Årsmodellen er gammel.

Because Norwegian usually writes compound nouns as a single word.

Here, år + modell become årsmodell, and the definite form is årsmodellen.

This is very common in Norwegian:

• bil
  • dør → bildør
• sommer
  • ferie → sommerferie

So English often uses two words where Norwegian prefers one compound word.

The -s- is a linking sound/letter used in many Norwegian compounds.

So the structure is:

• år = year
• modell = model
• årsmodell = year-model / model year

This -s- does not always mean possession the way English 's does. It is often just a normal part of compound formation.

Other examples:

• liv
  • historie → livshistorie
• arbeid
  • dag → arbeidsdag

The ending -en is the definite article attached to the noun.

In Norwegian, instead of putting a separate word like the before the noun, you usually add the definite ending to the noun itself.

So:

• en årsmodell = an annual model / a model year item
• årsmodellen = the annual model / the model in question

This is a key difference from English.

Because the noun modell is a masculine/common-gender singular noun, so the adjective uses the form gammel.

Compare:

• en modell er gammel
• et hus er gammelt
• modellene er gamle

So:

• gammel = singular common/masculine
• gammelt = singular neuter
• gamle = plural

In this sentence, årsmodellen is singular and not neuter, so gammel is correct.

Because gammel is a predicative adjective here: it comes after the verb er and describes the subject.

Pattern:

• Subject + er + adjective

So:

• Årsmodellen er gammel

This is like English:

• The model is old

If the adjective came before the noun, that would be a different structure:

• den gamle årsmodellen = the old annual model

So after er, the adjective normally comes after the noun phrase.

Er is the present tense of å være, which means to be.

So:

• å være = to be
• er = is / are

Examples:

• Hun er lærer = She is a teacher
• De er gamle = They are old

In your sentence, er simply links the subject to the description.

Because Norwegian usually marks definiteness with an ending on the noun, not with a separate article the way English does.

So instead of:

• the model

Norwegian often has:

• modellen

That final -en carries the meaning of the.

A separate determiner can appear in other structures, especially with adjectives:

• den gamle modellen = the old model

But in årsmodellen, the noun itself already shows definiteness.

The adjective would change to match.

Examples:

• Huset er gammelt = the house is old
  
  • hus is neuter, so gammelt
• Modellene er gamle = the models are old
  
  • plural, so gamle

Your sentence uses:

• årsmodellen = singular, non-neuter
• so the adjective is gammel

This kind of adjective agreement is an important pattern in Norwegian.