bottom.

Write to our board with your own examples of interesting compound nouns you have noted.